# Calculus III

## by Harrisburg Area Community College

To subscribe to an iTunes U course, click View in iTunes.

#### Course Description

This course covers vectors and vector-valued functions; partial differentiation; multiple integrals; space geometry; vector calculus.

This course requires a solid foundation in algebra and trigonometry and strong background in Calculus I and II - differentiation and integration. The prerequisite for the live Calculus III course is a minimum grade of C in Calculus II.

**You will NOT get any credit from taking this course in iTunes U though. You need to enroll as a regular student to receive credits. This course is offered year-round. Please visit this web site for more information. **

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1 | Desmos Graphing Calculator | Explore math with Desmos! Plot functions, create tables, add sliders, animate your graphs, and more -- all for free. At Desmos, we imagine a world of universal math literacy and envision a world where math is accessible and enjoyable for all students. We believe the key is learning by doing. To achieve this vision, we’ve started by building the next generation of the graphing calculator. Using our powerful and blazingly-fast math engine, the calculator can instantly plot any equation, from lines and parabolas up through derivatives and Fourier series. Sliders make it a breeze to demonstrate function transformations. It's intuitive, beautiful math. And best of all: it's completely free. Features: Graphing: Plot polar, cartesian, or parametric graphs. There’s no limit to how many expressions you can graph at one time - and you don’t even need to enter expressions in y= form! Sliders: Adjust values interactively to build intuition, or animate any parameter to visualize its effect on the graph. Try typing y=mx+b and adding sliders to get started. Tables: Input and plot data, or create an input-output table for any function. Statistics: Find best-fit lines, parabolas, and more. Calculus: Graph derivatives (d/dx) and explore key concepts by building secant and tangent line sliders. Graph Maclaurin Series (okay, all kinds of Taylor Series, but that guy gets no love...) Evaluate a definite integral (int) in an instant, or plot an integral with varying bounds. Zooming: Scale the axes independently or at the same time with the pinch of two fingers, or edit the window size manually to get the perfect window. Points of Interest: Touch a curve to show maximums, minimums, and points of intersection. Tap the gray points of interest to see their coordinates. Hold and drag along a curve to see the coordinates change under your finger. Scientific Calculator: Just type in any equation you want to solve and Desmos will show you the answer. It can handle square roots, logs, absolute value, and more. Inequalities: Plot cartesian and polar inequalities. Offline: No internet access required. Visit www.desmos.com to learn more and to see the free online version of our calculator. | -- | Free | View In iTunes |

2 | Free Graphing Calculator | *** Now over 4 million downloads. Thanks users!*** A powerful, flexible graphing calculator . . . and it's free! Does far more than most of the paid calculators out there . . . let alone the free ones. Features: 1) Scientific Calculator. Simple to grasp and easy to use, but powerful features are available when you need them. Available functions include the following: • the usual arithmetic functions and exponentiation. • square root, cube root, nth root, natural log, log base 10, log of arbitrary base, absolute value, factorial, permutations (nPr), combinations (nCr), modulus, random integer, bell curve, cumulative normal distribution, decimal to fraction. 2) Graphing. Capabilities: • Graph up to four equations at once. • Graphs are labeled. • You can drag the graph or pinch to zoom in or out. • Calculator can find roots and intersections. • Graph in polar coordinates. • Graph parametric equations • Can graph implicit functions, such as x^2+y^2-4=0. Most calculator apps can't do this! 3) A unit converter. With a tap, you can enter the result of your conversion into the calculator. Currently converts different units of the following: acceleration, angle, area, density, distance, energy, force, mass, power, pressure, speed, temperature, time, and volume. Great for doing physics homework! 4) Constants for scientific calculations -- speed of light, strength of gravity at Earth's surface, etc. etc. etc. Tapping on a constant will insert it into your calculation -- i.e, you don't have to key in the value. Again, great for doing physics homework! 5) It can make a table of the values of any function you care to enter. You can choose the starting x value of the table, as well as how much x increases for each successive row. 6) Help screens linked directly to many of the available functions and constants. Tap the disclosure arrow to see the definition. 7) Forgot the quadratic formula? Or the double-angle formulas for sine and cosine? The math/science reference hits the high points of various subjects. Currently includes algebra, differential and integral calculus, geometry, trigonometry, vectors, vector calculus, and classical mechanics. 8) Keep track of significant figures [AKA sig figs] 9) Statistics -- enter data and make a histogram, box and whisker plot, or scatter plot with optional regression line. If you are viewing this in iTunes, you will see five iPhone screenshots and five iPad screenshots. But even ten shots don't come close to showing everything this calculator can do. I'd love to hear your comments or suggestions. You can write me at mathscixyzgraphcalc@gmail.com -- but without the xyz. Thanks! | -- | Free | View In iTunes |

