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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMA970 - Introductory mathematical analysis
 
Syllabus adopted 2016-02-15 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
0197 Examination 6,0c Grading: TH   6,0c   27 Oct 2016 am SB,  22 Dec 2016 pm SB,  25 Aug 2017 am SB

In programs

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

Examiner:

Bitr professor  Jana Madjarova



  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.

Course specific prerequisites

Studies at the university begin with a two weeks
non-compulsory introduction which is a repetition of the main
features of high school mathematics. The introduction (about 30 hours) consists of:
- information and diagnostic test
- algebraic expressions
- trigonometry
- analytic geometry
- functions.
Literature: R. Pettersson: Förberedande kurs i matematik vid CTH

Aim

The course provides basic knowledge of
mathematical analysis, which is necessary for
most courses to follow at the Engineering
Physics programme.

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

- understand the fundamental notions and definitions of mathematical analysis;
- prove the most fundamental theorems within analysis of functions in one real variable;
- use mathematical induction to prove identities and inequalities;
- rewrite expressions which contain logarithms and the inverse of the trigonometric functions;
- use a combination of standard limits in order to find other limits;
- analyze functions in order to draw their graphs;
- use standard methods to find the antiderivatives of some elementary functions;
- use the main theorem of analysis to compute Riemann integrals;
- apply Riemann integration on length, area and volume computation;
- use comparison methods to determine convergence/divergence of improper integrals;
- use MATLAB for simple numerical computations within analysis in one real variable;
- give proves of his/her own;
- solve problems combining two or more of the above abilities.

Content

Elementary set theory and logics. Proof by induction. Real numbers, absolute value, inequalities, Dedekind's intersection theorem for intervals, supremum / infimum. Functions, inverse functions. Exponential, power and logarithmic functions. Trigonometric functions and their inverse functions. Limits, continuity. Derivatives, derivation rules, differentials, the mean value theorem of differential calculus. Construction of curves, asymptotics, local extrema, maximal / minimal values, convex functions. Numerical solution of equations, iterative methods, method of Newton - Raphson (MATLAB). Indefinite integrals, integration by parts, change of variables. The Riemann integral. Riemann sums and integration of continuous functions. The main theorem of integral calculus. The main theorem of analysis. The mean value theorem of integral calculus. Improper integrals. Numerical integration (MATLAB). Applications of integrals (volumes, length of curves etc).

Organisation

Lectures, exercises, Matlab .

Literature

Litteratur: A. Persson, L.C. Böiers: Analys i en variabel (Studentlitteratur, Lund)

Exercises: Analys i en variabel. Studentlitteratur.

Examination

Written paper which combines theory and problem solving.


Page manager Published: Thu 04 Feb 2021.