Course syllabus - Numerical methods with MATLAB

Objectives

The aim of the course is to provide knowledge about how numerical methods are applied when solving mathematical problems that are frequently occurring in natural and engineering sciences. These mathematical challenges are often very complex and cannot be treated analytically. To bypass the analytical restrictions, one resorts to numerical methods. The course focuses on development of introductory numerical methods and implementation of these algorithms using the software package MATLAB.

Learning outcomes

At the end of the course the student is expected to be able to
1. explain the basics of computer arithmetic, for example machine precision and rounding errors
2. approximate derivatives using various finite differences
3. use numerical methods, like bisection or Newton's method, to solve nonlinear equations
4. apply curve fitting to a given set of data points
5. construct interpolation polynomials with specified properties
6. approximate integrals numerically using quadratures
7. solve ordinary differential equations numerically using explicit and implicit Runge-Kutta methods
8. analyze and verify accuracy and stability properties of the studied methods
9. implement, in MATLAB, numerical methods covered in the course for solving different mathematical problems
10. compose structured reports while clearly presenting problem statement, methodology, analysis and assessment of results

Course content

- Introduction to MATLAB, basic programming algorithms and their implementation in MATLAB
- Basics of computer arithmetic (e.g. machine precision and rounding errors)
- Numerical approximation of derivatives using finite differences
- Numerical methods for solving nonlinear equations (e.g. bisection and Newton's method)
- Matrix factorization methods for solving systems of linear equations
- Curve fitting using the least squares method
- Interpolation
- Numerical methods for approximating integrals
- Numerical methods for ordinary differential equations (explicit and implicit Runge-Kutta methods)

Examination

TEN1, Written examination, 5 credits, individual written examination concerning learning outcomes 1-8, grades Fail (U), 3, 4, 5.
LAB1, Laboratory work, 2.5 credits, individual and/or group laboratory work concerning learning outcomes 1-10, grades Fail (U) or Pass (G).

There may also be optional assignments that give bonus points for the examinations above. See more information in the study guide.

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass with credit, Pass, Fail