Mathematics I. Instructor: Prof S. K. Ray, Department of Mathematics and Statistics, IIT Kanpur.
1. Calculus of Functions of One Variable
Real numbers, Functions, Sequences, Limit and Continuity, Differentiation : review, successive differentiation, chain rule and Leibnitz theorem, Rolle's and Mean Value Theorems, Maxima/ Minima, Curve sketching, Linear and quadratic approximations, Error estimates, Taylor's theorem, Newton and Picard methods, The Riemann integral, Approximate integration, Natural logarithm, Exponential function, Relative growth rates, L'Hospital's rule geometric applications of integrals, Infinite series, Tests of convergence, Absolute and conditional convergence, Taylor and maclaurin series.
2. Calculus of Functions of Several Variables
Scalar fields, Limit and continuity, Partial derivatives, Chain rules, Implicit differentiation, Directional derivatives, Total differential, Tangent planes and normals, Maxima, Minima and Saddle Points, Constrained maxima and minima, Double Integrals, Applications to Areas and Volumes, Change of variables.
3. Vector Calculus
Vector fields, divergence and curl, Line integrals, Green's theorem, Surface integrals, Divergence theorem, Stoke's theorem and application.
Instructor: Prof S. K. Ray, Department of Mathematics and Statistics, IIT Kanpur. Calculus of Functions of One Variable. Calculus of Functions of Several Variables. Vector Calculus.