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

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.

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