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1_1 Exponential Growth and Decay.flv
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Classroom Contents
Advanced Calculus - Multivariable Calculus
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- 1 1_1 Exponential Growth and Decay.flv
- 2 1_2 Exponential Growth and Decay.flv
- 3 1_3 Exponential Growth and Decay.flv
- 4 1_4 Exponential Growth and Decay
- 5 1_5 Euler Method
- 6 1_6 Euler Method
- 7 2_1 Sequences
- 8 2_2 Sequences
- 9 2_3 Sequences
- 10 2_4 Sequences
- 11 3_1 Introduction to Series
- 12 3_1_1 Introduction to Series
- 13 3_2 The Geometric Series
- 14 3_3 The Harmonic Series
- 15 3_4 Example Problems Involving Series
- 16 3_5_1 The Integral Test and Comparison Tests
- 17 3_5_2 The Integral Test and Comparison Tests
- 18 3_5_3 The Integral Test and Comaprison Tests
- 19 3_5_4 The Integral Test and Comparison Tests
- 20 3_6_2 Alternating Series
- 21 3_6_3 Alternating Series
- 22 3_7_1 Absolute Value Test
- 23 3_7_2 Ratio and Root Tests.flv
- 24 4_1_1 Power Series
- 25 4_1_2 Power Series
- 26 10_1_1 Vector Function Differentiation
- 27 10_1_2 Examples of Vector Function Differentiation
- 28 10_1_3 Examples of Vector Function Differentiation
- 29 11_1_1 Introduction to the Differentiation of Multivariable Functions
- 30 11_1_2 Example Problems on Partial Derivative of a Multivariable Function
- 31 11_2_1 The Geomtery of a Multivariable Function
- 32 11_3_1 The Gradient of a Multivariable Function
- 33 11_3_2 Working towards an equation for a tangent plane to a multivariable point
- 34 11_3_4 Working towards an equation for a tangent plane to a multivariable function
- 35 11_3_5 When is a multivariable function continuous
- 36 11_3_6 Continuity and Differentiablility
- 37 11_3_7 A Smooth Function
- 38 11_3_8 Example problem calculating a tangent hyperplane
- 39 11_4_1 The Derivative of the Composition of Functions
- 40 11_4_2 The Derivative of the Composition of Functions
- 41 11_5_1 Directional Derivative of a Multivariable Function Part 1
- 42 11_5_2 Directional Derivative of a Multivariable Function Part 2
- 43 11_6_1 Contours and Tangents to Contours Part 1
- 44 11_6_2 Contours and Tangents to Contours Part 2
- 45 11_6_3 Contours and Tangents to Contrours Part 3
- 46 11_7_1 Potential Function of a Vector Field Part 1
- 47 11_7_2 Potential Function of a Vector Field Part 2
- 48 11_7_3 Potential Function of a Vector Field Part 3
- 49 11_8_1 Higher Order Partial Derivatives Part 1
- 50 11_9_1 Derivative of Vector Field Functions
- 51 11_9_2 Conservative Vector Fields
- 52 12_1_1 Introduction to Taylor Polynomials
- 53 12_1_2 An Introduction to Taylor Polynomials
- 54 12_1_3 Example problem creating a Taylor Polynomial
- 55 12_2_1 Taylor Polynomials of Multivariable Functions
- 56 12_2_2 Taylor Theorem for Multivariable Polynomials
- 57 13_1 An Introduction to Optimization in Multivariable Functions
- 58 13_2 Optimization with Constraints
- 59 14_1 The Double Integral
- 60 14_2 The Type I Region
- 61 14_3 Type II Region with Solved Example Problem
- 62 14_4 Some Fun with the Volume of a Cylinder
- 63 14_5 The double integral calculated with polar coordinates
- 64 14_6 Changing between Type I and II Regions
- 65 14_7 Translation of Axes
- 66 14_8 The Volume of a Cylinder Revisited
- 67 14_9 The Volume between Two Functions
- 68 14_10 The Triple Integral by way of an Example Problem
- 69 14_11 The Translation of Axes in Triple Integrals
- 70 14_12 Translation to Cylindrical Coordinates
- 71 15_1 An Introduction to Line Integrals
- 72 15_2_1 Example Problem Explaining the Line Integral with Respect to Arc Length
- 73 15_2_2 Another Example Problem Solving a Line Integral
- 74 15_2_3 Another example problem without using a parametrized curve
- 75 15_3_1 Line integrals with respect to coordinate variables
- 76 15_3_2 Example problem with line integrals with respect to coordinate variables
- 77 15_3_3 Continuation of previous problem
- 78 15_4_1 Example problem with the line integral of a multivariable functions
- 79 15_4_2 Example problem with the line integral of a multivariable functions
- 80 15_4_3 Example problem with the line integrals of a multivariable functions
- 81 16_1 Introduction to line integrals of vector fields
- 82 16_2 Evaluating the force and the directional vector differential
- 83 16_3 Example problem solving the line integral of a vector field
- 84 16_4 Another example problem solving for the line integral of a vector field
- 85 16_5 Another example problem solving for the line integral of a vector field
- 86 16_6 Another problem solving for the line integral in a vector field
- 87 16_7 The fundamental theorem of line integrals
- 88 16_8 The line integral over a closed path
- 89 17_1 The surface integral
- 90 17_2 Example problem solving for the surface integral
- 91 18_1 Introduction to flux
- 92 18_2 Calculating the normal vector
- 93 18_3 Example problem for flux
- 94 19_1 Greens Theorem
- 95 19_1_2 Example problem using theorem of Green to solve for a line integral
- 96 19_1_3 Another example problem solving for the line integral using the theorem of Green
- 97 19_2 The Theorem of Stokes
- 98 19_2_1 Example problem using the theorem of Stokes
- 99 19_3_1 Example problem using the theorem of Gauss
- 100 19_3_2 Example problem using theorem of Gauss
- 101 Understanding the Euler Lagrange Equation
