M.Phil Mathematics

SEMESTER-I


Advanced Functional Analysis

Contraction mapping theorem and its applications to differential equation,
integral equation and system of linear equations. Equicontinuity, Arzla-Ascoli
theorem and its application to differential equations. Weierstrass’s
Approximation Theorem, Stone-Weierstrass’s Approximation Theorem. Semicontinuity
and its applications to Arclength.

Advanced Solid Mechanics

Non-Linear Theory
Deformation gradient tensor. Decomposition of a deformation stretch and
rotation. Strain tensors. Strain-displacement relations. Principal stretches.
Strain invariants. Length and angle changes. Deformation of volume and
surface elements. Homogeneous deformation-dilation, simple extension and
simple shear plane strain.