# MathsCasts II

## By Swinburne University of Technology

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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 | ||
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1 | CleanVideoIntroduction to half range (even or odd expansion) Fourier series (MathsCasts) | Demonstrates that symmetry of functions helps us to shorten the calculation of the integrals needed for the Fourier coeffici… | 7 3 2017 | Free | View in iTunes |

2 | CleanVideoHow do odd or even functions make calculation of Fourier series simpler? (MathsCasts) | Demonstrates that symmetry of functions helps us to shorten the calculation of the integrals needed for the Fourier coeffici… | 7 3 2017 | Free | View in iTunes |

3 | CleanVideoCalculating a Fourier series (MathsCasts) | Deals with the details of calculating Fourier series coefficients for a function. | 7 3 2017 | Free | View in iTunes |

4 | CleanVideoWhy are circles, ellipses, parabolas and hyperbolas called 'conic sections'? Part 2 (MathsCasts) | We solve simultaneously the equations of a plane and a cone and show that the intersections are circles, parabolas, ellipses… | 7 3 2017 | Free | View in iTunes |

5 | CleanVideoSketching polynomial graphs without calculus - Part 1 (MathsCasts) | Sketch of y = 2(x-1)^2-3. | 6 3 2017 | Free | View in iTunes |

6 | CleanVideoWhat is a Laplace transform and why do you need to study it? (MathsCasts) | Brief introduction to why we use Laplace transforms, with mention of tables. | 6 3 2017 | Free | View in iTunes |

7 | CleanVideoThe first shift theorem (MathsCasts) | Brief and simple introduction to the first shift theorem for Laplace transforms. | 6 3 2017 | Free | View in iTunes |

8 | CleanVideoLaplace transforms and inverse Laplace transforms to solve a differential equation (MathsCasts) | Detailed discussion of using Laplace transform to solve a 1st order ODE. | 6 3 2017 | Free | View in iTunes |

9 | CleanVideoTracing an error in a 2nd order DE solution (MathsCasts) | We solve a non-homogeneous 2nd order constant coefficient ODE with boundary conditions using the Laplace transform method. A… | 6 3 2017 | Free | View in iTunes |

10 | CleanVideoSketching polynomial graphs without calculus - Part 5 (MathsCasts) | Sketch of y = 2(x+2)(x-2)(x+3). | 6 3 2017 | Free | View in iTunes |

11 | CleanVideoExample of solving a differential equation using Laplace transforms (MathsCasts) | Demonstration of using Laplace transform to solve a 2nd order, linear, non-homogeneous, constant coefficient DE with boundar… | 6 3 2017 | Free | View in iTunes |

12 | CleanVideoExample of solving a set of simultaneous linear 1st order ODE's with Laplace transforms (MathsCasts) | Standard pair of linear, coupled 1st order DE's solved by Laplace transform method. | 6 3 2017 | Free | View in iTunes |

13 | CleanVideoDifferentiation using the inverse function rule (MathsCasts) | In this recording we look at an example of differentiation using the inverse function rule. | 6 3 2017 | Free | View in iTunes |

14 | CleanVideoSketching polynomial graphs without calculus - Part 4 (MathsCasts) | Sketch of y =(x+1)^3-2. | 6 3 2017 | Free | View in iTunes |

15 | CleanVideoThe quotient rule from 1st principles (MathsCasts) | The quotient rule for differentiation is proved from first principles. | 5 3 2017 | Free | View in iTunes |

16 | CleanVideoHow do odd or even functions make calculation of Fourier series simpler? (MathsCasts) | Demonstrates that symmetry of functions helps us to shorten the calculation of the integrals needed for the Fourier coeffici… | 5 3 2017 | Free | View in iTunes |

17 | CleanVideoIntroduction to bonus results from Fourier series (MathsCasts) | Simple demonstration of how to obtain a series to evaluate approximations to pi, using a specific and quite simple Fourier s… | 5 3 2017 | Free | View in iTunes |

18 | CleanVideoIntegration of sin(ax) cos(bx) and similar by an alternative method (MathsCasts) | The integral of sin(ax) sin(bx) is performed using integration by parts. | 5 3 2017 | Free | View in iTunes |

