# MathsCasts

## by MathsCasts

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#### Description

These MathsCasts are produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They are part of an ongoing collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. They are mostly targeted at prerequisite to first year level, in a range of subjects such as: Engineering, Sciences, Business, Computing and Technology. We have also commenced production of second year mathematics topics. MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License The three mathematics support centres can be contacted the following way: MASH Centre (Swinburne, Australia) http://www.swinburne.edu.au/engineering/mathematics/mash MLC (Limerick, Ireland) http://www.ul.ie/~mlc MLSC (Loughborough, UK) http://mlsc.lboro.ac.uk

Name | Description | Released | Price | ||
---|---|---|---|---|---|

1 | VideoLaplace transform solution of a pair of simultaneous, linear, 1st order ODEs (MathsCasts) | Laplace transforms are used to solve a pair of linear, 1st order ODE's with boundary conditions. Cramer's rule is used along the way. | 4/1/2014 | Free | View In iTunes |

2 | VideoThe exponential of a 2X2 matrix using Laplace transforms: an unusual method (MathsCasts) | We show an unusual approach to finding the exponential of a 2x2 matrix - using the Laplace transform. This method was suggested by a bright Swinburne student. | 4/1/2014 | Free | View In iTunes |

3 | VideoProof of the 2nd shift theorem for Laplace transforms (MathsCasts) | The 2nd shift theorem is proved using a change of integration variable then a simple example is presented. | 4/1/2014 | Free | View In iTunes |

4 | VideoDifferentiation of sin and cos from 1st principles: Part 2 Another important limit (MathsCasts) | In preparation for using the 1st principles method to find the derivatives of sin and cos, we evaluate the limit as x -> 0 of (1-cos(x))/x. | 3/31/2014 | Free | View In iTunes |

5 | VideoDifferentiation of sin and cos from 1st principles: Part 1 An important limit (MathsCasts) | In preparation for using the 1st principles method to find the derivatives of sin and cos, we evaluate the limit as x -> 0 of sin(x)/x. | 3/31/2014 | Free | View In iTunes |

6 | VideoDifferentiation of sin and cos from 1st principles: Part 3 The calculation (MathsCasts) | Derivatives of sin and cos are calculated from 1st principles using the limits evaluated in earlier parts. | 3/31/2014 | Free | View In iTunes |

7 | VideoDifferentiation of sin and cos from 1st principles: Part 4 Why radian? (MathsCasts) | We ask what happens in the 1st principles differentiation if the angle x is measured in degrees. The question is answered by referring to the limits calculated previously. | 3/31/2014 | Free | View In iTunes |

8 | VideoProof of Parseval's theorem (MathsCasts) | A proof of Parseval's theorem for trigonometric Fourier series is outlined. | 3/24/2014 | Free | View In iTunes |

9 | VideoExponential form of a complex number (MathsCasts) | We show that cis(x) can be written as the exponential of j x then derive Euler's results for cos and sin. | 3/24/2014 | Free | View In iTunes |

10 | VideoDifferentation using the inverse function rule (MathsCasts) | In this recording use the inverse function rule for differentiation to find the derivate of the inverse sine of x. This example includes discussion of the importance of looking at the graph of such a function, to see whether it is increasing or decreasing | 3/22/2014 | Free | View In iTunes |

11 | VideoMatrix multiplication using index notation (MathsCasts) | We show how to use index notation and sum over row and column indices to perform matrix multiplication. The Einstein summation convention is introduced. | 3/22/2014 | Free | View In iTunes |

12 | VideoBonus results from Fourier series - Part 3 (Using Parseval's theorem) (MathsCasts) | Parseval's theorem is used to achieve a bonus result for the sum of the series of reciprocal fourth powers of odd integers. | 3/18/2014 | Free | View In iTunes |

13 | VideoIntegration by substitution: What do we do with the integration limits? (MathsCasts) | We describe how to deal with integration limits when substitution is performed on a definite integral. | 3/17/2014 | Free | View In iTunes |

14 | VideoBonus results from Fourier series - Part 2 (MathsCasts) | Further use of Fourier series to find the sum of a series involving alternating signed reciprocals of odd integers. | 3/17/2014 | Free | View In iTunes |

15 | VideoBonus results from Fourier series - Part 1 (MathsCasts) | Starting with a known Fourier series, we derive results of sumes of series involving reciprocals of powers of the whole numbers.AC | 3/16/2014 | Free | View In iTunes |

16 | VideoExample of a less straightforward Fourier series (MathsCasts) | Fourier coefficients are evaluated for a piecewise function consisting partly of sin(t) and partly the constant 0. | 3/12/2014 | Free | View In iTunes |

17 | VideoSome trigonometric integrals useful in the study of Fourier series (MathsCasts) | Integrals whose integrand consists of products of sin and cos with themselves or each other are evaluated. | 3/12/2014 | Free | View In iTunes |

18 | VideoAdjusting a function to create odd or even symmetry before finding a Fourier series (MathsCasts) | A vertical shift is applied to a function before finding its Fourier series. This reduces the work in finding the Fourier coefficients. | 3/11/2014 | Free | View In iTunes |

19 | VideoWhy do we need the absolute value when we integrate 1 over x? (MathsCasts) | We look at the integral of 1 over x dx and explain the precise details that lead to the use of abs(x) in the log function obtained from antidifferentiation. | 1/18/2014 | Free | View In iTunes |

20 | VideoWhy are circles, ellipses, parabolas and hyperbolas called 'conic sections'? Part 1 (MathsCasts) | We solve simultaneously the equations of a plane and a cone and show that the intersections are circles, parabolas, ellipses, hyperbolas, straight lines or just the origin. | 1/17/2014 | Free | View In iTunes |

21 | VideoThe vector triple product (MathsCasts) | Simplification of a vector triple product. | 1/16/2014 | Free | View In iTunes |

22 | VideoThe vector (cross) product of two vectors - Part 3 (MathsCasts) | The cross products between the basis vectors i,j and k identified in part 2 are used to obtain an expression in components for the vector product of any pair of vectors. | 1/15/2014 | Free | View In iTunes |

23 | VideoThe vector (cross) product of two vectors - Part 2 (MathsCasts) | The definition of the vector product is used to identify the cross products of the various basis vectors i, j and k with each-other, in preparation for unravelling a component form for the vector product. | 1/14/2014 | Free | View In iTunes |

24 | VideoThe vector (cross) product of two vectors - Part 1 (MathsCasts) | The definition of the vector product is explained with reasons for making such a definition. | 1/13/2014 | Free | View In iTunes |

25 | VideoThe scalar (dot) product of two vectors - Part 3 (MathsCasts) | We investigate and prove frequently used properties of the scalar product. | 1/12/2014 | Free | View In iTunes |

26 | VideoThe scalar (dot) product of two vectors - Part 2 (MathsCasts) | We justify the definition of the scalar product using the example of work done by a force. | 1/11/2014 | Free | View In iTunes |

27 | VideoThe scalar (dot) product of two vectors - Part 1 (MathsCasts) | The definition of the scalar product is used to derive an expression for the product in terms of components. Some properties of the product are then summarized. | 1/10/2014 | Free | View In iTunes |

28 | VideoThe Laplace transform of ln(t) (MathsCasts) | Investigates the Laplace transform of the log function. | 1/9/2014 | Free | View In iTunes |

29 | VideoIrrotational vector fields, potential function and path integral - Part 2 (MathsCasts) | A vector field is introduced, it is shown to be irrotational then its potential is identified and the field is integrated along a specified path. | 1/8/2014 | Free | View In iTunes |

30 | VideoIrrotational vector fields, potential function and path integral - Part 1 (MathsCasts) | We explain the concept of an irrotational vector field and potential for such a field, then show how the potential is used to calculate a path integral of the vector filed given end-points for the path. A specified vector field shown to be irrotational. | 1/7/2014 | Free | View In iTunes |

31 | VideoIrrotational vector fields and the potential: Part 3 another example (MathsCasts) | Another irrotational vector field is introduced, and its potential is identified. The field is then integrated along a specified path. | 1/6/2014 | Free | View In iTunes |

32 | VideoIntroduction to Cartesian tensors - Part 1 The Kronecker delta (MathsCasts) | We introduce the Kronecker delta and identify it as just another way of writing the unit matrix. | 1/5/2014 | Free | View In iTunes |

33 | VideoClosed contour line integral - Part 2 Using Green's theorem in the plane (MathsCasts) | Evaluates the same line integral as was done in part 1, but using Green's theorem in the plane | 1/4/2014 | Free | View In iTunes |

34 | VideoA simple Fourier transform example - Part 3 (MathsCasts) | We find the Fourier transform of a simple piecewise function with values 0 and e^(-kt). | 1/3/2014 | Free | View In iTunes |

35 | VideoA simple Fourier transform example - Part 2 (MathsCasts) | We find the Fourier transform of a simple piecewise function with values 0 and t. | 1/2/2014 | Free | View In iTunes |

