Description:
| Aims: The aims of this unit are to introduce students to the practical use of computer modelling as a complement to theoretical and experimental solution of physical problems, to introduce a contemporary package available to the modeller, and to explore topics in physics that lend themselves to computational modelling.
Learning Outcomes: After taking this unit the student should be able to:
* identify the strengths and weaknesses of a computational approach to modelling;
* demonstrate a practical knowledge of the Maple computer algebra system;
* construct Maple worksheets to analyse physical problems;
* use computational modelling to perform in-depth investigations into selected topics;
* explain the methodology, relevant issues and output of the investigations performed.
Skills: Written Communication T/F A, Numeracy T/F A, Data Acquisition, Handling, and Analysis T/F A, Information Technology T/F A, Problem Solving T/F A.
Content: Introduction to computational modelling as a means of gaining physical insight: Contemporary applications of computer modelling.
Computer algebra packages as a scientific computer environment: Problems solved effectively in this environment and those that are not.
Practical introduction to Maple: Data structures; constants, variables, expressions, functions, lists, arrays, sets and strings. Basic calculus; integration, differentiation, limits, series, sums. Standard functions. Graphics; x-y plots, parametric plots, 3d plots, plot objects, animation. Data i/o. Solving equations; symbolic, numerical, systems of equations, ordinary differential equations. Linear Algebra; vectors, matrices, addition, subtraction, multiplication, dot & cross products, determinant, trace, eigenvalues, eigenvectors. Programming; logic, loops, procedures.
Exercises and projects based upon construction of Maple worksheets: Examples may include: Bound state problems in quantum physics by shooting method, basis set expansion. Coupled oscillators; normal modes, time-series analysis. Planetary dynamics; orbit prediction, three-body problems, chaotic motion. Electrons in molecules and solids; linear combination of atomic orbitals, energy levels/bands, bonding/antibonding. Fractals; generation, characterisation via fractal dimension. Stochastic systems; random walkers, diffusion limited aggregation. Dynamics of non-linear systems; logistic map, Lorentz equations, limit cycles, chaos. Percolation; cluster counting algorithms, percolation threshold.
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