19 | CleanVideoThe product rule from 1st principles (MathsCasts) | The product rule for differentiation is proved from first principles. | 5 3 2017 | Free | View in iTunes |

20 | CleanVideoThe chain rule from 1st principles (MathsCasts) | The chain rule for differentiation is proved from first principles. Use is made of the small difference formula, which is di… | 5 3 2017 | Free | View in iTunes |

21 | CleanVideoA further example of integration by parts using the tabular scheme (MathsCasts) | Integration by parts is used to integrate the product of two polynomials. | 5 3 2017 | Free | View in iTunes |

22 | CleanVideoThe chain rule: a pragmatic approach (MathsCasts) | It is demonstrated how to perform differentiation using the chain rule, side-stepping the use of new function names such as … | 2 3 2017 | Free | View in iTunes |

23 | CleanVideoThe Laplace transform of the rectified sine wave function (MathsCasts) | We find the Laplace transform of a triangle wave as an example of a periodic function. | 2 3 2017 | Free | View in iTunes |

24 | CleanVideoThe Laplace transform of the triangle wave (MathsCasts) | We find the Laplace transform of a triangle wave as an example of a periodic function. | 2 3 2017 | Free | View in iTunes |

25 | CleanVideoIntegral of exponential of negative x squared as an exercise in double integration (MathsCasts) | The integral of exp(-x^2) from 0 to infinity is evaluated using a double integral technique. | 2 3 2017 | Free | View in iTunes |

26 | CleanVideoDifferentiating integrals (MathsCasts) | We discuss the details involved in differentiating an integral, examine the notation used and outline the proof that the res… | 2 3 2017 | Free | View in iTunes |

27 | CleanVideoSecond example of 2nd order ODE with boundary conditions, solved by Laplace transform (MathsCasts) | Laplace transform is used to solve a second example of a 2nd order, constant coefficient ODE with boundary conditions. | 2 3 2017 | Free | View in iTunes |

28 | CleanVideoThe Laplace transform of e^(-t^2) (MathsCasts) | We calculate explicitly the Laplace transform of e^(-t^2) and demonstrate the need for the error function erf(s/2). | 1 3 2017 | Free | View in iTunes |

29 | CleanVideoDivision of complex numbers using 2 by 2 matrices (MathsCasts) | We exploit the analogy between complex numbers and 2 by 2 matrices to perform complex number reciprocals and division. | 1 3 2017 | Free | View in iTunes |

30 | CleanVideoIntegrating sec(x) (MathsCasts) | We show how to antidifferentiate sec(x) and hence gain insight also how to antidifferentiate cosec(x). | 1 3 2017 | Free | View in iTunes |

31 | CleanVideoAn unusual approach to the differentiation of x to the power of x (MathsCasts) | We revise the method of logarithmic diferentiation applied to the function y = x^x then view the result in an unconventional… | 1 3 2017 | Free | View in iTunes |

32 | CleanVideoIntegrating rational functions - Part 6 (MathsCasts) | In this recording, we look at the process of integrating rational functions of the form a divided by (bx+c)^m. | 28 2 2017 | Free | View in iTunes |

33 | CleanVideoIntegrating rational functions - Part 7 (MathsCasts) | In this recording we look at integrating proper rational functions. | 28 2 2017 | Free | View in iTunes |

34 | CleanVideoIntegrating rational functions - Part 4 (MathsCasts) | In this recording, we look at integrating rational functions where both the numerator and the denominator are linear functions. | 28 2 2017 | Free | View in iTunes |

35 | CleanVideoIntegrating rational functions - Part 8 (MathsCasts) | Demonstrates integrating an improper rational function, where first long division must be used to rewrite it as a polynomial… | 28 2 2017 | Free | View in iTunes |

36 | CleanVideoMultiplication of binary numbers (MathsCasts) | For a specific example, this recording demonstrates the process involved in multiplying two binary numbers using long mutlip… | 28 2 2017 | Free | View in iTunes |

