Course syllabus - Numerical Methods for Engineers

Objectives

The aim of the course is to provide knowledge about how numerical methods are applied when solving mathematical problems using a computer. Methods and algorithms are presented both from a mathematical viewpoint and through examples of relevance for the students' field of study.

Learning outcomes

Upon completion of this course the student is expected to be able to:

1. use and qualitatively compare numerical methods to solve non-linear equations
2. solve systems of linear equation numerically using matrix factorisation and iterative methods
3. approximate derivatives using various types of difference quotients
4. use and qualitatively compare numerical methods for integration
5. use and qualitatively compare numerical methods for solving differential equations
6. perform computationally focused projects in numerical methods using a computer, and be able to present the results by well-structured reports and oral presentations

Course content

- Non-linear equations: iterative methods such as the bisection method and Newton's method
- Systems of linear equations: condition number, matrix factorisation, iterative methods, rewrite systems in order to minimize error propagation
- Numerical differentiation: difference quotient, central difference quotient
- Numerical integration: quadrature formulas such as the trapezoidal method and Simpson's rule
- Numerically solving differential equations: explicit and implicit methods such as Euler's method and the Runge-Kutta method
- Error estimation and convergence rate for chosen numerical methods
-Computer based applications in the students' field of study

Tuition

Lectures, study groups and computer based laboratory work.

Specific requirements

Basic Vector Algebra, 7.5 credits, of which 2.5 credits must be completed at the beginning of the course, Fundamentals of Programming, 7.5 credits, of which 1.5 credits must be completed at te beginning of the course, Single Variable Calculus, 7.5 credits, or equivalent.

Examination

TEN1, Written examination, 4.5 credits, written examination concerning learning outcomes 1-5, grades Fail (U), 3, 4 or 5.
LAB2, Laboratory work, 3 credits, written and/or oral presentation concerning learning outcomes 1-6, grades Fail (U) or Pass (G).

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

Grading scale: 5, 4, 3