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

SYLLABUS

Semester I - Allied Mathematics - Paper I
(For Bio-Chemistry, Physics, Chemistry, Electronics Science, Geophysics and Computer Science Major only)

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

ALGEBRA:

Partial fractions, binomial, exponential and logarithmic series (without proof) summation and approximation-simple problems.

THEORY OF EQUATIONS:

Polynomial equations with real coefficients, irrational roots, complex roots, symmetric functions of roots, transformation of equation by increasing or decreasing roots by a constant, reciprocal equations. Newtons method to find a root approximately - simple problems.

MATRICES:

Symmetric, skew-symmetric, orthogonal and unitary matrices, rank of a matrix, consistency of equations, eigen values and eigen-vectors, Caley-Hamilton theorem (without proof) - verification Computation of inverse matrix using carey - Hamilton theorem.

FINITE DIFFERENCES:

Operators E, difference tables, Newton's forward and backward interpolation formulae, Lagrange's interpolation formulae.

TRIGONOMETRY:

Expansions of sinnθ, cosnθ, tannθ expansions of sinnθ, cosnθ, tannθ. Hyperbolic and inverse hyperbolic functions. Logarithms of complex numbers.

DIFFERENTIAL CALCULUS:

n^th derivatives, Leibnitz theorem (without proof) and applications, Jacobians, concepts of polar co-ordinates. Equations of straight line, circle and conic. Curvature and radius of curvature in Cartesian co-ordinates, maxima and minima of functions of two variables, Lagrange's multipliers - Simple problems.