37 | CleanVideoCalculating j to the power of j (MathsCasts) | We then also see that there are an infinite number of values for j to the power of j. | 28 2 2017 | Free | View in iTunes |

38 | CleanVideoIntegrating rational functions - Part 3 (MathsCasts) | This recording demonstrates how to integrate rational functions where the denominator is a quadratic function and the numera… | 27 2 2017 | Free | View in iTunes |

39 | CleanVideoSquare roots of a 2 by 2 matrix (MathsCasts) | We use the Cayley-Hamilton method to find all four square roots of a given 2 by 2 matrix. | 27 2 2017 | Free | View in iTunes |

40 | CleanVideoPowers of a 2 by 2 matrix (MathsCasts) | We show how the Cayley-Hamilton theorem can be used to give an expression for any power of a 2 by 2 matrix. The method is us… | 27 2 2017 | Free | View in iTunes |

41 | CleanVideoMore on linear (in)dependence (MathsCasts) | We investigate linear independence for a set of three vectors in four dimensions and demonstrate how to decide on their (in)… | 27 2 2017 | Free | View in iTunes |

42 | CleanVideoSolving equations involving radicals (MathsCasts) | This recording demonstrates the general method for solving an equation of form sqrt(ax^2+bx+c) = cx+d and then illustrates this with an example, including checking solutions that were generated by squaring both sides to see which ones satisfy the original equation. | 27 2 2017 | Free | View in iTunes |

43 | CleanVideoNewton-Raphson method: introduction (MathsCasts) | An introduction to the Newton-Raphson method for finding a numerical solution of f(x) = 0, explaining what the method is (in… | 17 5 2016 | Free | View in iTunes |

44 | CleanVideoExample of Newton-Raphson method (MathsCasts) | A demonstration of how to use the Newton-Raphson method: to find the positive solution of the equation x^2 = 2 | 17 5 2016 | Free | View in iTunes |

45 | CleanVideoVolumes of solids of revolution - example 2 (MathsCasts) | An example of using integration and the 'disk method' to find the volume of a 3D solid that is obtained when the region boun… | 17 5 2016 | Free | View in iTunes |

46 | CleanVideoIntegration by substitution example (MathsCasts) | An example of using integration by substitution to integrate the function (sqrt(1+sqrtx)) | 17 5 2016 | Free | View in iTunes |

47 | CleanVideoArea between two curves (MathsCasts) | An example of using integration to find the area of a region that is bounded by 2 curves | 17 5 2016 | Free | View in iTunes |

48 | CleanVideoVolumes of solids of revolution - example 1 (MathsCasts) | An example of using integration and the 'disk method' to find the volume of a 3D solid that is obtained when the region betw… | 17 5 2016 | Free | View in iTunes |

49 | CleanVideoIntegrals with even power of secx and any power of tan x (MathsCasts) | An example of integrating a function that is a product of an even power of sec x and a power of tanx | 17 5 2016 | Free | View in iTunes |

50 | CleanVideoIntegrals with odd power of tanx and any power of secx (MathsCasts) | An example of integrating a function that is a product of an odd power of tan x and a power of secx | 17 5 2016 | Free | View in iTunes |

51 | CleanVideoIntegrating cos^2 x and sin^2 x (MathsCasts) | An example of how double-angle formulae can be used to help with integrating sin^2 x and cos^2 x | 17 5 2016 | Free | View in iTunes |

52 | CleanVideoIntegrals with even powers of sinx and cosx- example 1 (MathsCasts) | Demonstrates an example of integrating a function that is a product of even powers of sinx and cos x, with assistance from d… | 17 5 2016 | Free | View in iTunes |

53 | CleanVideoIntegrals with even powers of sinx and cosx- example 2 (MathsCasts) | A more difficult example of integrating a function that is a product of even powers of sin x or cos x | 17 5 2016 | Free | View in iTunes |

54 | CleanVideoIntegrals involving odd powers of sinx or cos x: example 2 (MathsCasts) | A more difficult example of integrating a function that is a product of odd powers of sin x or cos x | 17 5 2016 | Free | View in iTunes |

