# InfoCoBuild

## Engineering Mathematics I

Engineering Mathematics I. Instructor: Prof. Jitendra Kumar, Department of Mathematics, IIT Kharagpur. This course is about the basic mathematics that is a fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The course consists of topics in differential calculus, integral calculus, linear algebra and differential equations with applications to various engineering problems. 1. Mean Value Theorems; Indeterminate Forms; Taylor's and Maclaurin's Theorems. Partial Derivatives; Differentiability; Taylor's Expansion of Functions of Several Variables. Maxima and Minima. 2. Improper Integrals. Differentiation under Integral Sign (Leibniz rule). Multiple Integrals and their Properties. Applications of Multiple Integrals. 3. System of Linear Equations. Vector Spaces; Basis and Dimension of a Vector Space. Rank of a Matrix and its Properties. Linear Transformation. Eigenvalues and Eigenvectors. Diagonalization. 4. First Order Differential Equations. Higher Order Differential Equations with Constant Coefficients. Cauchy-Euler Equations. System of Differential Equations. (from nptel.ac.in)

 Introduction

 Lecture 01 - Rolle's Theorem Lecture 02 - Mean Value Theorems Lecture 03 - Indeterminate Forms Lecture 04 - Indeterminate Forms (cont.) Lecture 05 - Taylor Polynomial and Taylor Series Lecture 06 - Limit of Functions of Two Variables Lecture 07 - Evaluation of Limit of Functions of Two Variables Lecture 08 - Continuity of Functions of Two Variables Lecture 09 - Partial Derivatives of Functions of Two Variables Lecture 10 - Partial Derivatives of Higher Order Lecture 11 - Derivative and Differentiability Lecture 12 - Differentiability of Functions of Two Variables Lecture 13 - Differentiability of Functions of Two Variables (cont.) Lecture 14 - Differentiability of Functions of Two Variables (cont.) Lecture 15 - Composite and Homogeneous Functions Lecture 16 - Taylor's Theorem for Functions of Two Variables Lecture 17 - Maxima and Minima of Functions of Two Variables Lecture 18 - Maxima and Minima of Functions of Two Variables (cont.) Lecture 19 - Maxima and Minima of Functions of Two Variables (cont.) Lecture 20 - Constrained Maxima and Minima Lecture 21 - Improper Integrals Lecture 22 - Improper Integrals (cont.) Lecture 23 - Improper Integrals (cont.) Lecture 24 - Improper Integrals (cont.) Lecture 25 - Beta and Gamma Function Lecture 26 - Beta and Gamma Function (cont.) Lecture 27 - Differentiation under Integral Sign Lecture 28 - Double Integrals Lecture 29 - Double Integrals (cont.) Lecture 30 - Double Integrals (cont.) Lecture 31 - Integral Calculus - Double Integrals in Polar Form Lecture 32 - Integral Calculus - Double Integrals: Change of Variables Lecture 33 - Integral Calculus - Double Integrals: Surface Area Lecture 34 - Integral Calculus - Triple Integrals Lecture 35 - Integral Calculus - Triple Integrals (cont.) Lecture 36 - System of Linear Equations Lecture 37 - System of Linear Equations - Gauss Elimination Lecture 38 - System of Linear Equations - Gauss Elimination (cont.) Lecture 39 - Linear Algebra - Vector Spaces Lecture 40 - Linear Independence of Vectors Lecture 41 - Vector Spaces - Spanning Set Lecture 42 - Vector Spaces - Basis and Dimension Lecture 43 - Rank of a Matrix Lecture 44 - Linear Transformations Lecture 45 - Linear Transformations (cont.) Lecture 46 - Eigenvalues and Eigenvectors Lecture 47 - Eigenvalues and Eigenvectors (cont.) Lecture 48 - Eigenvalues and Eigenvectors (cont.) Lecture 49 - Eigenvalues and Eigenvectors (cont.) Lecture 50 - Eigenvalues and Eigenvectors: Diagonalization Lecture 51 - Differential Equations - Introduction Lecture 52 - First Order Differential Equations Lecture 53 - Exact Differential Equations Lecture 54 - Exact Differential Equations (cont.) Lecture 55 - First Order Linear Differential Equations Lecture 56 - Higher Order Linear Differential Equations Lecture 57 - Solution of Higher Order Homogeneous Linear Equations Lecture 58 - Solution of Higher Order Non-Homogeneous Linear Equations Lecture 59 - Solution of Higher Order Non-Homogeneous Linear Equations (cont.) Lecture 60 - Cauchy-Euler Equations

 References Engineering Mathematics I Instructor: Prof. Jitendra Kumar, Department of Mathematics, IIT Kharagpur. The course consists of topics in differential calculus, integral calculus, linear algebra and differential equations with applications to various engineering problems.