SYLLABUS FOR SEMESTER I & II

2K6 EN101: ENGINEERING MATHEMATICS I

MODULE - I : ORDINARY DIFFERENTIAL EQUATIONS (16hrs)

A brief review of the method of solutions of first order equations - Seperable, homogenous and linear types - exact equations - orthogonal trajectries - General linear second order equations - homogenous linear equation of the second order with constant coefficients - fundemental system of solutions - method of variation of parameters - cauchy's equation.

MODULE - II : LAPLACE TRANSFORMS (17hrs)

Gamma and beta functions - definitions and simple properties - Laplace transform - Inverse transform - Laplace transform of derivatives and integrals - shifting theorem - differentiation and integration of transforms - transforms of unit step function and impulse function - transforms of periodic functions - solutions of ordinary differntial equation using transforms.

MODULE III : VECTOR DIFFERENTIAL CALCULUS ( 18 hrs)

Functions of more than one variable – Idea of partial differentiation – Euler’s theorem for homogenous functions – chain rule of partial differentiation – application in errors and approximation – vector function of single variable – differentiation of vector functions – scalar and vector fields – gradient of a scalar field – divergence and curl of vector fields – their physical meanings – relations between the vector differntial operators.

MODULE IV : FOURIER SERIES AND HARMONIC ANALYSIS (15 HRS )

Periodic functions – Trignometric series – Euler formula – Even and odd functions – functions having arbitrary period – half range expansions – Numerical method for determining Fourier coefficients – Harmonic analysis.