MATH49111 - 2010/2011
Specification
Aims
To develop the basic knowledge required to translate some common mathematical concepts used in scientific problem solving into an object-oriented programming language (in this case C++). Students will use a combination of writing their own codes, together with the use of scientific libraries (such as NAG).
Brief Description of the unit
The course will teach the syntax and logical structure of C++ programming and object-oriented development with no assumed prior knowledge. The emphasis is placed on the implementation of common mathematical tasks/algorithms in C++. The students must select two miniprojects from a list of available topics in applied maths. The projects will be assessed by a written report and a demonstration/oral description of the code.
Only a limited number of places are available on this course.
Learning Outcomes
On successful completion of this module students will be able to
- understand the basic structure, content and syntax of a C++ program,
- appreciate the generic concepts underlying the object oriented programming model,
- develop a C++ program that solves a problem in physical applied mathematics,
- debug a C++ program and validate results in the context of a mathematical problem.
Future topics requiring this course unit
None.
Syllabus
- Introduction to C++ programming language.
- Compiling/running/debugging programs.
- Data types - initialisation, scope, precision, input/output.
- Using functions and control structures to reproduce simple algorithms.
- Intrinsic and user-defined functions; call by value, call by reference, the const qualifier.
- Discussion of exception and error handling.
- Using the standard libraries in C++; vectors, lists, sets, maps, iterators, sorts, search, transforms.
- How to link external libraries such as the NAG routines.
- Discretisation of ODE/PDEs
- Object Orientated programming:
- constructors, destructors, methods, member data, public/private qualifiers
- public/private qualifiers, operator overloading
- inheritance; the protected qualifier, virtual methods and run-time polymorphism.
Some possible projects:
- ODE problems
- PDE problems
- Financial problems
- Biological problems
- Fluid Dynamics problems
Students on the Theoretical and Applied Fluid Mechanics MSc are required to choose their projects from the first 4 options on differential equations and continuation methods.
Textbooks
- G.D. Smith, Numerical Solution of Partial Differenctial Equations, Clarendon Press, Oxford, 1978.
- D. Alcock, Illustrating C, Cambridge University Press, 1992.
- D. Yang, C++ and object-oriented numeric computing for scientists and engineers, Springer, 2000.
- S. Meyers, Effective C++: 55 specific ways to improve your programs and designs, Addison-Wesley, 2005.
- T.J. Chung, Computational Fluid Dynamics, CUP, 2002
- Y. Saad, Iterative methods for sparse linear systems, 1996, PWS series in computer science.
Teaching and learning methods
Classes are weighted towards the first 5 weeks, with 2hr lecture/2hr labs, then 1hour/week class in weeks 7-12 where students can seek help with their chosen projects.
Project deadlines
Project 1: end of week 8.
Project 2: end of week 12.
Assessment
- Weekly courseworks: 10%
- Mini-Project 1: 40%
- Mini-Project 2: 50%