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

SYLLABUS

Semester III - Allied - Mathematics for Statistics I

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

Sets, Operations on sets - real valued functions - countability - real numbers bounds, supremum and infimum - sequence of real numbers - limit inferior and limit superior and limits of real sequences - limit theorems - summability of convergence and divergence of series with non-negative terms - alternating series - conditional and absolute convergence - rearrangement of series - test for absolute convergence - summation by parts.

Continuity and derivative - the derivative of a real function - mean value theorems Taylor's theorem - concept of uniform continuity - Riemann integrals, sufficient condition for Reimann integrability, Darboux theorem, fundamental theorem of integral calculus - first mean value theorem - concept of Riemann Stieltijes integral its existence and properties.

Improper and infinite Riemann integrals - Gamma beta integrals - multiple integrals - their evaluations using transformations of variables - simple example of multiple integrals relevant to statistical methods. Laplace Transformation (LT) - definitions, LT of the function t, eat, cos at, sin at eat cos bt. eat sin bt, Transform f' (t), f" (t) - inverse LT relating to the above standard functions.

Books for Study & Reference: