CCMAS Course Search

Sylow theorems; direct products; fundamental theorem of finite Abelean groups; field of quotients; Euclidean rings; Polynomial rings over commutative rings; inner product spaces; theory modules; sub-modules; quotient modules; modules over principal ideal domains; Applications finitely generated Abelean group fields extension fields elements of Galois theory; solvability radicals

Mathematical Methods of Deterministic or Stochastic aspects of Biological Systems e.g.; Population dynamics; species interaction malaria epidemic; etc

Categories; functors; natural-transformation; Functor categories; limits; Products and coproducts; Pushbacks and Pushouts; adjoint functors; Normal and exact categories: Abelian categories; quotient categories

Periodic functions; Weierstrass functions; elliptic curves; Modular forms; Algebraic functions; Riemann surfaces; Covering surfaces; covering transformations; Discontinuous groups of linear transforms; automorphic forms

Dynamical Systems in the State Space; Reachability; Stabilizability and Detectability; Equivalence of Controllability and Pole Assignability; The Calculus of Variations; Generalized Huygen's Principle; The Algebraic Riccati Equation; Lyapunov Stability; Applications to Economic Stabilization; Planning; Manpower Development; Resource Allocation under Constraints; etc; Case Studies

General Manifolds; Topics such as smooth mappings; Immersions; submersions; transversality; intersection theory; vector fields of manifold; orientation of manifolds: Gaussian curvature; Riemannian manifolds; differential forms; integration on manifolds tensors and connections are included

Formulation of the Linear Theory; General Theorems; Plane Strain and generalised Plane stress; Airy's solution: Papkovich-Neuber representation; Basic singular solutions; Boundary-value and Boundary-initial value problem

Maxwell's Equations; Electromagnetic Potentials: Tensor Calculus; Stress and Energy; Electro Static and Magnetostatics; plane Waves; cylindrical and Spherical waves; Boundary Value Problems; Relativistic Kinematics and Lorentz Transformation: Electrodynamics

Introduction to the Finite Element Method: Formulation of the Finite Element Method using the Principle and Virtual Displacement; General Isoparametric Formulation; and Variational Techniques; Generalization of the theory; Application of the Finite Element Method to the Solution of Engineering Problems e.g.; in Solid Mechanics; Heat Transfer; Fluid Dynamics and Mass Transfer; Development of appropriate Computer Programme; Case Studies

Thermodynamics Compressible flow; waves; shocks; supersonic flow; Boundary layer Theory; stability; Turbulence