Advanced Calculus (0331301)

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Page Content Advanced Calculus
Course Description:
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).
Textbooks:
 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)

14

The three linear operators:
(i) gradient, (ii) divergence,
(iii) curl.

58

Different types of integrals:
(i) line integral, (ii)
surface integral, (iii) volume integral

912

Six main theorems:
 Greens Theorem.
 Stokes Theorem
 Divergence
Theorem
 Implicit
Function Theorem
 Inverse mapping
Theorem
 Leibnitz Theorem

1315

Calculus of variation:
Functional of one variable

16

Short Syllabus: Click here!