55 | CleanVideoIntegrals involving odd powers of sinhx or coshx (MathsCasts) | An example of integrating a function that is a product of odd powers of sinh x or cosh x | 17 5 2016 | Free | View in iTunes |

56 | CleanVideoA scheme to make integration by parts easier - part 2 (MathsCasts) | The scheme already discussed for writing down the reults from integration by parts is applied to cyclic integration by parts… | 17 5 2016 | Free | View in iTunes |

57 | CleanVideoIntegration by parts scheme - supplement (MathsCasts) | We use the integration by parts scheme to address integrals with powers of x multiplied by ln(x) | 17 5 2016 | Free | View in iTunes |

58 | CleanVideoIntegrals involving odd powers of sinx or cos x: example 1 (MathsCasts) | An example of integrating a function that is a product of odd powers of sin x and cos x | 17 5 2016 | Free | View in iTunes |

59 | CleanVideoFinding the number of intersection points of two quadratics using the discriminant (MathsCasts) | For a quadratic equation of the form ax^2+bx+c=0, the discriminant function b^2-4ac is introduced, as a way of determining h… | 17 5 2016 | Free | View in iTunes |

60 | CleanVideoImplicit differentiation where the chain rule is required (MathsCasts) | Introduces how to use implicit differentiation to find dy/dx for an example where the chain rule is also required | 17 5 2016 | Free | View in iTunes |

61 | CleanVideoCalculating a second-order derivative where implicit differentiation is required (MathsCasts) | Gives an example of calculating the first and second derivatives of a function where implicit differentiation is required | 17 5 2016 | Free | View in iTunes |

62 | CleanVideoSolving an equation of the form ax^4+bx^2+c=0 (MathsCasts) | Shows how to solve an equation of the form ax^4+bx^2+c=0 by first making the substitution u = x^2 so that the associated qua… | 17 5 2016 | Free | View in iTunes |

63 | CleanVideoImplicit differentiation where the product rule is required (MathsCasts) | Introduces how to use implicit differentiation to find dy/dx for an example where the use of the product rule is also required | 17 5 2016 | Free | View in iTunes |

64 | CleanVideoImplicit differentiation where the quotient rule is required (MathsCasts) | Introduces how to use implicit differentiation to find dy/dx for an example where the use of the quotient rule is also required | 17 5 2016 | Free | View in iTunes |

65 | CleanVideoImplicit differentiation example (MathsCasts) | Introduces how to use implicit differentiation to find dy/dx for an example | 17 5 2016 | Free | View in iTunes |

66 | CleanVideoThe rule for differentiation of an inverse function (MathsCasts) | We investigate the rule for differentiating an inverse function then make some observations about reciprocals of 1st and 2nd… | 17 5 2016 | Free | View in iTunes |

67 | CleanVideoUsing complex exponentials to integrate exponential times cos or sin function (MathsCasts) | We use the complex exponential to integrate e^(ax) times cos(bx) or sin(bx) as real and imaginary parts of the same integral… | 17 5 2016 | Free | View in iTunes |

68 | CleanVideoComposite hyperbolic functions involving an inverse function- example 2 (MathsCasts) | In this recording we look at a second example of how to write a composite hyperbolic function as an algebraic function of x. | 17 5 2016 | Free | View in iTunes |

69 | CleanVideoDifferentiation by first principles example- the square root of x (MathsCasts) | Example of using differentiation by first principles to evaluate the derivative of the function y = square root of x | 17 5 2016 | Free | View in iTunes |

70 | CleanVideoDifferentiation by first principles example - Quadratic function (MathsCasts) | Example of using differentiation by first principles to evaluate the derivative of a quadratic function. | 17 5 2016 | Free | View in iTunes |

71 | CleanVideoDifferentiation by first principles example- 1 divided by x (MathsCasts) | Example of using differention by first principles to evaluate the derivative of the function y = 1 divided by x | 17 5 2016 | Free | View in iTunes |

72 | CleanVideoThe Laplace transform of a periodic function (MathsCasts) | We demonstrate how periodicity of a function affects the Laplace transform | 17 5 2016 | Free | View in iTunes |

