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Multivariable calculus

Indian Institute of Technology Roorkee via NPTEL

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Overview

This course is a basic course offered to UG and PG students of Engineering/Science background. It contains matrices computations involving rank, eigen values, eigen vectors, singularity transformations, (diagonalisation, Joradan canonical etc). It also convers vectors spaces, basis and dimension, linear transformation and their properties. Besides discussing the matrix theory, it also includes its applications in solving diverse science and engineering problems.

Syllabus

Week 1: Limits, continuity and partial derivatives of multivariable functions

Week 2: Differentiability and chain rule

Week 3: Change of variables, Euler’s theorem, tangent planes, normal lines and extreme values

Week 4: Taylor’s theorem, error approximation, polar curves and multiple integrals

Week 5: Change of order and change of variables in multiple integral

Week 6: Beta and gamma functions

Week 7: Normal vector and potential field

Week 8: vector identities and line integral

Taught by

S. K. Gupta and Sanjeev Kumar

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