**MDU/KU - Engineering Mathematics - 1**

**Section A**

**Infinite series**:

Convergence and divergence, comparison tests, D' Alembert's ratio test, integral test, Raabe’s test, logarithmic and Cauchy root tests, Gauss’s Test, alternating series, absolute and conditional convergence.

**Section B **

**Matrices & its Applications (For M.D.U.): **

Rank of a matrix, elementary transformations, elementary matrices, inverse using elementary transformations, normal form of a matrix, linear dependence and independence of vectors, consistency of linear system of equations, linear and orthogonal transformations, eigenvalues and eigenvectors, properties of eigenvalues, Cayley - Hamilton theorem and its applications, diagonalization of matrices, similar matrices, quadratic forms.

**Vector Calculus: (For K.U.)**

Differentiation of vectors, scalar and vector point functions. Gradient of a scalar field and directional derivative, divergence and curl of a vector field and their physical interpretations. Integration of vectors, line integral, surface integral, volume integral, Green, Stoke's and Gauss theorems (without proof) and their applications.

**Section C **

**Differential Calculus: **

Successive differentiation, Leibnitz Theorem and applications, Taylor's and Maclaurin's series, curvature, asymptotes, curve tracing. Functions of two or more variables, limit and continuity, partial derivatives, total differential and differentiability, derivatives of composite and implicit functions, Jacobians, higher order partial derivatives, homogeneous functions, Euler’s Theorem and applications. Taylor's series for functions of two variables (without proof), maxima-minima of function of two variables, Lagrange's method of undetermined multipliers, differentiation under integral sign (Leibnitz rule).

**Section D**

**Integral Calculus: **

Beta and gamma functions and relationship between them. Applications of single integration to find volume of solids and surface area of solids of revolution. Double integral, change of order of integration, double integral in polar coordinates, applications of double integral to find area enclosed by plane curves, triple integral, change of variables, volume of solids, Dirichlet’s integral.

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### Author : Mrs. Leena

This course has been prepared under the supervision of Mrs. Leena. She is a passionate and result-oriented teacher with more than 6 years of teaching experience.

She has done her MSc. with Mathematics from Maharishi Dayanand University, and currently pursuing PhD in the same field which marks her knowledge and learning in the subject. She has taught hundreds of MDU students and has simplified subject and made it very interesting, learning with Fun and Easy for the students