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### 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.

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### Description

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**)

### Course Curriculum

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

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