73 | CleanVideoDifferentiation by first principles- introduction (MathsCasts) | Background to the method of differentiation by first principles | 17 5 2016 | Free | View in iTunes |

74 | CleanVideoTrigonometric integrals in the complex plane - part 5 (MathsCasts) | We attempt to evaluate an integral that is not well-defined and investigate how this problem manifests itself in the complex… | 17 5 2016 | Free | View in iTunes |

75 | CleanVideoProof of sum and difference formulae for sin and cos using Euler's formulae (MathsCasts) | We prove the formulae for sin(A+B) and cos(A+B) using Euler's results for sine and cos. The other sum and difference formula… | 17 5 2016 | Free | View in iTunes |

76 | CleanVideoTrigonometric integrals in the complex plane - part 3 (MathsCasts) | We evaluate another integral similar to that in parts 1 and 2 but containing a sine rather than a cosine. Here we prepare th… | 17 5 2016 | Free | View in iTunes |

77 | CleanVideoTrigonometric integrals in the complex plane - part 4 (MathsCasts) | We complete the integration introduced in part 3, using Cauchy's residue theorem. | 17 5 2016 | Free | View in iTunes |

78 | CleanVideoTrigonometric integrals in the complex plane - part 1 (MathsCasts) | We prepare integral from 0 to 2 Pi of 1/(2+cos(theta)) for integration in the complex plane. | 17 5 2016 | Free | View in iTunes |

79 | CleanVideoTrigonometric integrals in the complex plane - part 2 (MathsCasts) | We complete the integration introduced in part 1, using Cauchy's residue theorem. | 17 5 2016 | Free | View in iTunes |

80 | CleanVideoDirectional derivative using the grad operator (MathsCasts) | We write the directional derivative on a surface z=z(x,y) in terms of the grad operator acting on z as a dot product with a … | 17 5 2016 | Free | View in iTunes |

81 | CleanVideoMultivariate chain rule example (MathsCasts) | Example of using the multivariate chain rule where in this case z=f(x,t) and x is a function of t. In this example the expr… | 17 5 2016 | Free | View in iTunes |

82 | CleanVideoA scheme to make integration by parts easier - Part 1 (MathsCasts) | Integration by parts using the formula is briefly revisited, then we look at how to code use of the formula into a visual pr… | 27 5 2014 | Free | View in iTunes |

83 | CleanVideoLaplace 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… | 1 4 2014 | Free | View in iTunes |

84 | CleanVideoProof 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. | 1 4 2014 | Free | View in iTunes |

85 | CleanVideoThe 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 sugges… | 1 4 2014 | Free | View in iTunes |

86 | CleanVideoDifferentiation 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 o… | 31 3 2014 | Free | View in iTunes |

87 | CleanVideoDifferentiation 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 o… | 31 3 2014 | Free | View in iTunes |

88 | CleanVideoDifferentiation 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. | 31 3 2014 | Free | View in iTunes |

89 | CleanVideoDifferentiation 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… | 31 3 2014 | Free | View in iTunes |

90 | CleanVideoExponential 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. | 24 3 2014 | Free | View in iTunes |

91 | CleanVideoProof of Parseval's theorem (MathsCasts) | A proof of Parseval's theorem for trigonometric Fourier series is outlined. | 24 3 2014 | Free | View in iTunes |

92 | CleanVideoDifferentation 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 exam… | 22 3 2014 | Free | View in iTunes |

93 | CleanVideoMatrix 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 summati… | 22 3 2014 | Free | View in iTunes |

94 | CleanVideoThe complex Fourier series of e^t (MathsCasts) | The complex Fourier coefficients are calculated for the function e^t with period 2 pi. | 22 3 2014 | Free | View in iTunes |

95 | CleanVideoBonus 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. | 18 3 2014 | Free | View in iTunes |

96 | CleanVideoIntegration 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. | 17 3 2014 | Free | View in iTunes |

97 | CleanVideoBonus 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. | 17 3 2014 | Free | View in iTunes |

98 | CleanVideoBonus 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 numb… | 16 3 2014 | Free | View in iTunes |