3 | yHomework - Math Solver | Having trouble with algebra? Equations, inequalities and graphs leave you frustrated? Tried to solve the problem but you're not sure you got it right? Meet yHomework - the math solver that actually works 100% of the time! No gimmicks, no fuss, no excuses - we simply give you the an instant full step-by-step solution and explanation. yHomework is an easy to use Math solver, just enter your question or equation, and the app will immediately give you the answer together with the full step-by-step solution! Say you have: 3x+5=8 Not sure what to do next? Just type it into the app and get the step-by-step solution with just one click! It's just that simple! 1.. 2.. 3.. and you're a math whiz! 3 MILLION USERS CAN'T BE WRONG! DOWNLOAD yHomework TODAY! Current material covers: Simplification, single unknown equation, 2 equation sets, quadratic equations, Inequalities, absolute value, function graphs, prime factorisation and derivatives. Questions? Comments? Contact us at: support@yhomework.com | -- | Free | View In iTunes |

4 | Symbolab - Calculator with steps | Math Solver, Solves any math problem with steps! Symbolab powerful calculator solves: Pre-Algebra - Order of operations (PEMDAS) - Factors & Primes - Fractions - Long Arithmetics - Decimals - Exponents & Radicals - Ratios & Proportions Algebra - Equations - Inequalities - System of Equations - Basic Operations (factor, join, cancel, simplify) - Partial Fractions - Polynomial Division - Percents Functions & Graphing - Line equations (line, slope, parallel, perpendicular, midpoint, distance) - Functions (domain, range, intercepts, asymptotes, extreme points, periodicity, inverse) - Function arithmetics and compositions Trigonometry: - Trig Equations - Trig identities proving - Trig function evaluation - Trig simplification Calculus - Limits - Integrals (definite, indefinite, multiple) - Derivatives - Partial derivatives - Series - ODE - Laplace Transform - Inverse Laplace Transform Matrices - Add, Subtract, Multiply and Power - Trace, Transpose, Determinant, Inverse, Rank, Reduce - Eigenvalues, Eigenvectors and Diagonalization Vectors - Add, Subtract - Scalar Multiplication - Cross Product - Magnitude, Angle, Unit, Projection, Scalar Projection (and more topics are added constantly) Get free solution to any problem. Upgrade to get unlimited access to all subjects with steps. History! Every problem you solved is saved in history and you can get back to it anytime you want. For middle school through college students, teachers and parents. | -- | Free | View In iTunes |

5 | GeoGebra | GeoGebra (www.geogebra.org) is free dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package. Interactive learning, teaching and evaluation resources created with GeoGebra can be shared and used by everyone at tube.geogebra.org. GeoGebra is the world’s favorite dynamic mathematics software, has received numerous educational software awards, and supports STEM education and innovations in teaching and learning worldwide. Join us. Dynamic Mathematics for Everyone. * Free to use software for learning, teaching and evaluation * Fully interactive, easy-to-use interface with many powerful features * Access to an ever-expanding pool of resources at tube.geogebra.org * Available in many languages * A fun way to really see and experience mathematics and science * Adaptable to any curriculum or project * Used by millions of people around the world | -- | Free | View In iTunes |

6 | Wolfram Calculus Course Assistant | Taking calculus? Then you need the Wolfram Calculus Course Assistant. This definitive app for calculus—from the world leader in math software—will help you work through your homework problems, ace your tests, and learn calculus concepts. Forget canned examples! The Wolfram Calculus Course Assistant solves your specific Calculus problems on the fly including step-by-step guidance for derivatives, integrals, and much more. This app covers the following topics applicable to Calculus, AP Calculus AB, AP Calculus BC, Calculus I, and Calculus II: - Evaluate any numeric expression or substitute a value for a variable. - Plot basic, parametric, or polar plots of the function(s) of your choice. - Determine the limit of a function as it approaches a specific value. - Differentiate any function or implicit function. - Find the critical points and inflection points of a function. - Identify the local and absolute extrema of a function. - Integrate a function, with or without limits. - Sum a function given a lower and upper bound. - Find the closed form of a sequence or generate terms for a specific sequence. The Wolfram Calculus Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica—the world's leading software system for mathematical research and education. The Wolfram Calculus Course Assistant draws on the computational power of Wolfram|Alpha's supercomputers over a 3G, 4G, or Wi-Fi connection. | -- | $3.99 | View In iTunes |

