Vector differential calculus: gradient, divergence, curl, curvilinear coordinates; vector integral calculus: line integral, surface integral volume integral, Green’s theorem, Stoke’s theorem, divergence theorem; implicit and inverse function theorems; Leibnitz theorem; calculus of variations (functionals of one variable).

- Calculus early transcendental, 8th Edition, by James Stewart.

- Advanced Calculus, 5th Edition, by Wilfred Kaplan​.

Topic Outline and Schedule:

The following is a rough plan. As the course progresses, I may include new topics and/or delete some of the ones listed here.

Topics	Week
Functions of several variables (limits, continuity, and partial derivatives)	1-4
The three linear operators: (i) gradient, (ii) divergence, (iii) curl.	5-8
Different types of integrals: (i) line integral, (ii) surface integral, (iii) volume integral	9-12
Six main theorems: Greens Theorem. Stokes Theorem Divergence Theorem Implicit Function Theorem Inverse mapping Theorem Leibnitz Theorem	13-15
Calculus of variation: Functional of one variable	16

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Short Syllabus: Click here!​​