99 | CleanVideoExample 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. | 12 3 2014 | Free | View in iTunes |

100 | CleanVideoSome 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. | 12 3 2014 | Free | View in iTunes |

101 | CleanVideoAdjusting 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 co… | 11 3 2014 | Free | View in iTunes |

102 | CleanVideoWhy 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 ob… | 18 1 2014 | Free | View in iTunes |

103 | CleanVideoWhy 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… | 17 1 2014 | Free | View in iTunes |

104 | CleanVideoThe vector triple product (MathsCasts) | Simplification of a vector triple product. | 16 1 2014 | Free | View in iTunes |

105 | CleanVideoThe 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 f… | 15 1 2014 | Free | View in iTunes |

106 | CleanVideoThe 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 eac… | 14 1 2014 | Free | View in iTunes |

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

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

109 | CleanVideoThe 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. | 11 1 2014 | Free | View in iTunes |

110 | CleanVideoThe 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… | 10 1 2014 | Free | View in iTunes |

111 | CleanVideoThe Laplace transform of ln(t) (MathsCasts) | Investigates the Laplace transform of the log function. | 9 1 2014 | Free | View in iTunes |

112 | CleanVideoIrrotational 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 al… | 8 1 2014 | Free | View in iTunes |

113 | CleanVideoIrrotational 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 t… | 7 1 2014 | Free | View in iTunes |

114 | CleanVideoIrrotational 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 spec… | 6 1 2014 | Free | View in iTunes |

115 | CleanVideoIntroduction 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. | 5 1 2014 | Free | View in iTunes |

116 | CleanVideoClosed 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 | 4 1 2014 | Free | View in iTunes |

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

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

119 | CleanVideoA 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 |

120 | CleanVideoVectors: Perpendicular Unit Vectors (MathsCasts) | Defines the perpendicular unit vectors i and j. | 23 12 2013 | Free | View in iTunes |

121 | CleanVideoWhat is a Vector (MathsCasts) | Introduces definition of a vector and states some simple examples of vectors. Explains difference between vector and scalar … | 23 12 2013 | Free | View in iTunes |

122 | CleanVideoVectors: 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 … | 23 12 2013 | Free | View in iTunes |

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

124 | CleanVideoVectors: 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 g… | 21 12 2013 | Free | View in iTunes |

125 | CleanVideoVectors: Adding One Dimensional Vectors (MathsCasts) | Simple example showing how to add one dimensional vectors. | 20 12 2013 | Free | View in iTunes |

126 | CleanVideoTwo 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 … | 19 12 2013 | Free | View in iTunes |

127 | CleanVideoThree Dimensional Vector (MathsCasts) | Representing a three dimensional vector in three dimensional space using the x,y and z axes. writing a three dimensional vec… | 17 12 2013 | Free | View in iTunes |

128 | CleanVideoThe 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 produc… | 16 12 2013 | Free | View in iTunes |

129 | CleanVideoThe 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. | 15 12 2013 | Free | View in iTunes |

130 | CleanVideoThe Dot Product (Geometry Proof) (MathsCasts) | Geometric proof of the dot product using Cosine rule. | 14 12 2013 | Free | View in iTunes |

131 | CleanVideoThe 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 … | 13 12 2013 | Free | View in iTunes |

132 | CleanVideoThe 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 ha… | 12 12 2013 | Free | View in iTunes |

133 | CleanVideoThe Angle Between Two Vectors (Part 2) (MathsCasts) | Worked example of finding the angle between two 3D vectors | 11 12 2013 | Free | View in iTunes |

134 | CleanVideoThe 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 t… | 10 12 2013 | Free | View in iTunes |

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

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

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

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

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

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

141 | CleanVideoSequences and Series: Interval of Convergence (MathsCasts) | Introduces the power series, the radius of convergence, and hence the interval of convergence before calculating the interva… | 1 12 2013 | Free | View in iTunes |

142 | CleanVideoSequences and Series: Factorials (MathsCasts) | Introduces the concept of factorials and how to simplify factorial expressions. | 30 11 2013 | Free | View in iTunes |

