# InfoCoBuild

## Mathematics I

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. (from nptel.ac.in)

 Real Numbers

 Lecture 01 - Real Numbers Lecture 02 - Sequences I Lecture 03 - Sequences II Lecture 04 - Sequences III Lecture 05 - Continuous Functions Lecture 06 - Properties of Continuous Functions Lecture 07 - Uniform Continuity Lecture 08 - Differentiable Functions Lecture 09 - Mean Value Theorem (One Variable) Lecture 10 - Maxima/ Minima (One Variable) Lecture 11 - Taylor's Theorem Lecture 12 - Curve Sketching Lecture 13 - Infinite Series I Lecture 14 - Infinite Series II Lecture 15 - Test of Convergence Lecture 16 - Power Series Lecture 17 - Riemann Integral Lecture 18 - Riemann Integrable Function Lecture 19 - Applications of Riemann Integral Lecture 20 - Length of a Curve Lecture 21 - Line Integrals Lecture 22 - Functions of Several Variables Lecture 23 - Differentiation Lecture 24 - Derivatives Lecture 25 - Mean Value Theorem (Multivariables) Lecture 26 - Maxima/ Minima (Multivariables) Lecture 27 - Method of Lagrange Multipliers Lecture 28 - Multiple Integrals Lecture 29 - Surface Integrals Lecture 30 - Green's Theorem Lecture 31 - Stokes' Theorem Lecture 32 - Gauss' Divergence Theorem

 References Mathematics I 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.