MATHS III
MA 231 No. of hrs/week = 04
Differential equations - basic concepts and definitions, formation of differential equation by eliminating arbitrary constants.
Solutions of first order differential equations by separation of variable method, solution of exact equations, evaluation of integrating factors, solution of first order linear differential equations, Bernoulli's equation, solution by inspection, application of first order differential equations. Some simple numerical methods for solutions of first order equations.
Higher order linear differential equations with constant coefficients, homogeneous and nonhomogeneous differential equations, solution method of variation of parameters and inverse differential operator method, solving nonhomogeneous equations, method of undermined coefficients.
Application of second order differential equations - vibration of spring.
Introduction to Laplace transforms, transforms of elementary functions, periodic functions, Step functions. Dirac Delta functions, inverse transforms, convolution theorem, solutions of initial value problems by Laplace transforms method.
Complex variables - Analytic functions, Cauchy - Riemann equations, Harmonic functions, Line integrals, Cauchy's integral theorem, Cauchy's integral formula. Laurent series, Residue calculus.
Partial differential equations - basic concepts, solutions of simple partial differential equations, method of separation variable and indicated transforms to solve partial differential equations.
REFERENCE:
1. A short course in Differential Equations by Earl.D.Rainville and Phillip E.Bedient (1989) -
Macmillan Publishers.
1. Higher Engineering Mathematics - B.S.Grewal, 23rd Edition, Khanna Publishers.
2. Numerical Methods for Engineers - S.S. Sastry. PHI publishers
3. Advanced Engineering Mathematics - Erwin Kreyszig, 7th edition, John Wiley & Sons
4. Complex Variables - Murrey R Speigel , Schaum Series