143 | CleanVideoSequences and Series: Definiton (MathsCasts) | Definition of a sequence and definition of a series. Introduces the concept of the convergence or divergence of a series usi… | 29 11 2013 | Free | View in iTunes |

144 | CleanVideoSequences and Series: Alternating Series Test (MathsCasts) | Introduces the concept of an alternating series and the Alternating Series test before utilizing this method to determine th… | 28 11 2013 | Free | View in iTunes |

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

146 | CleanVideoQuadratic Inequalities (Example 2) (MathsCasts) | Worked example of solving an inequality statement with a denominator . Explanation of why multiply both sides of inequality … | 26 11 2013 | Free | View in iTunes |

147 | CleanVideoProperties of the Dot Product of Vectors (Part 2) (MathsCasts) | Verifies distributive property of the dot product | 25 11 2013 | Free | View in iTunes |

148 | CleanVideoProperties 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 vect… | 24 11 2013 | Free | View in iTunes |

149 | CleanVideoProof: The vector ab is equal to the vector b minus the vector a (MathsCasts) | Proof of vector ab = vector b minus vector a explained | 23 11 2013 | Free | View in iTunes |

150 | CleanVideoPower 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 | 22 11 2013 | Free | View in iTunes |

151 | CleanVideoNewton's Method (MathsCasts) | Introduces Newton' Method and explains the procedure for finding a root | 21 11 2013 | Free | View in iTunes |

152 | CleanVideoNegative 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 whi… | 20 11 2013 | Free | View in iTunes |

153 | CleanVideoMultiplying a Vector by a Scalar (MathsCasts) | Simple examples showing the geometric and algebraic effect on magnitude and direction of vectors when multiplying vectors by… | 19 11 2013 | Free | View in iTunes |

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

155 | CleanVideoMaclaurin Series: Exponential Functions (MathsCasts) | Calculates the MacLaurin series for the exponential function. Also discusses the MacLaurin series for e^2x derived from the … | 17 11 2013 | Free | View in iTunes |

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

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

158 | CleanVideoComponents of a Vector (Part 1) (MathsCasts) | Explaination of how to resolve a vector into its horizontal and vertical components. | 13 11 2013 | Free | View in iTunes |

159 | CleanVideoCombined Inequalities (Introduction and Example 1) (MathsCasts) | Introduction to combined inequalities. Example of forming a combined inequality from a given word statement and worked examp… | 12 11 2013 | Free | View in iTunes |

160 | CleanVideoCombined Inequalities (Example 4) (MathsCasts) | Forming a combined inequality statement from a given word statement using symbols instead of the words 'or' or 'and' and sol… | 11 11 2013 | Free | View in iTunes |

161 | CleanVideoCombined Inequalities (Example 3) (MathsCasts) | Forming a combined inequality from a given word problem to estimate the distance between two homes, given the distance from … | 10 11 2013 | Free | View in iTunes |

162 | CleanVideoCombined Inequalities (Example 2) (MathsCasts) | Worked example of forming and solving a combined inequality statement from a given word statement. Term 'conjunction' explai… | 9 11 2013 | Free | View in iTunes |

163 | CleanVideoApplications 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. | 8 11 2013 | Free | View in iTunes |

164 | CleanVideoApplications 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. | 7 11 2013 | Free | View in iTunes |

165 | CleanVideoAlgebra: Multiplication of Letters and Numbers (MathsCasts) | Worked example explains how to multiply numbers and letters. Also explains the concepts of expressions, constants and coeffi… | 6 11 2013 | Free | View in iTunes |

166 | CleanVideoAdding 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 o… | 5 11 2013 | Free | View in iTunes |

167 | CleanVideoAbsolute 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 … | 4 11 2013 | Free | View in iTunes |

168 | CleanVideoAbsolute Value (Example 2 Inequality) (MathsCasts) | Worked example of solving an absolute value inequality statement and solutions checked. | 3 11 2013 | Free | View in iTunes |

169 | CleanVideoAbsolute Value (Definition and Example 1) (MathsCasts) | Definition of absolute value using simple examples. Worked example of solving an equation consisting of an absolute value sy… | 2 11 2013 | Free | View in iTunes |

