Course syllabus - Numerical Methods with MATLAB

Objectives

Numerical methods are used to solve mathematical problems by the help of computers. In economics and engineering different mathematical models are developed to analyse some interesting problems. These models are often very complex and involve a large number of variables and conditions. Different kinds of approximations can be used to solve such problems by a computer. This course focuses on some of the most important methods. The numerical software package MATLAB is introduced and used throughout the course. Basic algorithms and programming in MATLAB are included in the course.

Learning outcomes

At the end of the course the student is expected to be able to
- construct and apply small programs in MATLAB to mathematical problems.
- solve non-linear equations, in particular using fix-point iteration methods.
- solve linear equation systems using gaussian elimination and perform different kinds of matrix factorization (like LU-factorization).
- approximate derivatives using difference quotent and central-difference formulas.
- construct Taylor polynomials for a given function and interpolation polynomials, like Lagrange and Newton polynomials, for a given set of points.
- use numerical methods (like the methods of Euler, Heun and Runge-Kutta) to solve differential equations.
- use numerical methods (like Simpson's rule) to perform integration.
- carry out computational projects within numerical methods using MATLAB, to write structured reports and to perform oral presentations.

Course content

Introduction to MATLAB, basic algorithms in programming and programming in MATLAB. Numerical methods: non-linear equations, linear systems, interpolation, numerical differentiation, differential equations and numerical integration. Applications in economics.

Tuition

Methods and problems will be discussed during the lectures. To every lecture each student must prepare solutions to a set of proposed problems for each lecture (These problems are specified in the beginning of the course). All students must be ready to present what they have prepared at the whiteboard and be able to answer questions related to the topics of the lecture. Preparations, presentations and answering questions are essential parts of the examination so it is mandatory to attend each lecture.
Computer laborations will also be scheduled. In advance, a number of exercises should be prepared in order to implement MATLAB functions to solve these problems.

Specific requirements

Vector Algebra 7,5hp and Single Variable Calculus 7.5hp or corresponding.

Examination

Laboratory work (LAB1), computer project, 3 credits, marks Pass (G)
Folder examination and quizzes (PRO1), 4.5 credits, marks Pass (G) or Pass with distinction (VG)

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