MTL100 - Calculus

Class Description

Credit: 4 Credits (3-1-0)

Instructor: K. Sreenadh

Course Contents:

Sequences: Real number system, Archimedean property, Sequences of real numbers: Definitions of sequence and convergence, bounded sequences, Limit superior and inferior, Cauchy sequence, divergent sequences.

Differential Calculus: Limits, continuity and differentiability, uniform continuity, mean value theorems, Taylor's theorem, maxima and minima.

Infinite Series: Series of real numbers, absolute and conditional convergence, comparison, ratio and root tests for convergence, power series and review of Taylor series.

Definite Integral: Definition of Riemann integral, fundamental theorems, improper integrals of first and second kind, beta and gamma functions, applications to area, arc length, volume and surface area.

Multivariable Differential Calculus: Functions of several variables, limits, continuity, differentiability, gradient, directional derivatives, chain rule, Taylor's theorem, Maxima & minima and method of Lagrange multiplies.

Multivariable Integral Calculus: Double and triple integrals, Jacobian and change of variables formula. Applications to Area, Volume, Surface area and surface integrals.

Vector Calculus: Vector fields, divergence and curl, line integrals, Conservative vector fields, Tangents & Normals, Parametrization of curves and surfaces, Green, Gauss, Stokes theorems and applications .

Lecture Notes