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 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. solve systems of linear equations by using matrix factorization methods, for example LU factorization
5. apply curve fitting and construct interpolation polynomials, for example using monomial, Lagrange and Newton basis, for a given set of data points or given functions
6. approximate integrals numerically using quadratures, for example Trapezoidal and Simpson's rules
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 and interpolation (e.g. using monomial, Lagrange and Newton basis)
- Numerical methods for approximating integrals (e.g. Trapezoidal and Simpson's rules)
- Numerical methods for ordinary differential equations (explicit and implicit Runge-Kutta methods)

Specific requirements

Single Variable Calculus, 7.5 credits and Basic Vector Algebra 7.5 credits of which 2.5 credits must be completed at the beginning of the course, or equivalent.

Examination

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

For Pass with distinction (VG) on the course as a whole, the student must have earned that grade for TEN1.

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

Three-grade scale