William Lee

MS6021 Scientific Computation

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Teaching
Stout beer

MA4005 MS4414

Timetable

Mondays5pmC2062
Tuesdays3pmC2062
Thursdays11amSR2030

Office hours

Office hours for this course are 4pm Mondays A2016a.

Exams

The course will be examined by two small projects which will be set in week 5 and week 11. Students will have two weeks to complete the projects and be expected to hand in a one page report and working code. Each project will count for 50% of the marks for this course.

Acceptable collaboration: for the projects it is acceptable to discuss ideas and algorithms, but actual code must be developed independently.

Syllabus

Scientific computation using FORTRAN and Matlab.

Details: Introduction to Matlab and Fortran. Datatypes and control structures. Functions, proceedures, subroutines and modules. Input and output. One dimensional root finding. Linear algebra review. Simple linear systems. Factorisations. Overdetermined and underdetermined systems. Singular value decomposition. Sparse systems. Eigensystems review. Solving eigensystems. Multidimensional nonlinear root finding. Optimisation. Ordinary differential equations review. Runge-Kutta algorithms. Boundary layer problems. Singular pertubations and boundary layers. Stiff solvers. Richardson extrapolation. Partial differential equations review. Parabolic and elliptic equations. Hyperbolic systems. Introduction to mathematical modelling. Dimensional analysis and nondimensionalisation. Asymptotic simplification. Matlab PDE tolbox. NAG library. Making your own toolbox.

Textbooks

  • Higham and Higham. Matlab Guide.
  • Chapman. Introduction to Fortran 90/95
Other relevant texts
  • W. H. Press et al. Numerical Recipes.

Lectures

Lecture 1. Lecture 2. Lecture 3. Thomas algorithm. monopoly.m, monopoly_output.txt.

Worksheets

Worksheet 1. Worksheet 2. Worksheet 3. Worksheet 4. Worksheet 5. Worksheet 6.

Links

Matlab.

Octave.
Open source numerical computing environment with matlab like syntax.

Fortran 95 language summary.

Matlab quick reference
(12 pages, PDF).

Matlab cheat sheet
(1 page, PDF).

Fortran 90 refernce card
(2 pages PDF).

NAG
Numerical Algorithms Group.