MAT 101S CALCULUS AND VECTOR ANALYSIS

3 Hours/Week, 3 Credits

Calculus 1. Differential Calculus: Limits, continuity and differentiability; Successive differentiation of various types of functions; Leibnitzís Theorem; Rolleís Theorem; Mean value Theorem; Expansion of functions; Evaluation of indeterminate forms by LíHospitals rule; Partial differentiation; Euler's Theorem; Tangent and Normal; Maximum and minimum values of functions of single variable; Curvature, Asymptotes, Envelopes. 2. Integral Calculus: Definitions of integration; Integration by the method of substitutions; Integration by parts; Standard integrals; Integration by the method of successive reduction; Definite integrals and its use in summing series, Improper integrals, Beta function and Gamma function; Area under a plane curve; Area of the region enclosed by two curves; Volume of solids of revolution; multiple integrals and its application. 3. Vector Analysis: Scalars and vectors, Algebraic operations on vectors, Components of vectors, vectors products, angel between two vectors, Derivatives of vectors, Gradient, divergence and curl, vector integrals, line integrals, surface integrals, volume integrals and its applications. Recommended Books 1. Calculus and Analytical Geometry by Thomas and Finney 2. Vector Analysis by M.R. Spiegel