MA4090-Multivariable Calculus
Syllabus:
Functions of several-variables, Directional derivative, Partial derivative, Total derivative, Jacobian, Chain rule and Mean-value theorems, Interchange of the order of differentiation, Higher derivatives,
Taylor’s theorem, Inverse mapping theorem, Implicit function theorem, Extremum problems, Extremum problems with constraints, Lagrange’s multiplier method.
Multiple integrals, Properties of integrals, Existence of integrals, iterated integrals, change of variables.
Curl, Gradient, div, Laplacian cylindrical and spherical coordinate, line integrals, surface integrals, Theorem of Green, Gauss and Stokes.
Books for Reference:
Calculus on manifolds. A modern approach to classical theorems of advanced calculus by Michael Spivak
Calculus of Several Variables by Serge Lang.
Functions of several variables by Wendell Fleming.
Introduction to Analysis in Several Variables: Advanced Calculus by Michel E. Taylor.
Multivariable calculus with applications by Peter D Lax, Maria Shea Terrell.
Home Works: ONLY ACCESSIBLE VIA IIT-H ACCOUNT
End of the Semester test:
Date: 2nd of May, 2023.
Time: 10 am to 12 pm
ROOM: A221
NOT EVERYTHING WE DISCUSSED IN THE CLASSROOM IS MENTIONED IN THE NOTES.