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Syllabus for

Academic year
TMV125 - Introductory course in mathematics
Syllabus adopted 2013-02-21 by Head of Programme (or corresponding)
Owner: TKVOV
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Architecture and Engineering, Mathematics, Civil and Environmental Engineering

Teaching language: Swedish
Block schedule: LA

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0104 Examination 7,5 c Grading: TH   7,5 c   26 Oct 2013 am V,  18 Jan 2014 am V,  27 Aug 2014 am V

In programs

TKVOV CIVIL ENGINEERING, Year 1 (compulsory)


Univ lektor  Lennart Falk

Course evaluation:

  Go to Course Homepage


For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.


The purpose of the course is to strengthen, deepen and develop the knowledge in secondary school mathematics and to thereby give a solid ground for further studies in mathematics.

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

After this course the students should be able to fluently handle algebraic calculations and the elementary functions

- be able to fluently handle algebraic calculations and the elementary functions, both in problem solving and its theory. The student shall be able to draw graphs and solve equations. The student shall also be able to solve systems of linear equations and master vector algebra in two and three dimensions.


Algebraic calculations and the number systems. Fractions, rules for powers and
power expansions. Basic trigonometry. Analytic geometry.

Introduction to calculus: Real functions, graphs, limits, derivatives and
the use of these concepts in basic modeling.

Deductive reasoning. Elementary set theory and fundamentals of logic.
The general concept of functions.

The elementary functions: Polynomials, rational and power functions.
Inverse functions, exponentials, logarithms and inverse trigonometric functions.
The derivative of the elementary functions.

Applications of differentiation: Extreme values, numerical methods for
solving equations. Newton-Raphsons method and other iterations.
Sequences and limits. Mathematical induction.

Systems of linear equations and matrices. Vectors in two and three dimensions.
Dot product, cross product, area and volume.

The complex plane, rectangular and polar form. The complex exponential function.


Instruction is given in lectures and classes. More detailed information will be given on the course web page before start of the course.


Literature will be announced on the course web page before start of the course.


More detailed information about the examination will be given on the course web page before start of the course.
Examples of assessments are:
-selected exercises are to be presented to the teacher orally or in writing during the course,
-other documentation of how the student's knowledge develops,
-project work, individually or in group,
-written or oral exam during and/or at the end of the course.

Page manager Published: Thu 03 Nov 2022.