AE01 MATHEMATICS—I

1 Multivariate Calculus 18 hours

1.1 Limit and continuity of functions of several variables, Partial derivatives of one and higher order.

1.2 Total differential and its application to approximations and errors, Implicit and homogeneous functions, Euler ‘s theorem.

1.3 Taylor ‘s theorem and series of function of several variables, Maxima and minima of functions of two variables, Method of Lagrange multipliers.

1.4 Double and triple integrals, Change of order of integration, Application to computation of volumes and surface areas of simple solids.

II [2]

2 Ordinary Differential Equations 16 hours

2.1 Separable, homogeneous, exact and linear first order differential equation, Bernoulli ^‘s equation.

2.2 Homogeneous and non-homogeneous linear differential equation of second order, method of variation of parameters and method of undetermined coefficients, Euler - Cauchy equation, Higher order linear homogeneous differential equation with constant coefficients.

I [1, 2]; II [4, 5]

3. Matrices 16 hours

3.1 Addition, scalar multiplication and product of matrices, Elementary row operations.

3.2 Rank and inverse of a matrix, Consistency and solution of a system of linear equations.

3.3 Eigenvalues and eigenvectors, Hermitian, skew-Hermitian and unitary matrices, Diagonalization of matrices.

I [6, 7]; II [3]

4 Special Functions 10 hours

4.1 Power series solution of O.D.E., Series solution of Legendre and Bessel Equations.

4.2 Legendre polynomials and their properties, Bessel function of first kind and their properties, Recurrence relations for Bessel functions.

I [4]; II [6, 7]

Text Books

I. Erwin Kreyszig, “Advanced Engineering Mathematics” 8^th edition, John Wiley and Sons (Asia) --- 2000

II. R. K. Jain and S. R. K. Iyengar, “Advanced Engineering Mathematics”, Narosa Publishing House --- 2002

Reference Books

1. Peter V. O’neil, “Advanced Engineering Mathematics” 4^th edition Brooks / Cole Publishing Company ---1995