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## Syllabus for

LMA221 - Mathematical analysis, advanced course

Owner: TIMAL
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: A
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 No Sp 0101 Examination 5,0c Grading: TH 5,0c 16 Mar 2007 am L, 20 Jan 2007 am L, 28 Aug 2007 am L

#### In programs

TIMAL MECHANICAL ENGINEERING - Product Development, Year 3 (elective)
TIMAL MECHANICAL ENGINEERING - Production Engineering, Year 3 (elective)
TIMAL MECHANICAL ENGINEERING - Machine Design, Year 3 (elective)

#### Examiner:

Univ lektor  Thomas Wernstål

#### Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

#### Course specific prerequisites

First course in mathematical analysis in one variable.

#### Content

Aim: The course primarily aim is to prepare for continuation at Chalmers programme in Mechanical Engineering at masterlevel.

Goal: The goal of the course is to give the student deeper understanding of fundamental mathematical concepts and mathematical reasoning. After the course the student should be able to formulate mathematical modells, mathematically analyse the modell and present clear mathematical descriptions of problems and their solutions. The student should particulary have good knowledge with differensequations and orthogonal curves. The course participant should also be acquainted to the most fundamental subjects in numerical analysis and be familiar with the numerical computerprogramme MATLAB, including some skill in programming algoritms in MATLAB.

Contents: Following subjects will be treated:

• Fundamental concepts in numerical analysis, which include: different types of errors, different ways to measure the error, definition of a numerical problem and algoritm.
• Sequences och differensequations, which include: recursively defined sequences, limits of sequences, convergens of increasing and bounded sequences, the general solution to linear differensequations with constant coefficents, systems of differensequations.
• Numerical solutions to non-linear equations, which include: functionstudies, rough localization of roots by gradually halfing intervalls, Fixtpointiteration, Newton-Raphsons method, conditions for convergens with fixtpointiteration, different estimates of errors, the rate of convergens, systems of nonlinear equations.
• Numerical methods for calculating integrals, which include: the Trapezoid rule, Richardson Extrapolation, Simpsons formula, adaptiv integration, improper integrals.
• Numerical methods for finding solutions to ordinary differential equations, which include: slopefields, Eulers method for solutions to initial-value problems, errors in Eulers method, stability and badly conditioned problems, One differencemethod for solutions to boundary-value problems.
• Family of curves and orthogonal curves, which include: Geometrical interpretation and analytic calculation of orthogonal curves.

#### Organisation

The teaching will be organized in form of lectures and exercisegroupes (approx. 70 h). In addition some individuall work is required (approx. 110 h).

#### Literature

The litterature will primarily be supplied through the course website. Some extra material may be distributed in connection with the lectures.

#### Examination

Written and verbal examination.

Published: Wed 26 Feb 2020.