36 | VideoA simple Fourier transform example - Part 1 (MathsCasts) | We find the Fourier transform of a simple piecewise function with values 0 and 1. | 1/1/2014 | Free | View In iTunes |

37 | VideoA cautionary tale: The Laplace transform of the triangular wave (MathsCasts) | We revisit the Laplace transform of the triangular wave and expose a nasty trap it would be easy to fall into. | 12/31/2013 | Free | View In iTunes |

38 | VideoWhat is a Vector (MathsCasts) | Introduces definition of a vector and states some simple examples of vectors. Explains difference between vector and scalar quantity, ie. distance and displacement. | 12/23/2013 | Free | View In iTunes |

39 | VideoVectors: Perpendicular Unit Vectors (MathsCasts) | Defines the perpendicular unit vectors i and j. | 12/23/2013 | Free | View In iTunes |

40 | VideoVectors: Example of Expressing the Addition/Subtraction of Vectors as a Single Vector (MathsCasts) | Worked example shows how to use the triangle law, the definition of equal vectors and the definition of negative vectors to express the addition and subtraction of two or more vectors as a single vector. | 12/23/2013 | Free | View In iTunes |

41 | VideoVectors: Equal Vectors (MathsCasts) | Gives the conditions necessary for vectors to be considered equal. Briefly touches on negative vector also | 12/22/2013 | Free | View In iTunes |

42 | VideoVectors: Addition and Subtraction of Vectors Geometrically (MathsCasts) | Explains how to use the triangle law and the parallelogram law to add vectors geometrically. Shows how to subtract vectors geometrically by using the triangle law. | 12/21/2013 | Free | View In iTunes |

43 | VideoVectors: Adding One Dimensional Vectors (MathsCasts) | Simple example showing how to add one dimensional vectors. | 12/20/2013 | Free | View In iTunes |

44 | VideoTwo Dimensional Vectors (MathsCasts) | How to represent a two dimensional vector in terms of the basis unit vectors ; i and j , by decomposing the vector into its horizontal and vertical components. | 12/19/2013 | Free | View In iTunes |

45 | VideoThree Dimensional Vector (MathsCasts) | Representing a three dimensional vector in three dimensional space using the x,y and z axes. writing a three dimensional vector in terms of the perpendicular unit vectors; i, j and k. | 12/17/2013 | Free | View In iTunes |

46 | VideoThe Modulus and Dot Product of a 2d Vector (MathsCasts) | Outlines the definition of the modulus of a 2D vector showing a simple example and outlines the definition of the dot product (geometrical) of 2D vectors followed by a simple example. | 12/16/2013 | Free | View In iTunes |

47 | VideoThe Dot Product of 2d Vectors (Part 2) (MathsCasts) | Verifies formula for the dot product of 2D vectors expressed in terms of i and j and shows simple example. | 12/15/2013 | Free | View In iTunes |

48 | VideoThe Dot Product (Geometry Proof) (MathsCasts) | Geometric proof of the dot product using Cosine rule. | 12/14/2013 | Free | View In iTunes |

49 | VideoThe Cross Product of Vectors (Part 2) (MathsCasts) | Outline of formula for finding the cross product of two 3D vectors which are written in terms of i, j and k. Worked example of finding the cross product of two 3D vectors which are written in terms of i, j and k. | 12/13/2013 | Free | View In iTunes |

50 | VideoThe Cross Product of Vectors (Part 1) (MathsCasts) | Defines cross product of vectors and illustrates the geometrical representation of the cross product and use of the right hand rule. Outlines differences in results between dot product and cross product. | 12/12/2013 | Free | View In iTunes |

51 | VideoThe Angle Between Two Vectors (Part 2) (MathsCasts) | Worked example of finding the angle between two 3D vectors | 12/11/2013 | Free | View In iTunes |

52 | VideoThe Angle Between Two Vectors (MathsCasts) | Using the definition of the dot product to find formula for finding the angle between two vectors. Working through example to find the angle between two vectors which are expressed in terms of i and j. | 12/10/2013 | Free | View In iTunes |

53 | VideoTaylor Series: Logarithmic Functions (MathsCasts) | Calculates the Taylor series for the natural logarithmic function about the point x = 1. | 12/9/2013 | Free | View In iTunes |

54 | VideoTaylor Series: Definition (MathsCasts) | Firstly introduces the notion of approximating a function via a polynomial before defining the Taylor and MacLaurin series. | 12/8/2013 | Free | View In iTunes |

55 | VideoSequences and Series: The Ratio Test (MathsCasts) | Introduces the Ratio Test and it's convergence properties before utilizes this method on some simple examples. | 12/5/2013 | Free | View In iTunes |

56 | VideoSequences and Series: The P-Series (MathsCasts) | Introduces the P-Series and it's convergence properties before exploring some simple examples. | 12/4/2013 | Free | View In iTunes |

57 | VideoSequences and Series: Mixed Examples Part 2 (MathsCasts) | Tests more advanced examples for convergence using either the ratio test or limit comparison test. | 12/3/2013 | Free | View In iTunes |

58 | VideoSequences and Series: Mixed Examples Part 1 (MathsCasts) | Tests more advanced examples for convergence using either the ratio test or limit comparison test. | 12/2/2013 | Free | View In iTunes |

59 | VideoSequences and Series: Interval of Convergence (MathsCasts) | Introduces the power series, the radius of convergence, and hence the interval of convergence before calculating the interval of convergence of a power series. | 12/1/2013 | Free | View In iTunes |

60 | VideoSequences and Series: Factorials (MathsCasts) | Introduces the concept of factorials and how to simplify factorial expressions. | 11/30/2013 | Free | View In iTunes |

61 | VideoSequences and Series: Definiton (MathsCasts) | Definition of a sequence and definition of a series. Introduces the concept of the convergence or divergence of a series using basic examples. | 11/29/2013 | Free | View In iTunes |

62 | VideoSequences and Series: Alternating Series Test (MathsCasts) | Introduces the concept of an alternating series and the Alternating Series test before utilizing this method to determine the convergence of such a series. | 11/28/2013 | Free | View In iTunes |

63 | VideoSequences and Series: The Limit Comparison Test (MathsCasts) | Introduces the Limit Comparison Test and utilizes this method to determine the convergence of a series. | 11/27/2013 | Free | View In iTunes |

64 | VideoQuadratic Inequalities (Example 2) (MathsCasts) | Worked example of solving an inequality statement with a denominator . Explanation of why multiply both sides of inequality by denominator squared given. | 11/26/2013 | Free | View In iTunes |

65 | VideoProperties of the Dot Product of Vectors (Part 2) (MathsCasts) | Verifies distributive property of the dot product | 11/25/2013 | Free | View In iTunes |

66 | VideoProperties of the Dot Product of Vectors (Part 1) (MathsCasts) | Proof of some basic properties of the dot product.(i) Dot product of perpendicular vectors,(ii) Dot product of parallel vectors, (iii) Dot product of a vector with itself, and (iv) Commutative property of the dot product | 11/24/2013 | Free | View In iTunes |

67 | VideoProof: The vector ab is equal to the vector b minus the vector a (MathsCasts) | Proof of vector ab = vector b minus vector a explained | 11/23/2013 | Free | View In iTunes |

68 | VideoPower of a Complex Number: De Moivre's Formula (MathsCasts) | Explains the calculation of the power of a complex number using the exponential form to finally deduce De Moivre's Formula | 11/22/2013 | Free | View In iTunes |

69 | VideoNewton's Method (MathsCasts) | Introduces Newton' Method and explains the procedure for finding a root | 11/21/2013 | Free | View In iTunes |

70 | VideoNegative Vector and Single Letter (Position) Vectors (MathsCasts) | Defines negative vector and shows why vector ba is equal to vector -ab. Defines position vector and states that a vector which starts at the origin can be expressed in terms of its end point only, i.e.as a single letter vector. | 11/20/2013 | Free | View In iTunes |

71 | VideoMultiplying a Vector by a Scalar (MathsCasts) | Simple examples showing the geometric and algebraic effect on magnitude and direction of vectors when multiplying vectors by positive and negative scalars. | 11/19/2013 | Free | View In iTunes |

72 | VideoMaclaurin Series: Trigonometric Functions (MathsCasts) | Calculates the MacLaurin series for the trigonometric function sine x. Comments on the pattern of the series. | 11/18/2013 | Free | View In iTunes |

73 | VideoMaclaurin Series: Exponential Functions (MathsCasts) | Calculates the MacLaurin series for the exponential function. Also discusses the MacLaurin series for e^2x derived from the corresponding series for e^x. | 11/17/2013 | Free | View In iTunes |

74 | VideoMaclaurin Series: Composite Functions (MathsCasts) | Calculates the MacLaurin series for a composite function e^{sinx}. Highlights the fact that this series must be a polynomial. | 11/16/2013 | Free | View In iTunes |

75 | VideoComponents of a Vector (Part 2) (MathsCasts) | Worked example of finding the magnitude of the horizontal and vertical component of a soccer balls velocity. | 11/14/2013 | Free | View In iTunes |

