Foundations of Numerical Methods    
(Dr. Carla Figueira de Morisson Faria, term: October 2005 - December 2005)

Literature 

  • P. Brandimarte, "Numerical Methods in Finance" (Wiley, 2002)
    (very much MatLab based, and has a lot of financial applications, but does not have a strong emphasis on the numerical methods.)

 

  • R. Burden and J.D. Faires, "Numerical Analysis" (Brookes/Cole, 2001)
    (very complete, very clear, has all the methods (apart from Monte Carlo)-- more for scientists and engineers, but also has economics applications-- and some editions come with a CD with software in many programming languages--fortran, matlab, mathematica and C++--useful for the future as well!)

 

  • W.H. Press, S.A. Teukolsky, W. T. Vetterling, B.P. Flannery, "Numerical Recipes"(Cambridge University Press, 1986, 1992)
    (more for people working on fundamental science and with some pre-knowledge of the methods, but for some reason the syllabus at the CASS--even with the subdivisions--seems to have been copied from there. PLEASE NOTE: It has some material on random numbers and     Monte Carlo integration which is quite compact and may be useful)

 

  • J.H. Matthews, K. D. Fink, "Numerical Methods using Matlab"(Pearson Prentice Hall, 2004)
    (very clear, very complete and has all the methods (again apart from     Monte Carlo); in fact, in the style of Burden and Faires, but the maths is more formal, and it is more Matlab-based)

 

  • S. Wolfram, "The Mathematica Book" (Wolfram Research Inc.1988, 1991, 1996, 1999) (the built-in help function is also quite nice)
    (it is a very nice book for consulting, but you should only buy it if you intend to use Mathematica very intensively)


Please note:

  • You don't have to buy all these books!!This list is mainly for reference and one can, in principle, also borrow them from the library (I would strongly recommend that you have a look at them before making any purchase or taking a definitive decision)

 

  • There may be additions/deletions from the literature list

 

Programming languages:

    1. Mathematica (most recent version: 5.3; version used: 5.0; version at the CASS: 2.2)

 

2.     Matlab (most recent version: 7.1; version used: 7.1; version at the CASS: ???(around 2.0))

Lecture notes (will be constantly updated and/or improved):

  1. Preliminaries: Programme organization and control structures, Error, Accuracy and Stability
  2. Root finding and nonlinear sets of equations
  3. Solution of linear algebraic systems
  4. Interpolation and Extrapolation
  5. Integration of functions
  6. Random numbers
  7. Partial differential equations

 

Examples of codes:

  1. Examples from Lecture 1: mathematica file ;   print out

 

2.     Examples from Lecture 3 and Sheet 1:

1.     Nested if statements

2.     Nested do loops

3.     Mixed if statements and do loops

4.     Bisection

5.     Secant

Exercise sheets and solutions (pdf files):

6.     Sheet 1    Solution

7.     Sheet 2    Solution

8.     Sheet 3    Solution

9.     Sheet 4    Solution

10. Sheet 5    Solution

11. Sheet 6    Solution

12. Sheet 7 (with solutions)

 

Coursework      Solution

Deadline: 14/12/2005, noon

Please note:

The solution to question 1(a), which has led to some controversy, has been corrected. For the new version check the solution.
The coursework will no longer be accepted after the solution has been put on the web (19:20, December 14).

Surgery Hours: Mondays from  15:00 to 16:00 (call/write before to confirm)