170 | CleanVideoAbsolute Value (Example 4 Inequality) (MathsCasts) | Worked example of solving an inequality containing two absolute value symbols, solutions checked and graph of absolute value… | 1 11 2013 | Free | View in iTunes |

171 | CleanVideoPartial fractions: Multiplicity of a root (MathsCasts) | Explains the partial fraction expansion procedure when the denominator has repeated linear roots, and applies this technique… | 24 10 2013 | Free | View in iTunes |

172 | CleanVideoReciprocal Trigonometric Integrals (MathsCasts) | Discusses reciprocal trigonometric identities and investigates numerous examples, some of which involve reading the differen… | 24 10 2013 | Free | View in iTunes |

173 | CleanVideoPartial fractions: Mixed roots - Part 1 (MathsCasts) | Explains the partial fraction expansion procedure when the denominator has a mixture of linear roots and repeated linear roo… | 23 10 2013 | Free | View in iTunes |

174 | CleanVideoPartial fractions: Mixed roots - Part 2 (MathsCasts) | Uses the expansion from Part 1 to conduct the integration. Uses substitution in the resulting integrals. | 23 10 2013 | Free | View in iTunes |

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

176 | CleanVideoGraphing Linear Inequalities (MathsCasts) | Introduction to Linear Inequalities. Definitions. Simple Examples. | 20 10 2013 | Free | View in iTunes |

177 | CleanVideoPartial Fractions: Definition (MathsCasts) | Explains the concept of Partial Fractions. | 13 10 2013 | Free | View in iTunes |

178 | CleanVideoPartial fractions: Linear roots - Part 1 (MathsCasts) | Explains the partial fraction expansion procedure when the denominator has linear roots, and applies this technique to a sim… | 13 10 2013 | Free | View in iTunes |

179 | CleanVideoPartial 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 su… | 13 10 2013 | Free | View in iTunes |

180 | CleanVideoIterative reduction formula - Part 1 (Mathscasts) | Firstly discusses iterative functions and solutions while noting the usefulness of an Iterative Reduction Formula for multip… | 10 10 2013 | Free | View in iTunes |

181 | CleanVideoIterative reduction formula - Part 2 (Mathscasts) | Continues the previous simple indefinite example noting the construction of a base case. Then considers the corresponding de… | 10 10 2013 | Free | View in iTunes |

182 | CleanVideoCompleting 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 |

183 | CleanVideoWhy 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 … | 26 9 2013 | Free | View in iTunes |

184 | CleanVideoSimplifying 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 algeb… | 23 9 2013 | Free | View in iTunes |

185 | CleanVideoSolving 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 … | 23 9 2013 | Free | View in iTunes |

186 | CleanVideoThe Laplace transform of the error function erf(t) (MathsCasts) | We show how to calculate the Laplace transform of the error function erf(t) | 15 9 2013 | Free | View in iTunes |

187 | CleanVideoTransposition 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 i… | 9 9 2013 | Free | View in iTunes |

188 | CleanVideoInverse 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)… | 8 9 2013 | Free | View in iTunes |

189 | CleanVideoProperties of sin and cos - Part 1 (MathsCasts) | We prove that cos(-x) = cos(x) and sin(-x) = - sin(x|) | 5 9 2013 | Free | View in iTunes |

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

191 | CleanVideoWhat'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… | 4 9 2013 | Free | View in iTunes |

192 | CleanVideoPolitical 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. | 3 9 2013 | Free | View in iTunes |

193 | CleanVideoInverse 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)… | 2 9 2013 | Free | View in iTunes |

194 | CleanVideoLaplace 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'. | 2 9 2013 | Free | View in iTunes |

195 | CleanVideoIntegrating rational functions - Part 1 (MathsCasts) | This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is a l… | 28 8 2013 | Free | View in iTunes |

196 | CleanVideoIntegrating rational functions - Part 2 (MathsCasts) | This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is an … | 28 8 2013 | Free | View in iTunes |

197 | CleanVideoA 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 … | 27 8 2013 | Free | View in iTunes |

197 Items |

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