Applied Mathematics 3
Coordinator: Prof J. Larena
Our third year program in applied mathematics is made of 4 separate courses (2 in each semester).
This is a common course required by both MAP and MAT majors. Revision of complex numbers, Cauchy- Riemann equations, analytic and harmonic functions, elementary functions and their properties, branches of logarithmic functions, complex differentiation, integration in the complex plane, Cauchy’s Theorem and integral formula, Taylor and Laurent series, Residue theory and applications. Fourier Integrals.
Partial Differential Equations:
First-order partial differential equations, classification of second-order equations, construction and behaviour of solutions, the method of characteristics, shocks and nonlinear phenomena, maximum principles, energy integrals, Fourier transform methods.
Differential equations and iterated maps as dynamical systems. Geometric representation of trajectories. Limiting behaviour of trajectories in linear and nonlinear systems. Equilibria of linear systems and linearisation of hyperbolic equilibria of nonlinear systems. Invariant sets and attractors. Bifurcation and chaos in nonlinear maps. Notions of stability. Some applications of dynamical systems in modeling.
Systems of non-linear equations, polynomial interpolation, cubic splines, numerical linear algebra, numerical computation of eigenvalues, numerical differentiation and integration, numerical solution of ordinary and partial differential equations, finite differences,, approximation theory, discrete Fourier transform.
Last Modified: Mon, 08 Feb 2016 13:05:06 SAST