76 | VideoComponents of a Vector (Part 1) (MathsCasts) | Explaination of how to resolve a vector into its horizontal and vertical components. | 11/13/2013 | Free | View In iTunes |

77 | VideoCombined Inequalities (Introduction and Example 1) (MathsCasts) | Introduction to combined inequalities. Example of forming a combined inequality from a given word statement and worked example of solving a combined inequality consisting of the word 'or' and solutions checked. | 11/12/2013 | Free | View In iTunes |

78 | VideoCombined Inequalities (Example 4) (MathsCasts) | Forming a combined inequality statement from a given word statement using symbols instead of the words 'or' or 'and' and solving this combined inequality. Solutions also checked. | 11/11/2013 | Free | View In iTunes |

79 | VideoCombined Inequalities (Example 3) (MathsCasts) | Forming a combined inequality from a given word problem to estimate the distance between two homes, given the distance from both homes to Dublin Airport. | 11/10/2013 | Free | View In iTunes |

80 | VideoCombined Inequalities (Example 2) (MathsCasts) | Worked example of forming and solving a combined inequality statement from a given word statement. Term 'conjunction' explained and solutions checked. | 11/9/2013 | Free | View In iTunes |

81 | VideoApplications of Vectors (Part 2) (MathsCasts) | Worked example shows how to apply knowledge of vectors to determine the true course of a boat travelling across a river. | 11/8/2013 | Free | View In iTunes |

82 | VideoApplications of Vectors (Part 1) (MathsCasts) | Worked example shows how to apply knowledge of vectors to determine the work done in pulling a cart a certain distance. | 11/7/2013 | Free | View In iTunes |

83 | VideoAlgebra: Multiplication of Letters and Numbers (MathsCasts) | Worked example explains how to multiply numbers and letters. Also explains the concepts of expressions, constants and coefficients. | 11/6/2013 | Free | View In iTunes |

84 | VideoAdding and Subtracting Vectors Algebraically (MathsCasts) | Worked examples of adding and subtracting vectors algebraically in terms of i and j and also using the result of the proof of vector ab = vector b - vector a. | 11/5/2013 | Free | View In iTunes |

85 | VideoAbsolute Value (Example 3 Inequality) (MathsCasts) | Solving an inequality statement containing an absolute value symbol by isolating the absolute value term at one side of the inequality and solutions checked. | 11/4/2013 | Free | View In iTunes |

86 | VideoAbsolute Value (Example 2 Inequality) (MathsCasts) | Worked example of solving an absolute value inequality statement and solutions checked. | 11/3/2013 | Free | View In iTunes |

87 | VideoAbsolute Value (Definition and Example 1) (MathsCasts) | Definition of absolute value using simple examples. Worked example of solving an equation consisting of an absolute value symbol and checking solutions. | 11/2/2013 | Free | View In iTunes |

88 | VideoAbsolute Value (Example 4 Inequality) (MathsCasts) | Worked example of solving an inequality containing two absolute value symbols, solutions checked and graph of absolute values also shown to illustrate solution set. | 11/1/2013 | Free | View In iTunes |

89 | VideoPartial Fractions: Multiplicity of a Root (MathsCasts) | Explains the partial fraction expansion procedure when the denominator has repeated linear roots, and applies this technique to a simple example. Then applies this expansion to conduct the integration. Uses substitution in the resulting integrals. | 10/24/2013 | Free | View In iTunes |

90 | VideoReciprocal Trigonometric Integrals (MathsCasts) | Discusses reciprocal trigonometric identities and investigates numerous examples, some of which involve reading the differentiation tables. | 10/24/2013 | Free | View In iTunes |

91 | VideoPartial Fractions: Mixed Roots - Part 2 (MathsCasts) | Uses the expansion from Part 1 to conduct the integration. Uses substitution in the resulting integrals. | 10/23/2013 | Free | View In iTunes |

92 | VideoPartial Fractions: Mixed Roots - Part 1 (MathsCasts) | Explains the partial fraction expansion procedure when the denominator has a mixture of linear roots and repeated linear roots, and applies this technique to a simple example. | 10/23/2013 | Free | View In iTunes |

93 | VideoQuadratic Inequalities (Introduction and Example 1) (MathsCasts) | General form of a quadratic inequality outlined, some examples of where quadratic inequalities arise in real life mentioned. | 10/22/2013 | Free | View In iTunes |

94 | VideoGraphing Linear Inequalities (MathsCasts) | Introduction to Linear Inequalities. Definitions. Simple Examples. | 10/20/2013 | Free | View In iTunes |

95 | VideoPartial Fractions: Definition (MathsCasts) | Explains the concept of Partial Fractions. | 10/13/2013 | Free | View In iTunes |

96 | VideoPartial Fractions: Linear Roots - Part 2 (MathsCasts) | Firstly double checks the expansion from Part 1. Then shows the use of partial fractions to conduct the integration. Uses substitution in the resulting integrals. | 10/13/2013 | Free | View In iTunes |

97 | VideoPartial Fractions: Linear Roots - Part 1 (Mathscasts) | Explains the partial fraction expansion procedure when the denominator has linear roots, and applies this technique to a simple example. | 10/13/2013 | Free | View In iTunes |

98 | VideoCompleting the square (MathsCasts) | Explains the concept of completing the square with two practical examples resulting in trigonometric identities. | 10/10/2013 | Free | View In iTunes |

99 | VideoIterative reduction formula - Part 1 (Mathscasts) | Firstly discusses iterative functions and solutions while noting the usefulness of an Iterative Reduction Formula for multiple integration by parts. Then applies this to a simple indefinite case. | 10/10/2013 | Free | View In iTunes |

100 | VideoIterative reduction formula - Part 2 (Mathscasts) | Continues the previous simple indefinite example noting the construction of a base case. Then considers the corresponding definite case. | 10/10/2013 | Free | View In iTunes |

101 | VideoWhy is the graph of y = 1/x an hyperbola? (MathsCasts) | We demonstrate that the equation y = 1/x transforms to standard form for an hyperbola under rotation of the coordinate axes by 45 degrees. | 9/26/2013 | Free | View In iTunes |

102 | VideoSolving an equation of form rational function equals 0 (MathsCasts) | We discuss the solutions of the equation p(x)/q(x) = 0 where p and q are in principle any functions. We revise the meanings of the terms 'numerator' and 'denominator'. | 9/23/2013 | Free | View In iTunes |

103 | VideoSimplifying compositions of trig and inverse trig functions (MathsCasts) | Two examples of simplifying expressions of the form trig(inverse trig), using right angled triangles. The result is in algebraic form without trig functions | 9/23/2013 | Free | View In iTunes |

104 | VideoThe Laplace transform of the error function erf(t) (MathsCasts) | We show how to calculate the Laplace transform of the error function erf(t) | 9/15/2013 | Free | View In iTunes |

105 | VideoTransposition with required letter in numerator and denominator - Part 1 (MathsCasts) | This recording gives a demonstration of how to make a letter the subject of a formula in the case where the letter appears in both numerator and denominator of the original equation, but only to the power of 1 in each case. | 9/9/2013 | Free | View In iTunes |

106 | VideoInverse Laplace transforms with (s^2 + a^2)^2 in the denominator and numerator linear or quadratic in s - Part 1 (MathsCasts) | We use the result for inverse Laplace transform of a derivative to find the inverse transforms of g(s)/(s^2+a^2)^2 with g(s) constant, linear or quadratic in s. | 9/8/2013 | Free | View In iTunes |

107 | VideoProperties of sin and cos - Part 2 (MathsCasts) | We prove some results on horizontal shifts applied to the sin and cos functions. | 9/5/2013 | Free | View In iTunes |

108 | VideoProperties of sin and cos - Part 1 (MathsCasts) | We prove that cos(-x) = cos(x) and sin(-x) = - sin(x|) | 9/5/2013 | Free | View In iTunes |

109 | VideoWhat's wrong? Cancellation of algebraic fractions (MathsCasts) | We look at an example of a case where an algebraic fraction is actually already in its simplest form, and some of the common errors people make in trying to 'cancel' terms in this case. | 9/4/2013 | Free | View In iTunes |

110 | VideoPolitical differentiation, a quirky approach to the product and quotient rules (MathsCasts) | Simple political analogies are used with the intention of aiding the memory on the form of the product and quotient rules. | 9/3/2013 | Free | View In iTunes |

111 | VideoInverse Laplace transform with constant, s or s ^2 in the numerator and (s^2+a^2)^2 in the denominator - Part 2 (MathsCasts) | We use the result for inverse Laplace transform of a derivative to find the inverse transforms of g(s)/(s^2+a^2)^2 with g(s) constant, linear or quadratic in s. | 9/2/2013 | Free | View In iTunes |

112 | VideoLaplace transform solution of a 2nd order, constant coefficient, non-homogeneous ODE with boundary conditions (MathsCasts) | We solve a 2nd order, constant coefficient, non-homogeneous ODE with boundary conditions at t = 0 for y and y'. | 9/2/2013 | Free | View In iTunes |

