MTL100: Calculus (4 Credits)
Review of limit, continuity and differentiability, uniform continuity. Mean value theorems and applications, Taylor’s theorem, maxima and minima. Sequences and series, limsup, liminf, convergence of sequences and series of real numbers, absolute and conditional convergence. Riemann integral, fundamental theorem of integral calculus, applications of definite integrals, improper integrals, beta and gamma functions. Functions of several variables, limit and continuity, partial derivatives and differentiability, gradient, directional derivatives, chain rule, Taylor’s theorem, maxima and minima and the method of Lagrange multipliers. Double and triple integration, Jacobian and change of variables formula. Parameterization of curves and surfaces, vector fields, divergence and curl. Line integrals, Green’s theorem, surface integral, Gauss and Stokes’ theorems with applications.
Grading is absolute (except in very exceptional cases, don't pin hopes on this)
Try out exercise problems from K. Ross to get the hang of proof writing, which is what causes the most trouble in this course.
The course is very similar to the MTH101 course of IIT Kanpur. You can find useful resources including lecture notes, solved examples and practice problems here.