B.Sc Curriculum - Madras Christian College

Differential Equations, Laplace Transforms and Fourier Series
Part III (a) – Major Credits: 4
Semester II - Paper III Hours/ Cycle: 5
Unit I Hours: 12
Ordinary Differential Equations:Introduction to ordinary differential equations - First order
but of higher degree equations – solvable for p, solvable for x, solvable for y – Clairaut’s form –
simple problems. Second order equation with constant coefficient with particular integrals for
e ax x m , e ax sin mx, e ax cos mx.
Chapter 1: Sections 5.1 – 5.4, 6; Chapter 2: Sections 1, 2, 3, 4
Unit II Hours: 12
Second order differential equation with variable coefficients ax 2 d 2 y/dx 2 + bxdy/dx + cy = g(x) –
method of variation of parameters.
Chapter 2: Sections 8, 10
Unit III Hours: 18
Laplace Transforms: Introduction - Laplace transforms – inverse transform -Application of
Laplace to solution of first and second order linear differential equation with constant
coefficients.
Chapter 5: Sections 1 - 8
Unit IV Hours: 15
Partial Differential Equations: Introduction to partial differential equations (PDE) - Formation
of PDE by eliminating arbitrary constants and arbitrary functions – complete integral – singular
integral – general integral - Standard types f(p,q)=0; f(x,p,q)=0; f(y,p,q)=0; f(z,p,q)=0;
f(x,p)=f(y,q) – Clairaut’s form and Lagrange’s equation Pp+Qq = R . (Simple Problems)
Chapter 4: Sections 1, 2, 3, 5.1 – 5.4, 6
Unit V Hours: 18
Fourier Series: Introduction to Fourier series - Definition – Examples of Fourier series – Even
or odd functions – Fourier series for even and odd functions – Half range expansions. (Simple
problems).
Chapter 6: Sections 1, 2, 3, 4, 5
Treatment and content as in
Calculus, Volume 3, S. Narayanan and T.K. ManicavachagamPillai, S. Vishwanathan
Publications, 2010.
References
1. Engineering Mathematics Volume 3, Dr. M.K. Venkataraman,The National Publishing
Company, 2001.