113 | VideoIntegrating Rational Functions - Part 1 (MathsCasts) | This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is a linear function. Integration by substitution is used. | 8/28/2013 | Free | View In iTunes |

114 | VideoIntegrating Rational Functions - Part 2 (MathsCasts) | This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is an irreducible quadratic function. We complete the square on the denominator, then we integrate by substitution to find the answer. | 8/28/2013 | Free | View In iTunes |

115 | VideoA Geometric proof of the sum and difference formulae for sin and cos (MathsCasts) | We prove the formula for sin(A-B) using right-angled triangles then we show how the corresponding formulae for cos(A-B) and sin and cos of A+B can be deduced as a result. | 8/27/2013 | Free | View In iTunes |

116 | VideoPowers of complex numbers (MathsCasts) | Gives the general formula then applies this to an example. Cartesian form is convert to polar form, then the required power of the number is calculated, and finally the result is converted back into Cartesian form. | 7/9/2013 | Free | View In iTunes |

117 | VideoSimplifying algebraic fractions with cancellation Part 1 (MathsCasts) | We look at how to simplify algebraic fractions when there is a number and/ or power of a letter that is common to all terms on the numerator and denominator, thus allowing us to simplify the original fraction by cancelling out this common factor. | 6/26/2013 | Free | View In iTunes |

118 | VideoThe scalar triple product (MathsCasts) | Investigates the scalar triple product in the context of the volume of a parallellepiped. | 6/19/2013 | Free | View In iTunes |

119 | VideoEquation of the tangent to a curve (MathsCasts) | We find the equation of the tangent to a curve at a specific point, by first finding the general expression for the derivative of the curve, then evaluating it at the point, and then using this information to find the equation of the tangent. | 6/12/2013 | Free | View In iTunes |

120 | VideoIntroduction to implicit differentiation (MathsCasts) | Gives a basic example of implicit differentiation to find dy/dx, and compares this to the result from explicit differentiation for the same example. Second example is a circle, with graphical interpretation of dy/dx in two points. | 5/23/2013 | Free | View In iTunes |

121 | VideoTransposition with required variable in the denominator (MathsCasts) | In this recording we look at how to rearrange a formula where the letter that we want to make the subject is in the denominator. That is, we look how to make f the subject when presented with an expression of the form a/b = c/d + e/f. | 5/21/2013 | Free | View In iTunes |

122 | VideoThe Laplacian of f(r) and proof that 1 over r is harmonic (MathsCasts) | We derive a general formula for the Laplacian acting on a function f(r) then demonstrate that the Laplacian is zero in the case that f(r) = 1/r, thereby showing that 1/r is harmonic. | 5/20/2013 | Free | View In iTunes |

123 | VideoThe curl of the gradient and the divergence of the curl are zero (MathsCasts) | We show that div(curl(v)) and curl (grad f) are 0 for any vector field v(x,y,z) and scalar function f(x,y,z). | 5/16/2013 | Free | View In iTunes |

124 | VideoThe curl of the curl (MathsCasts) | We derive a formula to simplify the process of taking the curl of the curl of a vector field. The algebra is rather complicated! | 5/15/2013 | Free | View In iTunes |

125 | VideoHalf-range Fourier Series: Part 3 (MathsCasts) | We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range sine series for a linear f(t). | 5/15/2013 | Free | View In iTunes |

126 | VideoFinding the grad of a function f(x,y,z) (MathsCasts) | We choose a simple scalar function f(x,y,z) and calculate its gradient. | 5/14/2013 | Free | View In iTunes |

127 | VideoFinding the divergence and curl of a simple vector field (MathsCasts) | We calculate the divergence and curl of a simple vector field | 5/13/2013 | Free | View In iTunes |

128 | VideoChain rule or not? (MathsCasts) | Six short examples useful as preparation for implicit differentiation. Some require the chain rule, others are straightforward differentiations. | 5/9/2013 | Free | View In iTunes |

129 | VideoA matrix to the power of a matrix (MathsCasts) | We ask if a matrix can be raised to the power of a matrix and do a simple 2 by 2 example. | 5/8/2013 | Free | View In iTunes |

130 | VideoMatrix representation of complex numbers (MathsCasts) | We show how complex number arithmetic can be performed using matrices for the complex numbers. | 5/6/2013 | Free | View In iTunes |

131 | VideoAdding and Subtracting Surds (MathsCasts) | We look at cases when we can add and subtract surds- namely when terms can be re-written with the same number under the square root sign. Two examples are given- in the second example the surds need to be simplified before adding/ subtracting them. | 5/3/2013 | Free | View In iTunes |

132 | VideoComplex Impedance - Part 3 (MathsCasts) | We look at a numerical example for an RLC circuit and calculate the complex impedance and phase difference. | 5/1/2013 | Free | View In iTunes |

133 | VideoComplex Impedance - Part 2 (MathsCasts) | We continue investigation of the RLC circuit, introducing complex versions of voltage and current. The complex impedance results naturally from these quantities and gives a clear picture of why the current and voltage differ by a phase, and by how much. | 4/30/2013 | Free | View In iTunes |

134 | VideoAdding and subtracting fractions (MathsCasts) | We look at several examples of adding and subtracting fractions, by first obtaining a common denominator. | 4/29/2013 | Free | View In iTunes |

135 | VideoComplex Impedance - Part 1 (MathsCasts) | We investigate the RLC circuit and obtain a relation between voltage and current without use of complex quantities. We see that the relation is rather cumbersome and not transparent. | 4/24/2013 | Free | View In iTunes |

136 | VideoIntegrals of 1 over (a + b sin theta) and 1 over a + b cos theta) (MathsCasts) | We discuss integrals with a linear function of sin or cos in the denominator of the integrand. We address the question of existence then exhibit a substitution which allows for use of the residue theorem to evaluate the integral. | 4/15/2013 | Free | View In iTunes |

137 | VideoReversing the Order of Integration of a Double Integral 2 (MathsCasts) | Part 2 of 3. Continuation from part one, looking at increasingly complicated examples of reversal of integration order. | 4/12/2013 | Free | View In iTunes |

138 | VideoReversing the order of integration of a double integral 1 (MathsCasts) | Part 1 of 3. We show how to swap the order of integration in a double integral depending on x and y. We use the same examples as for the region of integration for double integrals. We start with constant integration limits and progress to variable limits. | 4/12/2013 | Free | View In iTunes |

139 | VideoGrad, div and curl (MathsCasts) | Introduces the del operator and gives brief discussion of how it is used as a gradient, divergence and curl, then in the formation of the Laplacian. | 4/11/2013 | Free | View In iTunes |

140 | VideoGraphing factorised polynomial functions (MathsCasts) | Looks at how linear factors to odd and even powers can help in sketching polynomial functions that can be factorised into all linear factors. | 4/9/2013 | Free | View In iTunes |

141 | VideoSome simple exercises on linear (in)dependence (MathsCasts) | We solve some basic exercises to decide on the linear dependence, or not, of some sets of vectors in 2 and 3 dimensions. These simple cases can be done by inspection without Gaussian elimination. | 4/8/2013 | Free | View In iTunes |

142 | VideoCartesian to polar form: Part 2 (MathsCasts) | Example of getting the polar form of a complex number if the cartesian form is known(number placed in the first quadrant). | 4/5/2013 | Free | View In iTunes |

143 | VideoFinding the Laplace transform of an integral (MathsCasts) | Knowing the Laplace transform of a function f(t) allows us also to calculate the transform of the integral of f(t). We show the simplest method of doing this here. | 4/5/2013 | Free | View In iTunes |

144 | VideoEigenvectors of a 3x3 matrix (MathsCasts) | We show how to find the eigenvectors for the 3 by 3 matrix whose eigenvalues were calculated in a separate presentation. | 4/3/2013 | Free | View In iTunes |

145 | VideoEigenvectors of a 2x2 matrix (MathsCasts) | We use the same 2 by 2 matrix whose eigenvalues were found in another MathsCast (Eigenvalues of a 2 by 2 matrix) and find the assocIated eigenvectors. | 3/25/2013 | Free | View In iTunes |

146 | VideoEigenvalues of a 3x3 matrix (MathsCasts) | Eigenvalues of a 3 by 3 matrix are calculated. Some useful advice is given concerning factorization of the characteristic equation. | 3/22/2013 | Free | View In iTunes |

147 | VideoEigenvalues of a 2x2 matrix (MathsCasts) | We show how to find eigenvalues for an NxN matrix then do a 2x2 example. This MathsCast follows from an introductory MathsCast on eigenvalues and eigenvectors and it is also helpful to view the presentations on linear dependence and independence first. | 3/21/2013 | Free | View In iTunes |

148 | VideoAddition of binary numbers (MathsCasts) | In this recording, addition of binary numbers is demonstrated, with reference to a specific example. | 3/13/2013 | Free | View In iTunes |

