Acharya Nagarjuna University, Andhra Pradesh, Electronics and Communication engineering Semester 1, MATHEMATICS I Syllabus

Unit I:Matrix Operations and Solving Systems of Linear Equations
Rank of a matrix by echelon form, solving system of homogeneous and non-homogeneous
equations linear equations. Eigen values and Eigen vectors and their properties, Cayley-Hamilton
theorem (without proof), finding inverse and power of a matrix by Cayley-Hamilton theorem,
diagonalisation of a matrix, quadratic forms and nature of the quadratic forms, reduction of
quadratic form to canonical forms by orthogonal transformation.

Unit II: Mean Value Theorems
Rolle’s Theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem, Taylor’s and
Maclaurin theorems with remainders (without proof);
 

Unit III: Multivariable calculus
Partial derivatives, total derivatives, chain rule, change of variables, Jacobians, maxima and
minima of functions of two variables, method of Lagrange multipliers.

Unit IV: Double Integrals
Double integrals, change of order of integration, double integration in polar coordinates, areas
enclosed by plane curves.

Unit V: Multiple Integrals and Special Functions 
Evaluation of triple integrals, change of variables between Cartesian, cylindrical and spherical
polar co-ordinates, Beta and Gamma functions and their properties, relation between beta and
gamma functions.

Textbooks:
1. Erwin Kreyszig, Advanced Engineering Mathematics, 10/e, John Wiley & Sons, 2011.
2. B. S. Grewal, Higher Engineering Mathematics, 44/e, Khanna Publishers, 2017.
References:
1. R. K. Jain and S. R. K. Iyengar, Advanced Engineering Mathematics, 3/e, Alpha Science
International Ltd., 2002.
2. George B. Thomas, Maurice D. Weir and Joel Hass, Thomas Calculus, 13/e, Pearson
Publishers, 2013.
3. Glyn James, Advanced Modern Engineering Mathematics, 4/e, Pearson publishers, 201.