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## Syllabus for

TMA976 - Real analysis

Owner: TKTFY
6,0 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Mathematics, Engineering Physics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0105 Examination 6,0 c Grading: TH 6,0 c 15 Jan 2016 pm SB 07 Apr 2016 am M, 18 Aug 2016 am SB

#### In programs

TKTFY ENGINEERING PHYSICS, Year 1 (compulsory)
TKTEM ENGINEERING MATHEMATICS, Year 1 (compulsory)

#### Examiner:

Univ lektor  Peter Kumlin

#### Replaces

TMA975   Real analysis

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### Aim

The course provides basic knowledge of the fundamental theories within mathematical physics

#### Learning outcomes (after completion of the course the student should be able to)

To formulate and solve differential equations and to treat problems with series.

#### Content

Ordinary differential equations: linear equations of the first order, separable equations, linear differential equations of arbitrary order with constant coefficients, systems of equations, some special types such as Euler's differential equation. Mathematical models giving rise to differential equations. Numerical solution of differential equations.
Taylor's formula, computation of limits, l'Hospital's rules.
Difference equations. Sequences, series, power series, convergence criteria, solution of differential equations by means of power series. Uniform convergence of function sequences and function series.
The vector space Rn, polar and spherical coordinates, some topological concepts.

#### Organisation

Lectures and exercises. Computer exercises with Matlab.

#### Literature

A. Persson, L.-C. Böiers: Analys i en variabel, Studentlitteratur, Lund.
A. Persson, L.-C. Böiers: Analys i flera variabler, Studentlitteratur, Lund.
Övningar till Analys i en variabel, Matematiska institutionen, Lunds tekniska högskola.
Övningar till Analys i flera variabler, Matematiska institutionen, Lunds tekniska högskola.
F. Eriksson, E. Larsson, G. Wahde: Matematisk analys med tillämpningar, del 3.

OTHER LITERATURE
L. Råde, B. Westergren: BETA - Mathematics Handbook, Studentlitteratur, Lund.
E. Pärt-Enander, A. Sjöberg: Användarhandledning för Matlab 6, Uppsala universitet.

#### Examination

A written examination.

Page manager Published: Mon 28 Nov 2016.