149 | VideoGeometric series: Part 3 (MathsCasts) | We introduce geometric series involving a combination of partial fractions derived from a quadratic denominator. It is shown how to develop series which converge for any value of x by treating the partial fractions in different ways before expansion. | 2/27/2013 | Free | View In iTunes |

150 | VideoAdding and subtracting example (MathsCasts) | We look at several examples of adding and subtracting positive and negative numbers, including examples where there are two immediately adjacent signs (e.g. two negative signs). | 2/21/2013 | Free | View In iTunes |

151 | VideoPrime factors (MathsCasts) | We look at how to factorise a number into a product of prime factors, with several examples. | 2/20/2013 | Free | View In iTunes |

152 | VideoRearranging equations (MathsCasts) | Two examples are given of rearranging an equation or formula to make a particular letter the subject. This is done by first considering each operation that was originally done to the required letter, and then reversing these operations. | 2/14/2013 | Free | View In iTunes |

153 | VideoFinding the least common multiple (MathsCasts) | We look at how to find the least common multiple of two or more whole numbers, by first factorising the numbers into a product of prime numbers and then comparing the results. | 2/13/2013 | Free | View In iTunes |

154 | VideoSimplifying surds (MathsCasts) | We look at how to simplify surds. This is done by finding the largest perfect square that is a factor of the number under the square root and hence bringing this part of the expression outside the square root. | 2/6/2013 | Free | View In iTunes |

155 | VideoCompass directions: Part 2 (MathsCasts) | We look at a second example involving combinations of direction, one of which is none of north, south, east or west. | 1/30/2013 | Free | View In iTunes |

156 | VideoPythagoras theorem (MathsCasts) | Explains the concept of a right angled triangle and introduces pythagoras theorem. | 1/24/2013 | Free | View In iTunes |

157 | VideoCompass directions: Part 1 (MathsCasts) | We introduce the points of the compass and solve a simple example using distances and basic directions (N,S,E,W) to find resulting distance and angle. | 1/23/2013 | Free | View In iTunes |

158 | VideoThe trapezoidal rule (MathsCasts) | The general principle of the trapezoidal rule of numerical integration is given. A specific example of applying it is then given. | 1/17/2013 | Free | View In iTunes |

159 | VideoReversing the order of integration of a double integral 3 (MathsCasts) | Part 3 of 3. Continuation from part one, looking at increasingly complicated examples of reversal of integration order. | 1/16/2013 | Free | View In iTunes |

160 | VideoInverse functions: example 1 (MathsCasts) | Gives the definition and conditions for the inverse of a function to exist, and then applies this to an example the case of finding the inverse of a one-to-one function. | 1/11/2013 | Free | View In iTunes |

161 | VideoBinomial series: Part 3 (MathsCasts) | We expand the binomial series for the case n = 1/2 to evaluate an approximation for the square root of 2. Convergence is discussed briefly then we deal with the case when the first term in the binomial expression is a constant other than one. | 1/7/2013 | Free | View In iTunes |

162 | VideoInverse functions: example 2 (MathsCasts) | Gives the definition and conditions for the inverse of a function to exist, and then applies this to an example where the original function is not one-to-one and where the domain of f(x) hence needs to be restricted in order to define the inverse function | 1/4/2013 | Free | View In iTunes |

163 | VideoVector subtraction including boat example (MathsCasts) | Introduction to 'head to tail' vector subtraction in the geometric sense. This is then applied to an example of working out a boat's velocity relative to water given the velocity of the current and the velocity of the boat relative to land are both known | 11/16/2012 | Free | View In iTunes |

164 | VideoVector addition including a boat example (MathsCasts) | Introduction to "head to tail" vector addition in the geometric sense. This is then applied to an example of working out a boat's velocity relative to land given the velocity of the current and the velocity of the boat relative to water are both known. | 11/13/2012 | Free | View In iTunes |

165 | VideoDetermining linear (in)dependence (MathsCasts) | We investigate the linear dependence or independence of a set of 3 vectors in 3 dimensions. We show how the determinant of a 3 by 3 matrix can assist in this process. | 11/8/2012 | Free | View In iTunes |

166 | VideoFactorising by grouping Part 3 (MathsCasts) | Examples of how to factorise expressions whose terms don't have any common factor (other than 1) by grouping pairs that do have factors in common. | 11/7/2012 | Free | View In iTunes |

167 | VideoFactorising by grouping Part 2 (MathsCasts) | Examples of how to factorise expressions whose terms don't have any common factor (other than 1) by grouping pairs that do have factors in common. | 11/2/2012 | Free | View In iTunes |

168 | VideoSolving quadratic inequalities: example 2 (MathsCasts) | We investigate inequalities involving quadratic expression and show how to use a combination of algebraic rearrangement and graph sketching to find solutions. The solutions are written as inequalities and as intervals. | 11/1/2012 | Free | View In iTunes |

169 | VideoLaplace transform of an integral using reversal of order of a double integral (MathsCasts) | We use the known result for Laplace transform of a derivative sF(s) to speculate about the result for the transform of an integral. We guess that it might involve division by s. This result is proven using a double integration method. | 10/31/2012 | Free | View In iTunes |

170 | VideoVisualising solution of 3 linear equations in 3 unknowns (MathsCasts) | Examples are given of the visual interpretation of systems of 3 simultaneous linear equations in 3 unknowns for the case where there is a unique solution, an infinite number of solutions, and no solutions. | 10/30/2012 | Free | View In iTunes |

171 | VideoConverting a double integral from Cartesian to circular polar coordinates (MathsCasts) | After a brief review of circular polar coordinates, a double integral is written using Cartesian coordinates. We draw the region of integration and describe it in terms of polar coordinates in order to rewrite the integral in polar coordinates. | 10/29/2012 | Free | View In iTunes |

172 | VideoFinding the inverse of a 2x2 matrix (MathsCasts) | Outlines the general formula for finding the Inverse of a 2x2, then goes through one simple example. | 10/26/2012 | Free | View In iTunes |

173 | VideoSolving equations using logarithms (MathsCasts) | The general definition of logarithms is given and the general principle of solving equations of from a^x=b is introduced. Two examples to apply this method are then given. | 10/25/2012 | Free | View In iTunes |

174 | VideoChanging base of logarithms (MathsCasts) | The general principle of changing base of logs (logarithms) is given and then this is illustrated with a specific example. | 10/24/2012 | Free | View In iTunes |

175 | VideoTransition Curves (MathsCasts) | This recording first explains what a transition curves is and gives formulae to calculate the angle theta as well as any point on the curve (x,y). It then works through an example. | 10/23/2012 | Free | View In iTunes |

176 | VideoPartial fractions example 3 (MathsCasts) | An example of calculating partial fractions when one of the factors on the denominator is an irreducible quadratic factor | 10/22/2012 | Free | View In iTunes |

177 | VideoWriting composite trigonometric functions as algebraic expressions (MathsCasts) | Several examples are given of rewriting composite circular functions, where the inner function is an inverse trigonometric function, as an algebraic function in terms of x. | 10/19/2012 | Free | View In iTunes |

178 | VideoRelated rates of change - Example 2 (MathsCasts) | Outlines the general process for setting up and solving a related rates problem (where related quantities change over time). This is then applied to an example involving a chemical being drained out of a cylindrical tank. | 10/16/2012 | Free | View In iTunes |

179 | VideoRelated rates of change - Example 1 (MathsCasts) | Outlines the general process for setting up and solving a related rates problem (where related quantities change over time). This is then applied to an example involving the relative speed and distance apart of two bicycles at a specified time. | 10/15/2012 | Free | View In iTunes |

180 | VideoIntroduction to factorising (MathsCasts) | Basic explanation of what factorising is, why it is used, and a couple of simple examples. | 10/12/2012 | Free | View In iTunes |

181 | VideoWork done using vectors (MathsCasts) | An example of using the scalar product to determine the work done on an object by a force, when the force is expressed in vector form. | 10/11/2012 | Free | View In iTunes |

182 | VideoPartial fractions example 2 (MathsCasts) | An example of calculating partial fractions when one of the factors on the denominator is a repeated linear factor. | 10/10/2012 | Free | View In iTunes |

183 | VideoPartial fractions example 1 (MathsCasts) | An example of calculating partial fractions when the denominator can be factorised into single distinct linear factors | 10/9/2012 | Free | View In iTunes |

184 | VideoProving hyperbolic ids (MathsCasts) | Demonstrates the general method and two examples of using the definitions of sinh(x) and cosh(x) to prove hyperbolic function identities | 10/8/2012 | Free | View In iTunes |

185 | VideoLaplace transform of the derivative of a function (MathsCasts) | We derive the formula for the Laplace transform of df/dt in terms of that for f(t) and f(0). It is then shown how to extrapolate the rule to write down the transforms for 2nd, 3rd and higher derivatives. | 10/4/2012 | Free | View In iTunes |

