Calculus of Several Variables (Prof.Joydeep Dutta, IIT Kanpur) | Mathematics

Calculus of Several Variables

Calculus of Several Variables. Instructor: Prof.Joydeep Dutta, Department of Humanities and Social Sciences, IIT Kanpur. This course introduces the very important subject called the calculus of several real variables, which has important applications in science and engineering. The modern world would have been impossible without it. We introduce and discuss the subject in a non-traditional way taking the vector approach in most places. We start with the basics of Vectors, study continuity and partial derivatives, study multiple integrals and their applications and end with the Stokes Theorem and Gauss divergence theorem. (from nptel.ac.in)

Introduction

Lecture 01 - Vectors in Plane and Space

Lecture 02 - Inner Product and Distance

Lecture 03 - Application to Real World Problems

Lecture 04 - Matrices and Determinants

Lecture 05 - Cross Product of Two Vectors

Lecture 06 - Higher Dimensional Euclidean Space

Lecture 07 - Functions of More Than One Real Variable

Lecture 08 - Partial Derivatives and Continuity

Lecture 09 - Vector-valued Maps and Jacobian Matrix

Lecture 10 - Chain Rule for Partial Derivatives

Lecture 11 - The Gradient Vector and Directional Derivative

Lecture 12 - The Implicit Function Theorem

Lecture 13 - Higher Order Partial Derivatives

Lecture 14 - Taylor's Theorem in Higher Dimension

Lecture 15 - Maxima and Minima for Several Variables

Lecture 16 - Second Derivative Test for Maximum and Minimum

Lecture 17 - Constrained Optimization and the Lagrange Multiplier Rule

Lecture 18 - Vector Valued Function and Classical Mechanics

Lecture 19 - Arc Length

Lecture 20 - Vector Fields

Lecture 21 - Multiple Integral I

Lecture 22 - Multiple Integral II

Lecture 23 - Multiple Integral III

Lecture 24 - Multiple Integral IV

Lecture 25 - Cylindrical and Spherical Coordinates

Lecture 26 - Multiple Integrals and Mechanics

Lecture 27 - Line Integral I

Lecture 28 - Line Integral II

Lecture 29 - Parametrized Surfaces

Lecture 30 - Area of a Surface Integral

Lecture 31 - Area of Parametrized Surface

Lecture 32 - Surface Integrals

Lecture 33 - Green's Theorem

Lecture 34 - Stoke's Theorem

Lecture 35 - Examples of Stoke's Theorem

Lecture 36 - Gauss Divergence Theorem

Lecture 37 - Facts about Vector Fields

References

Calculus of Several Variables
Instructor: Prof.Joydeep Dutta, Department of Humanities and Social Sciences, IIT Kanpur. This course introduces the very important subject called the calculus of several real variables, which has important applications in science and engineering.