Teaching language: Swedish
Course module 

Credit distribution 

Examination dates 
Sp1 
Sp2 
Sp3 
Sp4 
Summer course 
No Sp 
0197 
Examination 
6,0 c 
Grading: TH 

6,0 c







29 Oct 2015 am M, 
07 Jan 2016 pm M, 
22 Aug 2016 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
introduction which is a repetition of the main
features of high school mathematics. The introduction (30 hours) consists of:
 information and diagnostic test
 algebraic expressions
 trigonometry
 analytic geometry
 functions
At the end of this introductory part of the course
the students have to take a written exam. Good
control of the topics in this introduction is necessary for successful further studies.
Nevertheless, students are allowed to
continue with Introductory mathematical
analysis and further courses even if they
have not passed the introduction exam.
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.