186 | VideoSketching the region of integration of double integrals (MathsCasts) | We examine some double integrals with Cartesian variables x and y. We investigate the integration limits and relate them to the 2D region of integration in the x-y plane. This is preparatory to reversing the order of integration. | 10/3/2012 | Free | View In iTunes |

187 | VideoEquating complex numbers (MathsCasts) | The conditions for equality of complex numbers are given. An example of grouping and then equating real and inaginary parts of complex numbers on both sides of an equation to find unknown quantities is then given. | 10/2/2012 | Free | View In iTunes |

188 | VideoWorking with Zero (MathsCasts) | Gives basic arithmetic rules and index laws for working with 0 and applies them to several examples. | 10/1/2012 | Free | View In iTunes |

189 | VideoDifferentiation involving roots (MathsCasts) | Provides 2 worked examples of differentiating square roots, cube roots, etc. of x. Gives the viewer 3 sample questions of a similar nature at the end with solutions. | 9/28/2012 | Free | View In iTunes |

190 | VideoFinding the determinant of a 3x3 matrix (MathsCasts) | Covers one example of finding the determinant of a 3x3 matrix. Note at the end regarding the fact that if the determinant equals zero then that matrix has no inverse. | 9/27/2012 | Free | View In iTunes |

191 | VideoFinding the determinant of a 2x2 matrix (MathsCasts) | Outlines the general formula for finding the determinant of a 2x2, then goes through one simple example. Note at the end regarding the fact that if the determinant equals zero then that matrix has no inverse. | 9/26/2012 | Free | View In iTunes |

192 | VideoQuotient rule Part 2 (MathsCasts) | Further example of how to apply the Quotient rule. Recapped on the steps involved also. Practice questions at the end with solutions for students to try themselves | 9/25/2012 | Free | View In iTunes |

193 | VideoQuotient rule Part 1 (MathsCasts) | Introduction to the Quotient rule, outlining when and how to apply it with one example. Steps involved are outlined also. | 9/24/2012 | Free | View In iTunes |

194 | VideoEvaluating double integrals by reversing the order of integration (MathsCasts) | We examine two double integrals in which the anti-differentiation is at first sight impossible. We then reverse the order of integration and sidestep the problem of seemingly impossible integration. The integrals are thus evaluated. | 9/20/2012 | Free | View In iTunes |

195 | VideoDifferentiation involving e (MathsCasts) | Completes 4 examples of differentiation involving 'e'. Shows the rule outlined in the log tables relevant to this and provides 3 sample questions at the end with solutions. | 9/19/2012 | Free | View In iTunes |

196 | VideoSolving Quadratic Equations Using the Formula - Part 2 (MathsCasts) | Example of how to apply the formula for solving quadratic equations | 9/18/2012 | Free | View In iTunes |

197 | VideoSolving Quadratic Equations Using the Formula - Part 1 (MathsCasts) | Example of how to apply the formula for solving quadratic equations | 9/17/2012 | Free | View In iTunes |

198 | VideoThe small element of area for circular polar coordinates (MathsCasts) | We investigate a small piece of area in a 2D region. We justify pictorially, the factor of r in the form dA = r dr theta. The Jacobian determinant is given for circular polars, which is then shown to yield r as the appropriate factor in the area dA. | 9/14/2012 | Free | View In iTunes |

199 | VideoSimple Differentiation Part 3 (MathsCasts) | Completes examples on differentiating simple functions and provides practice questions and answers at the end for viewer to work on themselves. | 9/13/2012 | Free | View In iTunes |

200 | VideoSimple Differentiation Part 2 (MathsCasts) | Completes 3 examples of differentiating constants and explains why they differentiate to zero. Completes 3 examples of differentiating simple functions. | 9/12/2012 | Free | View In iTunes |

201 | VideoSimple Differentiation Part 1 (MathsCasts) | Defines basic rule for differentiation and completes 3 basic examples involving x to a power of 2 or greater, then completes 3 more examples, this time all with x to the power of 1. | 9/3/2012 | Free | View In iTunes |

202 | VideoFurther properties of Odd and Even Functions (MathsCasts) | We discuss combinations of even and odd functions involving sums, products etc and investigate their odd and even properties. We show the use of such properties in reducing the work needed to evaluate a certain kind of integral. | 8/31/2012 | Free | View In iTunes |

203 | VideoThe binomial series: Part 2 (MathsCasts) | We extend the expansion of the nth power of a binomial and investigate the power series for the nth power of (1+x). For all n, Infinite Maclaurin series are obtained and the coefficients identified. We revisit part 1 where n is positive integer. | 8/30/2012 | Free | View In iTunes |

204 | VideoThe binomial series: Part 1 (MathsCasts) | Positive integer powers of the binomial (a+b) are examined. It is shown how to expand the brackets to obtain a finite series using coefficients from the Pascal triangle. Later these coefficients are identified as the nCr coefficients. | 8/29/2012 | Free | View In iTunes |

205 | VideoWhat's wrong? Differentiation with a variable in the exponent (MathsCasts) | Shows two incorrect solutions to finding the derivative of (3x+5)^2x and discusses why they are incorrect. The correct approach is then explained. | 8/27/2012 | Free | View In iTunes |

206 | VideoThe multivariate chain rule: example 2 (MathsCasts) | An example of using the multivariate chain rule, where in this case we are finding dz/dx given z = f(x,y) and y = y(x). | 8/24/2012 | Free | View In iTunes |

207 | VideoSecond order differential equations: example 1 (MathsCasts) | Example of solving a second-order linear ordinary differential equation with constant coefficients in the case where the auxiliary equation has a repeated root and the right hand side of the equation is a polynomial. | 8/23/2012 | Free | View In iTunes |

208 | VideoSolving equations involving exponents (MathsCasts) | A demonstration of how to tranpose the formula y=(ae^t+be^(-t))/(ce^t+de^(-t)) to make t the subject. | 8/22/2012 | Free | View In iTunes |

209 | VideoDifferentiating Trig Functions (MathsCasts) | 3 completed examples of differentiating trigonometric functions. Similar questions at the end for students to try themselves, solutions provided also. | 8/21/2012 | Free | View In iTunes |

210 | Video2nd order differential equation initial value problem (MathsCasts) | An example of solving a second order differential equation (where the right hand side is an exponential function), given specific initial conditions y(0) and y'(0) are also provided | 8/20/2012 | Free | View In iTunes |

211 | VideoHalf-range Fourier series: Part 2 (MathsCasts) | We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t). | 8/17/2012 | Free | View In iTunes |

212 | VideoSeries, partial sums and convergence (MathsCasts) | We state what is meant by a series, express series using the summation sign, define the partial sums and briefly discuss convergence and divergence giving examples. | 8/16/2012 | Free | View In iTunes |

213 | VideoSimplifying expressions using logarithm laws (MathsCasts) | Three basic laws of logarithms are introduced and two examples then demonstrate how these laws can be used to simply logarithmic expressions. | 8/15/2012 | Free | View In iTunes |

214 | VideoEvaluating Limits as x approaches infinity Part 3 (MathsCasts) | Worked example for solving limits where x is approaching infinity. Includes graph of the function, explanation of the steps involved and why these steps are taken. | 8/14/2012 | Free | View In iTunes |

215 | VideoEvaluating Limits as x approaches infinity Part 2 (MathsCasts) | Worked example for solving limits where x is approaching infinity. Includes graph of the function, explanation of the steps involved and why these steps are taken. | 8/13/2012 | Free | View In iTunes |

216 | VideoComplex regions involving inequalities (MathsCasts) | A discussion of how to sketch complex regions of form Iz-z0I<r, lz-zol>r and related cases, This is then demonstrated with a specific example. | 8/10/2012 | Free | View In iTunes |

217 | VideoThe quadratic formula: three examples (MathsCasts) | This recording demonstrates use of the quadratic formula in relation to three examples: one with 2 distinct solutions, one with a repeated solution and one with no real solutions. The discrminant function is introduced in relation to this. | 8/9/2012 | Free | View In iTunes |

218 | VideoThe relationship between cosh (x) and sinh (x) (MathsCasts) | A demonstration of how to apply the identity (cosh(x))^2-(sinh(x))^2 = 1 and the graphical properties of sinh(x) and cosh(x) to finding sinh(x) if cosh(x) is known and vice versa. | 8/8/2012 | Free | View In iTunes |

219 | VideoDifferentiating Logs (MathsCasts) | 3 examples based on differentiating logs with questions at the end for students to try themselves, solutions given also. | 8/7/2012 | Free | View In iTunes |

220 | VideoThe derivative of a Laplace transform (MathsCasts) | We investigate the significance of differentiating a Laplace transform and relate the derivative to the inclusion of an extra factor of 't' in the original transform. The idea is extended to multiple derivatives and powers of t. | 8/2/2012 | Free | View In iTunes |

221 | VideoThe heaviside step: function as a switch (MathsCasts) | We introduce the Heaviside step function and show how it can be used to turn other functions on and off at different positions along the t-axis. | 8/1/2012 | Free | View In iTunes |

