Course syllabus adopted 2021-01-15 by Head of Programme (or corresponding).
Overview
- Swedish nameInledande matematisk analys
- CodeTMA970
- Credits6 Credits
- OwnerTKTFY
- Education cycleFirst-cycle
- Main field of studyMathematics, Engineering Physics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 57121
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0197 Examination 6 c Grading: TH | 6 c |
|
In programmes
- TKTEM - ENGINEERING MATHEMATICS, Year 1 (compulsory)
- TKTFY - ENGINEERING PHYSICS, Year 1 (compulsory)
Examiner
Jana Madjarova- Professor, Analysis and Probability Theory, Mathematical Sciences
Eligibility
General entry requirements for bachelor's level (first cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
The same as for the programme that owns the course.Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
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
To provide basic knowledge in mathematical analysis, which is necessary knowledge for most courses in the programs Engineering physics and Engineering mathematics.
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; - 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. 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. Applications of integrals on e.g. length of curves, volumes etc.
Organisation
Lectures, exercises .
Literature
Litteratur: A. Persson, L.C. Böiers: Analys i en variabel (Studentlitteratur, Lund) Exercises: Analys i en variabel. Studentlitteratur.
Examination including compulsory elements
Written paper which combines theory and problem solving.
The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.