7 | WolframAlpha | Remember the Star Trek computer? It's finally happening--with Wolfram|Alpha. Building on 25 years of development led by Stephen Wolfram, Wolfram|Alpha has rapidly become the world's definitive source for instant expert knowledge and computation. Across thousands of domains--with more continually added--Wolfram|Alpha uses its vast collection of algorithms and data to compute answers and generate reports for you. Parts of Wolfram|Alpha are used in the Apple Siri Assistant; this app gives you access to the full power of the Wolfram|Alpha computational knowledge engine. Domains covered by Wolfram|Alpha include: MATHEMATICS Elementary Math Numbers Plotting Algebra Matrices Calculus Geometry Trigonometry Discrete Math Number Theory Applied Math Logic Functions STATISTICS & DATA ANALYSIS Descriptive Statistics Regression Statistical Distributions Probability PHYSICS Mechanics Electricity & Magnetism Optics Thermodynamics Relativity Nuclear Physics Quantum Physics Particle Physics Statistical Physics Astrophysics CHEMISTRY Elements Compounds Ions Solutions Reactions Chemical Thermodynamics MATERIALS Alloys Minerals Crystallography Plastics Woods ENGINEERING Acoustics Aeronautics Electric Circuits Fluid Mechanics Steam Tables Psychrometrics Refrigeration ASTRONOMY Star Charts Astronomical Events Planets Moons Space Weather Stars Pulsars Galaxies Star Clusters Nebulae Astrophysics EARTH SCIENCE Geology Geochronology Geodesy Earthquakes Tide Data Atmosphere Climate LIFE SCIENCES Animals & Plants Dinosaurs DNA Sequence Lookup Proteins Genomes Metabolic Pathways COMPUTATIONAL SCIENCES Cellular Automata Substitution Systems Turing Machines Computational Complexity Algebraic Codes Fractals Image Processing UNITS & MEASURES Conversions Comparisons Dimensional Analysis Industrial Measures Paint DATES & TIMES Date Computations Time Zones Calendars Holidays Geological Time WEATHER Current & Historical Weather Forecasts Wind Chill Hurricanes Clouds Climate PLACES & GEOGRAPHY Maps Projections Geodesy Navigation Distances Geomagnetism Geocoding Countries Cities Elevation Data Oceans Lakes Rivers Islands Mountains PEOPLE & HISTORY People Genealogy Names Occupations Political Leaders Historical Events, Periods & Countries Historical Money CULTURE & MEDIA Books Movies Video Games Fictional Characters Mythology Television Programs Awards MUSIC Musical Notes Intervals Chords Scales Audio Waveforms Instruments Songs WORDS & LINGUISTICS Word Properties Dictionary Lookup Puzzles Anagrams Languages Document Length Morse Code Soundex SPORTS & GAMES Football Baseball Olympics Stadiums Lotteries Card Games COLORS Color Names & Systems Color Addition Temperatures Wavelengths MONEY & FINANCE Stock Data Indices Mutual Funds Futures Mortgages Present Value Currency Conversion Bonds Derivatives Valuation Wages Sales Tax SOCIOECONOMIC DATA Demographics Countries US States US Counties Cities Economics Agriculture Energy Salaries Unemployment Cost of Living Health Care Housing Social Statistics Crime Military Religion HEALTH & MEDICINE Body Measurements Growth Charts Exercise Diseases Mortality Data Medical Test Data FOOD & NUTRITION Foods Dietary References EDUCATION International Education Universities Public Schools Standardized Tests ORGANIZATIONS Companies Hospitals Foundations International Organizations TRANSPORTATION Airports Airlines Aircraft Flight Data Gasoline Prices Tides TECHNOLOGICAL WORLD Communications Satellites Space Probes Photography Barcodes WEB & COMPUTER SYSTEMS Website Data IP Lookup Notable Computers String Processing Hashing Unicode Lookup (Wolfram|Alpha Pro capabilities such as file upload and personal analytics are not yet available through this app.) | -- | $2.99 | View In iTunes |

