University of Madras - Syllabus of Bachelor of Science (BSc) Mathematics - Semester II - Allied Mathematics - Paper II

(For Physics, Chemistry, Bio-Chemsistry, Geophysics, Computer Science & Electronic Science Major only)

UNIVERSITY OF MADRAS

B.Sc. DEGREE COURSE IN MATHEMATICS

SEMESTER SYSTEM WITH CREDITS

(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester II - Allied Mathematics - Paper II

(For Physics, Chemistry, Bio-Chemsistry, Geophysics, Computer Science & Electronic Science Major only)

Duration of Examination: 3 hrs

Maximum Marks: 100

Credits: 4

INTEGRAL CALCULUS:

Integration of irrational, trigonometric functions, Bernoulli's formula for integration by parts, reduction formulae, properties of definite integral and simple problems, Evaluation of double, triple integrals, simple applications to area, volume and centroid, Fourier series for functions in (0, 2π, -π, π)

ORDINARY DIFFERENTIAL EQUATIONS:

First order and higher degree equations solvable for p, y, x.

Second order dineen differential equations with constant coefficients;

a + b + cy = θ

where = x

^{m}, e

^{αx} x

^{m}. e

^{αx} sinmx, e

^{αx} cosmx

PARTIAL DIFFERENTIAL EQUATIONS:

Formation, complete integrals and general integrals, four standard types of lagrange's equations.

LAPLACE TRANSFORMS:

Laplace transformations of standard functions and simple properties, inverse laplace transforms
Application to solution of linear differential equations of order 1 and 2 - simple problems.

VECTOR ANALYSIS:

Scalar point functions, vector point functions, gradient, divergence, curl, directional derivatives, normal to a surface. Line and surface integrals; Gauss, Stoke's and Green's theorems (without proofs). Simple problems on these.

REFERENCE:

1. Allied maths volumes 1 and 2 by Prof. P. Duraipandian and Dr.S.Udayabaskaran, Muhil publishers, Chennai.

2. Ancillary mathematics volume 1 and 2 by P.Balasubramanian & K.G.Subramanian.

3. lntegrai calculus and differential equations by Dipak Chatterjee, Tata Mcgraw Hill publishers co ltd.,

4. Ancillary mathematics by S.Narayanan and others, S.Viswanathan publishers.

5. Allied Mathematics by Dr. P. R. Vittal (Margham Publications).