This is part of a standard course contents in Several Variable Calculus. The idea of the course is to provide students with different backgrounds a common platform to take up further topics in Mathematics, Physics and Engineering.
Week. No.
Topics
1
Functions of several variables and examples; continuity; concept of distances in higher dimension; examples; how to define differentiable functions.
2
Directional derivatives as direct generalization from one variable; drawbacks; definition of differentiable functions of several variable; examples; matrix of a linear transformation; Jacobian matrix; recovering directional derivative from derivative; chain rule.
3
Comparison with one variable calculus: version of MVT, higher derivatives and Taylor’s formula; Sufficient condition for equality of mixed derivatives; extremas for real valued function and special case for functions with two variables.
4
Statement of Implicit Function Theorem and Inverse Function Theorem.; deriving Inverse Function Theorem form Implicit Function Theorem; Illustration of Implicit Function Theorem for function of two variables; examples from solutions of ordinary differential equations; proof of Implicit Function Theorem; Lagrange’s Multipliers.
A course in one variable calculus
Principles of Mathematical Analysis, W. Rudin
Calculus ? T. Apostol
Mathematical Analysis, T. Apostol
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