222 | VideoEvaluating Limits as x approaches infinity Part 1 (MathsCasts) | Worked example for solving limits where x is approaching infinity. Includes graph of the function, explanation of the steps involved and why these steps are taken. | 7/31/2012 | Free | View In iTunes |

223 | VideoEven and odd rational functions (MathsCasts) | Shows how to check if a polynomial is even or odd, and extends this to a rational function. | 7/30/2012 | Free | View In iTunes |

224 | VideoLaplace transform of piecewise-defined functions (MathsCasts) | We investigate the Laplace transform of a function when multiplied by the Heaviside step-function. The 2nd shift theorem is introduced. It is shown how to prepare a function for use with the 2nd shift theorem. | 7/27/2012 | Free | View In iTunes |

225 | VideoIntroduction to Laplace transforms (MathsCasts) | Defines the Laplace transform. Briefly describes the uses of a Laplace transform then deals with technical issues such as what is meant by infinity integration limit. Concludes with explanation of the restrictions on the Laplace variable 's'. | 7/26/2012 | Free | View In iTunes |

226 | VideoSeparable Differential Equations Example 2 (MathsCasts) | This screencast demonstrates how to solve a first-order separable differential equation in the case where the right hand side of the equation is a mixture of x and y terms that needs to be factorised so that the equation can be separated and solved. | 7/25/2012 | Free | View In iTunes |

227 | VideoSeparable Differential Equations Example 1 (MathsCasts) | This screencast gives an example of how to solve the first order separable differential equation: 2x/((1+x^2)y) | 7/23/2012 | Free | View In iTunes |

228 | VideoEigenvalues and eigenvectors (MathsCasts) | Explains graphically what it means to multiply a matrix and a vector. Then introduces eigenvectors as vectors belonging to the matrix with a special property in matrix vector multiplication. Eigenvalues are also explained in this context. | 7/20/2012 | Free | View In iTunes |

229 | VideoEven functions (MathsCasts) | We explain what is meant by an even function in terms of symmetry, then give a rule satisfied by the function. We show how to test for evenness then discuss the area under the graph of an even function between points an equal distance of the y axis. | 7/19/2012 | Free | View In iTunes |

230 | VideoOdd functions (MathsCasts) | We explain what is meant by an odd function in terms of symmetry, then give a rule satisfied by the function. We show how to test for oddness then discuss the area under the graph of an even function between points an equal distance of the y axis. | 7/19/2012 | Free | View In iTunes |

231 | VideoHalf-range Fourier series: Part 1 (MathsCasts) | We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t). | 7/19/2012 | Free | View In iTunes |

232 | VideoVelocity and acceleration given position vector (MathsCasts) | This recording shows how velocity and acceleration of a particle travelling through 3D space are calculated given we have a general vector expression for the position vector at time t - this is then illustrated with a specific example. | 7/17/2012 | Free | View In iTunes |

233 | VideoRoots of a complex number: Part 2 (MathsCasts) | Solve a question about finding the roots of a complex number. | 7/13/2012 | Free | View In iTunes |

234 | VideoThe Sigma notation for sums (MathsCasts) | Introduction to the Sigma notation for sums, with examples. Also highlights that infinity is not a number. | 7/12/2012 | Free | View In iTunes |

235 | VideoIntegrals using Laplace transforms (MathsCasts) | Shows how to use known Laplace transforms to evaluate infinite integrals involving exponentials in product with other functions. We extend the idea to products of an exponential with another fctn and with t using the derivative of Laplace transform method | 7/11/2012 | Free | View In iTunes |

236 | VideoSolving equations with complex roots (MathsCasts) | An example of solving a degree four polynomial where all powers are even. The substitution w = z^2 is used to rewrite as quadratic, the quadratic formula is applied to find the two solutions and then the complex square roots of both values of w are found. | 7/10/2012 | Free | View In iTunes |

237 | VideoProduct rule Part 2 (MathsCasts) | Further example of how to apply the product rule. Recapped on the steps involved also. Practice questions at the end with solutions for students to try themselves. | 7/6/2012 | Free | View In iTunes |

238 | VideoProduct rule Part 1 (MathsCasts) | Introduction to the product rule - when and how to use it with steps and one example. | 7/3/2012 | Free | View In iTunes |

239 | VideoSketching 3D curves (MathsCasts) | Shows how to sketch a 3D curves which is given in vector form on 2D paper. The curve is rewritten in scalar parametric form, values for the parameter t are selected, and points on the curve calculated. These are then plotted and the curve is sketched. | 7/2/2012 | Free | View In iTunes |

240 | VideoIntroduction to limits (MathsCasts) | Introduces the concept of a limit with graphed examples. Also, simple limit examples are completed. | 6/28/2012 | Free | View In iTunes |

241 | VideoRange and domain of composite functions (MathsCasts) | Finds domain and range of a quadratic function, a hyperbola, and the two composite functions. Shows how to exclude values from the domain and range. | 6/27/2012 | Free | View In iTunes |

242 | VideoFind the rational function 2 (MathsCasts) | This screencast compares the graph of a rational function four possible functions and discusses which rational function has produced the graph. | 6/26/2012 | Free | View In iTunes |

243 | VideoFind the rational function 1 (MathsCasts) | This screencast compares the graph of a rational function four possible functions and discusses which rational function has produced the graph. | 6/25/2012 | Free | View In iTunes |

244 | VideoMultiplication and division of complex numbers in polar form (MathsCasts) | The general formulae for multiplication and division of complex numbers in polar form are given and their use is then demonstrated in relation to a particular example | 6/22/2012 | Free | View In iTunes |

245 | VideoMultiplying by variables in an inequality (MathsCasts) | This recording shows that it is possible to multiply by an expression containing a variable in an inequality - as long as one keeps track of when the expression is positive or negative. | 6/21/2012 | Free | View In iTunes |

246 | VideoThe factorial function (MathsCasts) | Defines the factorial function and shows examples where it is used: e.g. in the MacLaurin series for exp(x), for cos(x), but also in nCr (n choose r). It concludes with a proof that 0!=1, using the Gamma function. | 6/20/2012 | Free | View In iTunes |

247 | VideoSolving Quadratic Equations - Part 2 (MathsCasts) | Example of how to use the Guide Number method to solve a quadratic equation | 6/19/2012 | Free | View In iTunes |

248 | VideoSolving Quadratic Equations - Part 1 (MathsCasts) | Example of how to use the Guide Number method to solve a quadratic equation | 6/18/2012 | Free | View In iTunes |

249 | VideoConverting a line from Cartesian to vector form (MathsCasts) | Starts with an introduction to the equation of a straight line in 3D in both Cartesian and vector form. An example is then given of converting the Cartesian equations of a straight line into its scalar parametric equations and hence its vector equation. | 6/15/2012 | Free | View In iTunes |

250 | VideoDefined matrix operations (MathsCasts) | A discussion of when matrix addition, subtraction and multiplication are defined, and when it is possible to calculate matrix determinants and inverses, based on the order of the matrices concerned. | 6/14/2012 | Free | View In iTunes |

251 | VideoA Fourier series integral (MathsCasts) | We examine the integration involved in calculating some Fourier coefficients and discuss the approach to be taken when one has a formula sheet in comparison with having to calculate the integral on paper. | 6/13/2012 | Free | View In iTunes |

252 | VideoGeometric Series 2 (MathsCasts) | We introduce geometric series in which the variable is a quantity other than x or the constant is not 1. Convergence is discussed and we show how to get a series that converges when the absolute value of x is greater than 1 or some other number. | 6/12/2012 | Free | View In iTunes |

253 | VideoGeometric series: Part 1 (MathsCasts) | We introduce the basic geometric series in powers of x, investigate the partial sums and demonstrate that the series sums to 1/(1-x) for x between -1 and 1. | 6/8/2012 | Free | View In iTunes |

254 | VideoFactorising quadratic equations: Part 4 (MathsCasts) | Examples of how to factorise quadratics using the Guide Number method. | 6/7/2012 | Free | View In iTunes |

255 | VideoFactorising quadratic equations: Part 3 (MathsCasts) | Examples of how to factorise Quadratics using the Guide Number method. | 6/5/2012 | Free | View In iTunes |

256 | VideoFactorising Quadratic Equations - Part 2 (MathsCasts) | Examples of how to factorise Quadratics using the Guide Number method. | 6/4/2012 | Free | View In iTunes |

257 | VideoFactorising quadratic equations: Part 1 (MathsCasts) | Examples of how to factorise Quadratics using the Guide Number method. | 6/1/2012 | Free | View In iTunes |

258 | VideoFactorising quadratic equations: introduction (MathsCasts) | Introduction to what quadratic equations are and where they are used. Explanation of the Guide Number method for factorising these equations. | 5/31/2012 | Free | View In iTunes |

259 | VideoFactorising Basic Expressions Part 2 (MathsCasts) | Examples of factorising simple expressions that have one or two common factors | 5/29/2012 | Free | View In iTunes |

