Applied Numerical Mathematics (CH3131a)

Course Prerequisites

• Course Prerequisites
  Basic notions of calculus of a function in one variable (derivative, integral, Taylor sequences) and more variables (partial derivatives, surface and volume integrals), Fourier series and numerical methods (difference formula and quadrature);
  Link to the course 4052NUMTEY taught be Ferdinand Grozema.
  Expand this part to a refreshers and/or online courses?

Two Day Matlab Introduction

• Introduction slides
  Introduction slides.pdf
  
  
• Matlab Introduction
  Getting Started in Matlab Please work yourself through the tutorial step by step.
  More introductory material on Matlab Work your way through this more advanced introduction in case finished with the previous one.
  Additional exercises
  Non-Linear Heat Transfer in a Thin Plate (Advanced students only!) Discover this amazing tool when done with the introductory material.
  
  

Part 2 of the Course taught by D. Lahaye

Boundary and Initial Value Problems

• One-dimensional elliptic boundary value problem:
  problem statement, difference approximation to the derivative, stencil, matrix, handling of Dirichlet and Neumann boundary conditions, linear system solve recap on sparse matrices and linear systems .
• One-dimensional (space) parabolic (time) boundary value problem:
  problem statement, difference approximation to the space and time derivative, semi-discrete linear system, time integration recap on ODEs.
• Two-dimensional elliptic boundary value problem:
  as one-dimensional case plus construction of discrete operator using the tensor product, extension with a convective term
• Iterative Methods for Linear Systems:
  Jacobi, Gauss-Seidel, CG, PCG and GMRES
• not in this course :
  hyperbolic PDEs

Fitting Problems to Data

• Linear interpolation (interp), polynomial interpolation (polyfit) and splines (spline)
• Continuous and discrete Fourier transform
• Linear and Non-Linear Least squares fit
  system of normal equations in linear case (beware what linear refers to), sum of squares minimizes by fminunc in the non-linear case.

Optimization Methods

• Unconstrained gradient-based:
  one-dimensional case, multi-dimensional case, recap on root finding Newton's method
• Derivative free methods: genetic algorithms, selection, cross-over (or mating) and mutation (ga, traveling_salesman_demo)
• Constrained gradient-based

Tutorials and Homework Assignments

Exam Matrix

Previous Exams

Back to Domenico Lahaye's homepage

This page is maintained by Domenico Lahaye.