8 | 11.2 Vectors I | -- | 25:49 | Free | View In iTunes |

9 | 11.2 Vectors I | -- | -- | Free | View In iTunes |

10 | 11.2 Vectors II | -- | 10:41 | Free | View In iTunes |

11 | 11.2 Vectors II | -- | -- | Free | View In iTunes |

12 | 11.3 Dot Product I | -- | 22:04 | Free | View In iTunes |

13 | 11.3 Dot Product I | -- | -- | Free | View In iTunes |

14 | 11.3 Dot Product II | -- | 24:08 | Free | View In iTunes |

15 | 11.3 Dot Product II | -- | -- | Free | View In iTunes |

16 | 12.1 Vector Functions I | -- | 25:03 | Free | View In iTunes |

17 | 12.1 Vector Functions I | -- | -- | Free | View In iTunes |

18 | 12.1 Vector Functions II | -- | 13:06 | Free | View In iTunes |

19 | 12.1 Vector Functions II | -- | -- | Free | View In iTunes |

20 | 12.2 Derivatives of Vector Functions I | -- | 28:58 | Free | View In iTunes |

21 | 12.2 Derivatives of Vector Functions I | -- | -- | Free | View In iTunes |

22 | 12.3 Integrals of Vector Functions I | -- | 19:02 | Free | View In iTunes |

23 | 12.3 Integrals of Vector Functions I | -- | -- | Free | View In iTunes |

24 | 12.4 Motion of Projectiles I | -- | 25:21 | Free | View In iTunes |

25 | 12.4 Motion of Projectiles I | -- | -- | Free | View In iTunes |

26 | 12.4 Motion of Projectiles II | -- | 36:16 | Free | View In iTunes |

27 | 12.4 Motion of Projectiles II | -- | -- | Free | View In iTunes |

28 | 12.5 Arc Lengths I | -- | 16:17 | Free | View In iTunes |

29 | 12.5 Arc Lengths I | -- | -- | Free | View In iTunes |

30 | 12.5 Arc Lengths II | -- | 21:55 | Free | View In iTunes |

31 | 12.5 Arc Lengths II | -- | -- | Free | View In iTunes |

32 | 12.6 Curvature I | -- | 24:53 | Free | View In iTunes |

33 | 12.6 Curvature I | -- | -- | Free | View In iTunes |

34 | 12.6 Curvature II | -- | 32:37 | Free | View In iTunes |

35 | 12.6 Curvature II | -- | -- | Free | View In iTunes |

36 | 12.6 Curvature III | -- | 23:54 | Free | View In iTunes |

37 | 12.6 Curvature III | -- | -- | Free | View In iTunes |

38 | 12.6 Curvature IV | -- | 18:19 | Free | View In iTunes |

39 | 12.6 Curvature IV | -- | -- | Free | View In iTunes |

40 | 13.1 Functions of Several Variables I | -- | 27:21 | Free | View In iTunes |

41 | 13.1 Functions of Several Variables I | -- | -- | Free | View In iTunes |

42 | 13.1 Functions of Several Variables II | -- | 14:40 | Free | View In iTunes |

43 | 13.1 Functions of Several Variables II | -- | -- | Free | View In iTunes |

44 | 13.2 Limits I | -- | 13:39 | Free | View In iTunes |

45 | 13.2 Limits I | -- | -- | Free | View In iTunes |

46 | 13.2 Limits II | -- | 24:57 | Free | View In iTunes |

47 | 13.2 Limits II | -- | -- | Free | View In iTunes |

48 | 13.4 Partial Derivatives I | -- | 45:07 | Free | View In iTunes |

49 | 13.4 Partial Derivatives I | -- | -- | Free | View In iTunes |

50 | 13.4 Partial Derivatives II | -- | 34:52 | Free | View In iTunes |

51 | 13.4 Partial Derivatives II | -- | -- | Free | View In iTunes |

52 | 13.4 Partial Derivatives III | -- | 27:47 | Free | View In iTunes |

53 | 13.4 Partial Derivatives III | -- | -- | Free | View In iTunes |

54 | 13.4 Partial Derivatives IV | -- | 24:15 | Free | View In iTunes |

55 | 13.4 Partial Derivatives IV | -- | -- | Free | View In iTunes |

56 | 13.5 Chain Rule I | -- | 29:00 | Free | View In iTunes |

57 | 13.5 Chain Rule I | -- | -- | Free | View In iTunes |

58 | 13.5 Chain Rule II | -- | 24:48 | Free | View In iTunes |

59 | 13.5 Chain Rule II | -- | -- | Free | View In iTunes |

60 | 13.5 Chain Rule III | -- | 24:25 | Free | View In iTunes |

61 | 13.5 Chain Rule III | -- | -- | Free | View In iTunes |

62 | 13.6 Directional Derivatives and Grad I | -- | 30:46 | Free | View In iTunes |

63 | 13.6 Directional Derivatives and Grad I | -- | -- | Free | View In iTunes |

64 | 13.6 Directional Derivatives and Grad II | -- | 15:44 | Free | View In iTunes |

