# Vector Calculus

### Course Description

In this course, Prof. Chris Tisdell gives 88 video lectures on Vector Calculus. This is a series of lectures for "Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. This playlist provides a shapshot of some lectures presented in Session 1, 2009 and Session 1, 2011. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, this playlist may be useful to students of mathematics, but also to those of engineering, physics and the applied sciences. There is an emphasis on examples and also on proofs. Dr Chris Tisdell is Senior Lecturer in Applied Mathematics.

Prof. Chris Tisdell in Lecture 65: Reversing Order in Double Integrals.
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### Video Lectures & Study Materials

# Lecture Play Lecture
1 Applications of Double integrals Play Video
2 Path Integrals: How to Integrate Over Curves Play Video
3 What is a Vector Field? Play Video
4 What is the Divergence? Play Video
5 What is the Curl? Play Video
6 What is a Line Integral? Play Video
7 Applications of Line Integrals Play Video
8 Fundamental Theorem of Line Integrals Play Video
9 What is Green's Theorem? Play Video
10 Green's Theorem Play Video
11 Parametrised Surfaces Play Video
12 What is a Surface Integral? (Part I) Play Video
13 More On Surface Integrals Play Video
14 Surface Integrals and Vector Fields Play Video
15 Divergence Theorem of Gauss Play Video
16 How to Solve PDEs via Separation of Variables and Fourier Series Play Video
17 Vector Revision Play Video
18 Intro to Curves and Vector Functions Play Video
19 Limits of Vector Functions Play Video
20 Calculus of Vector Functions: One Variable Play Video
21 Calculus of Vector Functions Tutorial Play Video
22 Vector Functions Tutorial Play Video
23 Intro to Functions of Two Variables Play Video
24 Limits of Functions of Two Variables Play Video
25 Partial Derivatives Play Video
26 Partial Derivatives and PDEs Tutorial Play Video
27 Multivariable Functions: Graphs and Limits Play Video
28 Multivariable Chain Rule and Differentiability Play Video
29 Chain Rule: Partial Derivative of \$\arctan (y/x)\$ w.r.t. \$x\$ Play Video
30 Chain Rule & Partial Derivatives Play Video
31 Chain Rule: Identity Involving Partial Derivatives Play Video
32 Multivariable Chain Rule Play Video
33 Leibniz' Rule: Integration via Differentiation Under Integral Sign Play Video
34 Evaluating Challenging Integrals via Differentiation: Leibniz Rule Play Video
35 Gradient and Directional Derivative Play Video
36 Gradient and Directional Derivative Play Video
37 Directional dDerivative of \$f(x,y)\$ Play Video
38 Tangent Plane Approximation and Error Estimation Play Video
39 Gradient and Tangent Plane Play Video
40 Partial Derivatives and Error Estimation Play Video
41 Multivariable Taylor Polynomials Play Video
42 Taylor Polynomials: Functions of Two Variables Play Video
43 Multivariable Calculus: Limits, Chain Rule and Arc Length Play Video
44 Critical Points of Functions Play Video
45 How to Find Critical Points of Functions Play Video
46 How to Find Critical Points of Functions Play Video
47 Second Derivative Test: Two Variables Play Video
48 Multivariable Calculus: Critical Points and Second Derivative Test Play Video
49 How to Find and Classify Critical Points of Functions Play Video
50 Lagrange Multipliers Play Video
51 Lagrange Multipliers: Two Constraints Play Video
52 Lagrange Multipliers: Extreme Values of a Function Subject to a Constraint Play Video
53 Lagrange Multipliers Example Play Video
54 Lagrange multiplier Example: Minimizing a Function Subject to a Constraint Play Video
55 Second Derivative Test, Max/Min and Lagrange Multipliers Play Video
56 Intro to Jacobian Matrix and Differentiability Play Video
57 Jacobian Chain Rule and Inverse Function Theorem Play Video
58 Intro to Double Integrals Play Video
59 Double Integrals Over General Regions Play Video
60 Double Integrals: Volume Between Two Surfaces Play Video
61 Double Integrals: Volume of a Tetrahedron Play Video
62 Double Integral Play Video
63 Double Integrals and Area Play Video
64 Double Integrals in Polar Co-ordinates Play Video
65 Reversing Order in Double Integrals Play Video
66 Double Integrals: Reversing the Order of Integration Play Video
67 Applications of Double Integrals Play Video
68 Double Integrals and Polar Co-ordinates Play Video
69 Double Integrals Play Video
70 Centroid and Double Integral Play Video
71 Center of Mass, Double Integrals and Polar Co-ordinates Play Video
72 Triple Integral Play Video
73 Triple integrals in Cylindrical and Spherical Coordinates Play Video
74 Triple integrals & Center of Mass Play Video
75 Change of Variables in Double Integrals Play Video
76 Path Integral (Scalar Line Integral) From Vector Calculus Play Video
77 Line Integral Example in 3D-Space Play Video
78 Line Integral From Vector Calculus Over a Closed Curve Play Video
79 Line Integral Example From Vector Calculus Play Video
80 Divergence of a Vector Field Play Video
81 Curl of a Vector Field (ex. no.1) Play Video
82 Curl of a Vector Field (ex. no.2) Play Video
83 Divergence Theorem of Gauss Play Video
84 Intro to Fourier Series and How to Calculate Them Play Video
85 How to Compute a Fourier Series: An Example Play Video
86 What are Fourier Series? Play Video
87 Fourier Series Play Video
88 Fourier Series and Differential Equations Play Video