Introduction to Scientific Computation
| Code | School | Level | Credits | Semesters |
| MATH2033 | School of Mathematical Sciences | 2 | 20 | Full year China |
- Code
- MATH2033
- School
- School of Mathematical Sciences
- Level
- 2
- Credits
- 20
- Semesters
- Full year China
Summary
This module introduces basic techniques in numerical methods and numerical analysis which can be used to generate approximate solutions to problems that may not be amenable to analytical techniques. Specific topics include:
• Nonlinear equations (bisection method, fixed-point iteration, Newton’s method, convergence);
• Linear systems of equations: Direct methods (Gaussian elimination, operation count, pivoting strategies, matrix factorisation, special matrices: diagonally dominant, symmetric positive definite);
• Linear systems of equations: Iterative techniques (matrix norms, Jacobi & Gauss-Seidel method, convergence);
• Polynomial interpolation (Lagrange polynomials, Lagrange form, error analysis);
• Numerical calculus (difference formulae, numerical quadrature: trapezoidal, Simpson & midpoint rule, composite rules, Richardson extrapolation);
• Numerical ODEs (Euler’s method, wellposedness of IVPs, higher-order RK methods, local truncation error);
• Implementing algorithms in Python; Basic elements of finite digit arithmetic.
Target Students
Single Honours students from the School of Mathematical Sciences.
Classes
- One 1-hour workshop each week for 24 weeks
- One 2-hour lecture each week for 24 weeks
Assessment
- 10% Coursework 1: Autumn Semester Coursework 1
- 10% Coursework 2: Autumn Semester Coursework 2
- 10% Coursework 3: Spring Semester Coursework 1
- 10% Coursework 4: Spring Semester Coursework 2
- 60% Exam 1 (3-hour): Written examination
Assessed by end of spring semester
Educational Aims
This module aims to introduce the concept of numerical approximation to problems that cannot be solved analytically, and to develop skills in Python through implementation of numerical methods. This module provides an important foundation on which students can develop skills and understanding in computational applied mathematics.Learning Outcomes
A student who completes this module successfully will be able to:
• L1 - solve nonlinear equations (approximately) using rootfinding methods, and analyse their convergence;
• L2 - solve linear systems of equations using direct methods, and analyse their computational complexity;
• L3 - solve linear systems of equations using iterative techniques, and analyse their convergence;
• L4 - approximate functions by polynomial interpolants, and analyse their accuracy;
• L5 - approximate derivatives and definite integrals using numerical differentiation and integration, and analyse their convergence;
• L6 - approximate ODEs using numerical methods, and analyse their convergence;
• L7 - implement reusable codes in Python.
Conveners
- Dr Richard Rankin