# Numerical Algorithms, 6 credits (TADI02)

Numeriska algoritmer, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

### Examiner

Ingegerd Skoglund

### Director of studies or equivalent

Ingegerd Skoglund
Course offered for Semester Period Timetable module Language Campus VOF
6IDAT Computer Engineering, B Sc in Engineering (Embedded Systems) 5 (Autumn 2017) 1 2 Swedish Linköping v
6IDAT Computer Engineering, B Sc in Engineering (Software Engineering) 5 (Autumn 2017) 1 2 Swedish Linköping v
6IELK Engineering Electronics 5 (Autumn 2017) 1 2 Swedish Linköping v
6IMAS Mechanical Engineering, B Sc in Engineering 5 (Autumn 2017) 1 2 Swedish Linköping v

### Main field of study

Mathematics, Applied Mathematics

First cycle

G2X

### Course offered for

• Computer Engineering, B Sc in Engineering
• Engineering Electronics
• Mechanical Engineering, B Sc in Engineering

### Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

### Prerequisites

Basic courses in calculus, linear algebra and programming.

### Intended learning outcomes

Scientific computing is the art of developing and analysing numerical algorithms for solving mathematical problems in for example natural science and technology. After finishing the course the student should be able to

• explain and separate fundamental terms and concepts in scientific computing
• use a selection of numerical algorithms for solving given mathematical problems using a pocket calculator
• estimate the accuracy of calculated results
• use mathematical software
• implement and validate numerical methods

### Course content

• Error analysis: Error propagation and cancellation.
• Floting point numbers: Floating point systems, machine epsilon and round off.
• Linear systems of equations: LU decomposition, pivoting, backward and forward substitution, condition and arithmetic complexity.
• Interpolation and approximation: Newton's and Lagrange's methods, splines, Horner's scheme, least squares and overdetermined systems.
• Differentiation and integration: Difference approximation, order of accuracy, Richardson extrapolation, the trapezoidal rule, Simpon's rule and Romberg's method.
• Ordinary differential equations: Runge Kutta methods, local and global truncation error, stability and convergence.
• Non-linear equations: The bisection method, Newton-Raphson's method, fixed point iteration, condition and order of convergence.

### Teaching and working methods

The course is divided into a number of sections that are described under Course contents below. Each sections begins with a preparatory computer laboration that gives training in using mathematical software and raises questions about the properties of the numerical algorithms. These questions are answered during lectures, when the algorithms are explained.

The ability to explain and separate terms and concepts in scientific computing, the ability to use numerical algorithms using a pocket calculator and the ability to estimate the accuracy of calculated results are trained during exercise time.

A number of minor projects are also carried out, where acquired knowledge and skills are used. The results are discussed at the seminars and reported in short written reports.

### Examination

 LAB1 Laboratory work U, G 2.5 credits TEN1 Written examination U, 3, 4, 5 3.5 credits
The first three course aims are examined with TEN1. The other two are examined with LAB1. Laboratory work includes computer exercises, minor projects, written reports and seminars.

Four-grade scale, LiU, U, 3, 4, 5

### Other information

Supplementary courses: Numerical linear algebra, Numerical linear calculus

### Department

Matematiska institutionen

### Director of Studies or equivalent

Ingegerd Skoglund

### Examiner

Ingegerd Skoglund

### Education components

Preliminär schemalagd tid: 54 h

### Course literature

#### Kompletterande litteratur

##### Böcker
L Eldén, L Wittmeyer-Koch, (2001) Numeriska beräkningar - analys och illustrationer med MATLAB fjärde upplagan Studentlitteratur
##### Kompendier
H Brandén, Formelsamling i BeräkningsvetenskapH Brandén, Övningar i Beräkningsvetenskap

### Books

L Eldén, L Wittmeyer-Koch, (2001) Numeriska beräkningar - analys och illustrationer med MATLAB fjärde upplagan Studentlitteratur

### Compendia

H Brandén, Formelsamling i Beräkningsvetenskap
H Brandén, Övningar i Beräkningsvetenskap