Course syllabus adopted 2025-02-14 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 57135
- 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
Anna Karlsson- Part-time fixed-term teacher, Algebra and Geometry, 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; - show ability to perform computations, typical for the analysis of functions in one real variable; show ability to work with inequalities/estimates; - accomplish fundamental proofs within analysis of functions in one real variable; - 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. Combination of standard limits in order to find other limits. Derivatives, derivation rules, differentials, the mean value theorem of differential calculus. Analyzing functions - construction of curves with 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 about disability study support.