Vector Calculus

Vector Calculus (2009, UNSW). This is a collection of video lectures given by Professor Chris Tisdell, presenting vector calculus in an applied and engineering context. This is a series of lectures for "Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, the lectures 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.

Lecture 01 - Applications of Double Integrals
Lecture 02 - Path Integrals - How to Integrate over Curves
Lecture 03 - What is a Vector Field?
Lecture 04 - What is the Divergence?
Lecture 05 - What is the Curl?
Lecture 06 - What is a Line Integral?
Lecture 07 - Applications of Line Integrals
Lecture 08 - Fundamental Theorem of Line Integrals
Lecture 09 - What is Green's Theorem?
Lecture 10 - Green's Theorem (cont.)
Lecture 11 - Parametrized Surfaces
Lecture 12 - What is a Surface Integral?
Lecture 13 - More on Surface Integrals
Lecture 14 - Surface Integrals + Vector Fields
Lecture 15 - How to Solve PDEs via Separation of Variables