65 | 13.6 Directional Derivatives and Grad II | -- | -- | Free | View In iTunes |

66 | 13.6 Directional Derivatives and Grad III | -- | 7:37 | Free | View In iTunes |

67 | 13.6 Directional Derivatives and Grad III | -- | -- | Free | View In iTunes |

68 | 13.7 Tangent Planes I | -- | 22:54 | Free | View In iTunes |

69 | 13.7 Tangent Planes I | -- | -- | Free | View In iTunes |

70 | 13.7 Tangent Planes II | -- | 33:30 | Free | View In iTunes |

71 | 13.7 Tangent Planes II | -- | -- | Free | View In iTunes |

72 | 13.8 Differentials I | -- | 31:51 | Free | View In iTunes |

73 | 13.8 Differentials I | -- | -- | Free | View In iTunes |

74 | 13.9 Extreme Values I | -- | 29:22 | Free | View In iTunes |

75 | 13.9 Extreme Values I | -- | -- | Free | View In iTunes |

76 | 13.9 Extreme Values II | -- | 17:35 | Free | View In iTunes |

77 | 13.9 Extreme Values II | -- | -- | Free | View In iTunes |

78 | 13.9 Extreme Values III | -- | 25:32 | Free | View In iTunes |

79 | 13.9 Extreme Values III | -- | -- | Free | View In iTunes |

80 | 13.10 Lagrange Multipliers I | -- | 36:40 | Free | View In iTunes |

81 | 13.10 Lagrange Multipliers I | -- | -- | Free | View In iTunes |

82 | 13.10 Lagrange Multipliers II | -- | 28:26 | Free | View In iTunes |

83 | 13.10 Lagrange Multipliers II | -- | -- | Free | View In iTunes |

84 | 13.11 Partials w Constrained Variables I | -- | 18:29 | Free | View In iTunes |

85 | 13.11 Partials w Constrained Variables I | -- | -- | Free | View In iTunes |

86 | 13.11 Partials w Constrained Variables II | -- | 18:23 | Free | View In iTunes |

87 | 13.11 Partials w Constrained Variables II | -- | -- | Free | View In iTunes |

88 | 14.1 Double Integrals Over Rectangles I | -- | 23:28 | Free | View In iTunes |

89 | 14.1 Double Integrals Over Rectangles I | -- | -- | Free | View In iTunes |

90 | 14.1 Double Integrals Over Rectangles II | -- | 23:52 | Free | View In iTunes |

91 | 14.1 Double Integrals Over Rectangles II | -- | -- | Free | View In iTunes |

92 | 14.2 Double Integrals Over Gen R I | -- | 31:16 | Free | View In iTunes |

93 | 14.2 Double Integrals Over Gen R I | -- | -- | Free | View In iTunes |

94 | 14.2 Double Integrals Over Gen R II | -- | 23:24 | Free | View In iTunes |

95 | 14.2 Double Integrals Over Gen R II | -- | -- | Free | View In iTunes |

96 | 14.2 Double Integrals Over Gen R III | -- | 18:52 | Free | View In iTunes |

97 | 14.2 Double Integrals Over Gen R III | -- | -- | Free | View In iTunes |

98 | 14.2 Double Integrals Over Gen R IV | -- | 34:53 | Free | View In iTunes |

99 | 14.2 Double Integrals Over Gen R IV | -- | -- | Free | View In iTunes |

100 | 14.3 Double Int in Polar Coord I | -- | 30:28 | Free | View In iTunes |

101 | 14.3 Double Int in Polar Coord I | -- | -- | Free | View In iTunes |

102 | 14.5 Momemts and Center of Mass I | -- | 33:55 | Free | View In iTunes |

103 | 14.5 Moments and Center of Mass I | -- | -- | Free | View In iTunes |

104 | 14.6 Triple Integrals I | -- | 14:53 | Free | View In iTunes |

105 | 14.6 Triple Integrals I | -- | -- | Free | View In iTunes |

106 | 14.6 Triple Integrals II | -- | 29:47 | Free | View In iTunes |

107 | 14.6 Triple Integrals II | -- | -- | Free | View In iTunes |

108 | 14.6 Triple Integrals III | -- | 19:00 | Free | View In iTunes |

109 | 14.6 Triple Integrals III | -- | -- | Free | View In iTunes |

110 | 14.6 Triple Integrals IV | -- | 30:35 | Free | View In iTunes |

111 | 14.6 Triple Integrals IV | -- | -- | Free | View In iTunes |

111 Items |

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