MATHEMATICS – II

Credits	Periods			Exam Hrs.	Sessional Marks	Exam Marks	Total Marks
	Theory	Tutorial	Lab
4	3	1	-	3	30	70	100

Linear Algebra

Rank of a matrix, Eigen values, Eigen vectors of a Matrix, Cayley Hamilton theorem, Consistency of equations, Matrix invertion, Gaussian elimination scheme, Cholesky factorization, Jacobi and Gauss-Seidal iterative methods for solving simultaneous equations, Eigen value solution using forward iteration, Inverse itrration, Hermitian and skew Hermitian forms, Unitary Matrix, Functions of a Matrix, Quadratic forms and conical forms.

Differential Equations of First Order and its Applications

Formation of differential equation, Solution of a differential equation, Geometrical meaning, Equations of the first order and first degree, Variables separable, Homogeneous equations, Linear equations, Bernoulli’s equation, Exact equations, Equation reducible to exact equations, Equations of the first order and higher degree, Calirut’s equation, Geometric applications, Orthogonal trajectories, Physical applications, Simple electric circuits, Heat flow, Chemical applications, Newton’s law of cooling.

Linear Differential Equations

Higher order linear differential equations with constant coefficients, Deflection of beams, Simple harmonic motion, Oscillatory electric circuits.

Series Solution of Differential Equations

Frobenis method, Special function as solution from series, Bessel equation, Bessel functions of first and second kind, Equation reducible to Bessel’s equations, Legender’s equations, Legender polynomial, Rodrigues formula, Generating functions, Recurrence relation, Orthonogolity relation for Bessel functions and Legendre polynomial.

Laplace Transforms

Transforms of elementary functions, Properties of Laplace transforms, Existence conditions, Inverse transforms, Transform of derivatives, Transform of Integrals, Multiplication’s by ‘t’ – division by ‘t’, Convolution theorem, Application to ordinary differential equations and simultaneous linear equations with constant coefficients, Unit step function, Impulse functions and periodic functions.

Textbooks:

Theory of Matrices by Shantinarayanan

Higher Engineering Mathematics by B.S. Grewal

Advanced Mathematics for Engineering Students, Vol. 2 by Narayana, Manieavachgon Pillay, Ramanaiah

Reference Books:

Higher Engineering Mathematics by M.K. Venkataraman

Advanced Engineering Mathematics by Erwin Kreyozig

Engineering Mathematics by P.P. Gupta

A textbook on Engineering Mathematics by N.P. Bali