Scientific Computation
| Code | School | Level | Credits | Semesters |
| MATH2105 | Mathematical Sciences | 2 | 20 | Spring UK |
- Code
- MATH2105
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 20
- Semesters
- Spring UK
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.
• Linear systems of equations: Direct methods
• Linear systems of equations: Iterative techniques.
• Polynomial interpolation.
• Numerical calculus.
• Numerical ODEs.
• Implementing algorithms in Python: Basic elements of finite arithmetic.
Target Students
Single Honours and Joint Honours students from the School of Mathematical Sciences, Natural Sciences students, Liberal Arts students.
Classes
- Eleven 1-hour workshops each week for 2 weeks
- Eleven 2-hour lectures each week for 2 weeks
Teaching will be through a variety of methods, with the delivery tailored to the material on a week-by-week basis.
Assessment
- 40% Coursework 1: Summative assessment based on tasks distributed through the semester.
- 60% Exam 1 (2-hour): Written examination – Spring
Assessed by end of spring semester
Educational Aims
This course 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 course provides an important foundation on which students can develop skills and understanding in computational applied mathematics.Learning Outcomes
A student who completes this course successfully will be able to:
L1 – Select and apply suitable numerical methods to a range of mathematical problems, examples of which can be found in the summary of content.
L2 – Construct rigorous mathematical proofs to analyse the convergence and computational complexity of a given numerical method.
L3 – Develop and justify a mathematical framework using numerical methods to solve given routine and novel problems with a high level of accuracy.
L4 – Make effective use of Python to implement numerical methods to solve a range of problems, from simple idealised scenarios to real-world applications.