260 | VideoFactorising Basic Expressions Part 1 (MathsCasts) | Basic explanation of what factorising is, why it is used, and a couple of simple examples. | 5/28/2012 | Free | View In iTunes |

261 | VideoDivision of fractions: Part 2 (MathsCasts) | Examples of how to divide one fraction into another. | 5/25/2012 | Free | View In iTunes |

262 | VideoDivision of fractions: Part 1 (MathsCasts) | Introduction to division of fractions and examples of real life applications of division of fractions. | 5/24/2012 | Free | View In iTunes |

263 | VideoMultiplication of Fractions - Part 2 (MathsCasts) | Examples of the multiplication of basic fractions. | 5/22/2012 | Free | View In iTunes |

264 | VideoMultiplication of fractions: Part 1 (MathsCasts) | Examples of the multiplication of basic fractions and a brief introduction to the method used as well as some real life examples. | 5/21/2012 | Free | View In iTunes |

265 | VideoExpressing one number as a percentage of another (MathsCasts) | Outlines, using examples, the method for expressing one number as a percentage of another number. | 5/17/2012 | Free | View In iTunes |

266 | VideoPercentage word problem: Part 3 (MathsCasts) | Example of a word problem involving percentages - how to interpret it and apply algorithms to solve it. | 5/16/2012 | Free | View In iTunes |

267 | VideoConverting Percentages to Fractions and Decimals (Mathscasts) | Examples of the methods used for converting Percentages to Fractions and Decimals | 5/15/2012 | Free | View In iTunes |

268 | VideoConverting Decimals to Fractions and Percentages (Mathscasts) | Examples of the methods used for converting various decimals to fractions and percentages | 5/14/2012 | Free | View In iTunes |

269 | VideoPercentage word problem: Part 2 (MathsCasts) | Example of a word problem involving percentages - how to interpret it and apply algorithms to solve it. | 5/9/2012 | Free | View In iTunes |

270 | VideoConverting Fractions to Decimals and Percentages (Mathscasts) | Examples of the methods used for converting various fractions to Decimals and Percentages. | 5/7/2012 | Free | View In iTunes |

271 | VideoPercentage word problem: Part 1 (MathsCasts) | Example of a word problem involving percentages - how to interpret it and apply algorithms to solve it. | 5/4/2012 | Free | View In iTunes |

272 | VideoPartial differentiation using the quotient rule (MathsCasts) | The quotient rule is reviewed and then demonstrated for an example involving calculation of partial derivatives. | 5/3/2012 | Free | View In iTunes |

273 | VideoIntroduction to sequences (MathsCasts) | Introduces the concept of finite and infinite sequences with examples and demonstrates examples of using notation to define sequences. | 5/2/2012 | Free | View In iTunes |

274 | VideoParallel planes (MathsCasts) | Explains how the equations of two parallel planes are related - then solves a problem where a plane parallel to a given plane, passing through a point, is to be found. | 4/27/2012 | Free | View In iTunes |

275 | VideoRoots of a complex number: Part 1 (MathsCasts) | Deduces de formula for finding the roots of a complex number using as an example the cube roots of unity | 4/19/2012 | Free | View In iTunes |

276 | VideoExponential form: Part 2 (MathsCasts) | Covers the multiplication and division of complex numbers given in exponential and their equivalent formulas in polar form (deduced from the exponential ones) as an introduction to the deduction of De Moivre's Formula and its use to find complex roots. | 4/18/2012 | Free | View In iTunes |

277 | VideoExponential form: Part 1 (MathsCasts) | Introduces the exponential form of a complex number with a brief mention to power series so students can understand the importance of the angle being in radians. | 4/13/2012 | Free | View In iTunes |

278 | VideoFraction word problem (MathsCasts) | Example of a word problem involving fractions - how to interpret it and apply algorithms to solve it. | 4/12/2012 | Free | View In iTunes |

279 | VideoCartesian to polar form: Part 3 (MathsCasts) | Example of getting the polar form of a complex number if the cartesian form is known(number placed in the fourth quadrant). | 4/11/2012 | Free | View In iTunes |

280 | VideoAbsolute value: Less than (Part 3) (MathsCasts) | Part 3: Shows how to solve absolute value inequalities, example abs(2x-1)5 | 4/4/2012 | Free | View In iTunes |

281 | VideoAbsolute value: Greater than (Part 2) (MathsCasts) | Part 2: Shows how to solve absolute value inequalities, example abs(1-2x)>-3 | 3/29/2012 | Free | View In iTunes |

282 | VideoAbsolute value: Introduction (Part 1) (MathsCasts) | Part 1: Explains how to solve simple equalities/inequalities of the type abs(x)=constant, abs(x) constant. | 3/28/2012 | Free | View In iTunes |

283 | VideoCartesian to polar form: Part 1 (MathsCasts) | This video reviews the variables involved in both forms of a complex numbers and deduces how to get the modulus and the angle when given a complex number in Cartesian form. | 3/23/2012 | Free | View In iTunes |

284 | VideoPolynomial division (MathsCasts) | Explains how to rewrite a cubic polynomial as the product of a linear term and a quadratic, by dividing the cubic by the linear term. | 3/22/2012 | Free | View In iTunes |

285 | VideoComplex regions (MathsCasts) | This recording looks at how to identify the nature of the region in the complex plane that satisfies |z-z0|=r. This is then illustrated further with a specific example. | 3/21/2012 | Free | View In iTunes |

286 | VideoAdding fractions: Part 2 (MathsCasts) | Adding basic fractions by finding a common denominator. | 3/15/2012 | Free | View In iTunes |

287 | VideoAdding fractions: Part 1 (MathsCasts) | Adding basic fractions by finding a common denominator. | 3/14/2012 | Free | View In iTunes |

288 | VideoAdding fractions: introduction (MathsCasts) | Simple example of how to add basic fractions by finding a common denominator. Real life example: the number of quarters played over the course of 4 games by Lebron James (Basketball). | 3/13/2012 | Free | View In iTunes |

289 | VideoRoots of a complex number: introduction (MathsCasts) | Introduction - motivation to finding the roots of acomplex number. Also explains how to plot complex numbers known modulus and angle and covers when two complex numbers are equal. | 3/8/2012 | Free | View In iTunes |

290 | VideoFrom polar form to Cartesian form (MathsCasts) | Example of getting the Cartesian form of a complex number if the polar form is known. | 3/7/2012 | Free | View In iTunes |

291 | VideoProjectiles: velocity and position (MathsCasts) | This screencast gives an example of a projectile in 2D space where gravity is the only force acting. Vector methods are hence used to find the velocity and position vector of the projectile, given that its initial velocity and position are known. | 3/6/2012 | Free | View In iTunes |

292 | VideoSolving equations of form (det(A-lambda_I)=0) (MathsCasts) | An example is given of solving an equation of the form det(A-lambda*I)=0, where in this case A is a 2x2 matrix, I is the unit matrix and lambda is the scalar that we solve for | 3/5/2012 | Free | View In iTunes |

293 | VideoThe Argand diagram (MathsCasts) | Covers the grahical representation of a complex number in the Argand diagram including a couple of examples. | 3/1/2012 | Free | View In iTunes |

294 | VideoComplex polar form (MathsCasts) | General explanation is given of how a complex number in Cartesian form can be converted to polar form z=rcis(@) and then 3 examples are given to illustrate this | 2/28/2012 | Free | View In iTunes |

295 | VideoComplex Exponential to Cartesian Form (Mathscasts) | Three examples are given to demonstrate how to convert complex numbers written in exponential polar form into Cartesian form. | 2/27/2012 | Free | View In iTunes |

296 | VideoComplex Cube Roots (Mathscasts) | An example of finding the cube roots of a complex number by first converting the number from Cartesian to polar form, then hence using De Moivre's Theorem to find the roots in polar form, and then converting the roots into Cartesian form | 2/24/2012 | Free | View In iTunes |

297 | VideoComplex numbers division (MathsCasts) | The general principle is explained of how to divide one complex number by another when both numbers are written in Cartesian form, so that the denominator of the final answer is a real number. A specific example of using this process is then given. | 2/22/2012 | Free | View In iTunes |

298 | VideoTrigonometric ratios in all quadrants Part 2 (MathsCasts) | Explains how to deal with the trig ratios of angles above 90. By using the unit circle the sign of the trig ratios in all quadrants are obtained. Second part | 2/21/2012 | Free | View In iTunes |

299 | VideoTrigonometric ratios in all quadrants Part 1 (Mathscasts) | Explains how to deal with the trig ratios of angles above 90. By using the unit circle the sign of the trig ratios in all quadrants are obtained. | 2/20/2012 | Free | View In iTunes |

300 | VideoTrigonometric Ratios 2 (MathsCasts) | Example of the solution of right-angled triangles using trigonometric ratios. | 2/16/2012 | Free | View In iTunes |

301 | VideoTrigonometric Ratios 1 (Mathscasts) | Define the main trigonometric ratios: sine, cosine and tangent | 2/15/2012 | Free | View In iTunes |

301 Items |

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