UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN MATHEMATICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - Paper V - Differential Equations and Laplace Transforms

Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4

First order but of higher degree equations - solvable for p, solvable for x, solvable for y, Clairaut's form - simple problems.

Second order equations with constant coefficients with particular integrals for e^ax-x^m, e^axsinmx, e^axcosmx.

Second order differential equations with variable coefficients ax² d²y/dx² + bx dy/dx + cy = q (x);

method of variation of parameters; Total differential equations, simple problems.

Partial Differential Equations :-

Formation of P.D.E by eliminating arbitrary constants and arbitrary functions; Complete Integral; Singular Integral; General Integral; Charpit's method and the 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.

Laplace Transform; Inverse Laplace Transform (usual types); Applications of Laplace Transform to solution of first and second order linear differential equations (constant coefficients) and simultaneous linear differential equations - simple problems.

Reference Books :-

1. Engineering Mathematics Volume 3: M. K. Venkataraman (National Publishing Co.)

2. Engineering Mathematics Volume 3: P. Kandasamy and others (S. Chand and Co.)

3. Integral Calculus and differential equations : Dipak Chatterjee (TATA McGraw Hill Publishing company ltd.)

4. Advanced Engineering mathematics: Erwin Kreyszig (John Wiley and sons New York 1999)

5. Calculus: Narayanan and others (S. Viswanathan publishers)

6. Differential Equations & Integral Transforms: Dr. S. Sudha (Emerald Publishers).