Part II Computational Projects Manual (July 2012 Edition)

Please note: this edition is valid only for the Part II academic year 2012/13.

Background

This is the on-line version of the Part II Computational Projects Manual for the academic year 2012/13.

It is available in Portable Document Format (PDF): most computers will be able to read this format automatically, but if not then you should download Adobe Reader. In cases of difficulty, the CATAM demonstrators can help you display or print the files.

Misprints that are discovered in the manual will be announced via CATAM News. The on-line version will be corrected, and so should be up to date. However, it should always be read in conjunction with CATAM News.

The unit allocation for each project is given in brackets after its title. Some of the projects require data files, which can be found here.

Complete Manual

All Sections

Manual by Section

Contents

Introduction

1. Numerical Methods

1.3 Parabolic Partial Differential Equations (6)

1.8 Hyperbolic Partial Differential Equations (7)

2. Waves

2.7 Soliton Solutions of the KdV Equation (7)

2.10 Phase and Group Velocity (8)

3. Fluid and Solid Mechanics

3.1 Boundary Layer Flow (6)

3.4 Convection of Magnetic Flux (10)

4. Dynamics

4.3 The Rotating Top (6)

5. Quantum Mechanics

5.3 Bound State Energies for One-Dimensional Potentials (9)

6. Electromagnetism

6.1 Diffraction Pattern due to a Current Strip (7)

7. Mathematical Methods

7.5 Padé Approximants (8)

7.6 Insulation (10)

9. Dynamic Programming

9.1 Policy Improvement for a Markov Decision Process (4)

9.3 Protein Comparison in Bioinformatics (8)

10. Statistics

10.14 The Google PageRank Algorithm (5)

10.15 Variable Selection and the Bias-Variance Tradeoff (8)

11. Statistical Physics

11.3 Classical Gasses with a Demon Algorithm (8)

12. Nonlinear Dynamics & Dynamical Systems

12.2 Bifurcations in Differential Equations (10)

12.8 A Nonlinear Map and the Dynamics of Hydrogen Atoms in Electric Fields (7)

14. General Relativity

14.1 Particle or Photon Orbits near a Black Hole (8)

14.6 Isolating Integrals for Geodesic Motion (8)

15. Number Theory

15.1 Primality Tests (9)

15.3 Positive Definite Binary Quadratic Forms (9)

15.8 Elliptic Curves (8)

16. Algebra

16.1 The Galois Group of a Polynomial (7)

16.8 The Character Table of a Finite Group (9)

17. Combinatorics

17.4 Connectivity (7)

17.5 Matchings (6)

19. Communication Theory

19.2 Information Content of Natural Language (4)

20. Probability

20.1 The Percolation Model (7)

20.2 Importance Sampling and Fast Simulation (5)

23. Astrophysics

23.4 Stellar Structure (8)

23.8 Chaos in the Encounter Map (8)

This page was last modified in July 2012.