MA207

Real Analysis and Partial Differential Equations ( 3 -1- 0 ) 4

Real number system. Sets, relations and functions. Properties of real numbers. Numerical sequences. Cauchy sequences. Bolzano-Weierstrass and Heine-Borel properties.

Functions of real variables. Limits, continuity and differentiability. Taylor’s formula. Implicit and inverse function theorems. Extrema of functions.

Reimann integral. Mean value theorems. Differentiation under integral sign. Improper and multiple integrals. Change-of-variables formula.

Sequences and series of functions. Pointwise and uniform convergence. Power series and Taylor series.

Laplace and Helmholtz equations. Boundary and initial value problems. Solution by separation of variables and eigen function expansion.

References:

Guenther,R..B. & Lee,J.W., Partial Differential Equations of Mathematical Physics and Integral Equations, Prentice Hall.

Kreiszig,E., Advanced Engineering Mathematics,John Wiley.

Mattuck,A., Introduction to Analysis, Prentice-Hall.