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SYLLABUS
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Numerical methods for partial
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Numerical methods for partial
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1 INTRODUCTION
Contents
1 INTRODUCTION
1.1 About this course
1.2 Differential Equations
1.3 Prototype problems
1.4 Numerical discretization
1.5 Computer quiz
1.6 Exercises
1.7 Further reading
1.8 Interactive evaluation form
2 FINITE DIFFERENCES
2.1 Explicit 2 levels
2.2 Explicit 3 levels
2.3 Lax-Wendroff
2.4 Leap-frog, staggered grids
2.5 Implicit Crank-Nicholson
2.6 Computer quiz
2.7 Exercises
2.8 Further reading
2.9 Interactive evaluation form
3 FINITE ELEMENT METHOD
3.1 Mathematical background
3.2 An engineer's formulation
3.3 Numerical quadrature
3.4 Implementation and solution
3.5 Linear solvers
3.6 Variational inequalities
3.7 Computer quiz
3.8 Exercises
3.9 Further Reading
3.10 Interactive evaluation form
4 FOURIER TRANSFORM
4.1 FFT with the computer
4.2 Linear equations.
4.3 Aliasing, filters and convolution.
4.4 Non-linear equations.
4.5 Computer quiz
4.6 Exercises
4.7 Further Reading
4.8 Interactive evaluation form
5 MONTE-CARLO METHOD
5.1 Monte Carlo integration
5.2 Stochastic theory
5.3 Particle orbits
5.4 A scheme for the advection diffusion equation
5.5 When should you use Monte Carlo methods?
5.6 Computer quiz
5.7 Exercises
5.8 Further Reading
5.9 Interactive evaluation form
6 LAGRANGIAN METHOD
6.1 Splitting advection from the rest
6.2 Cubic-Interpolated Propagation (CIP)
6.3 Non-Linear equations with CIP
6.4 Quiz
6.5 Exercises
6.6 Further Reading
6.7 Interactive evaluation form
7 WAVELETS
7.1 Remain a matter of research
8 THE JBONE USER MANUAL
8.1 Source code & installation
8.2 Program execution
8.3 Program structure & documentation
8.4 An object-oriented example: Monte Carlo in JBONE
8.5 Interactive evaluation form
9 PROBLEM BASED LEARNING ENVIRONEMENT
9.1 Typesetting with TEX
9.2 Programming in JAVA
9.3 Parameters and switches in HTML
9.4 Interactive evaluation form
10 COURSE EVALUATION AND PROJECTS
10.1 Interactive evaluation form
10.2 Suggestions for one-week projects