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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMA976 - Real analysis
 
Syllabus adopted 2010-02-26 by Head of Programme (or corresponding)
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 6,0c Grading: TH   6,0c   13 Jan 2017 pm SB,  11 Apr 2017 am SB,  17 Aug 2017 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


  Go to Course Homepage

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: Thu 04 Feb 2021.