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Syllabus for

Academic year
TMV130 - Calculus in one variable
Syllabus adopted 2011-02-22 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   18 Dec 2013 am V,  25 Apr 2014 am V,  29 Aug 2014 am V

In programs

TKVOV CIVIL ENGINEERING, Year 1 (compulsory)


Docent  Johan Karlsson

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.

Course specific prerequisites

Introductory course in mathematics


The purpose of the course is to, together with the other math courses in the program, provide a general knowledge in the mathematics required in further studies as well as in the future professional career.

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

After this course the student should

-have deepened knowledge of elementary functions.

- have attained good knowledge about the integral and its relation to differentiation.

- be acquainted to both analytical and numerical methods for calculating integrals.

- have a good understanding of the meaning of an ordinary differential equation.

- be familiar with both analytical and numerical methods for solving ordinary differential equations.

- be familiar with how functions can be approximated by polynomials and represented by power series.

- be able to use and combine different concepts in problem solving.

- be able to use the software MATLAB in problem solving.


Anti-derivatives and integrals, methods of integration.
Improper integrals.
Applications of integration: Area, volume, centre of mass, arc length,
area and volume of solids of revolution
Introduction to numerical analysis, computer arithmetic.
Numerical integration: the trapezoid rule, Simpson's rule.

Taylor's formula, series and power series.

Theory of algebraic equations with complex coefficients.

Ordinary differential equations: First-order equation in general,
analytical solution of separable and linear equations. Second-order
linear equations with constant coefficients, the equations of simple and
damped harmonic motion. Higher-order linear equations with constant
coefficients. Change of variables in ordinary differential equations.

Numerical derivatives and numerical solution of ordinary differential
Introduction to MATLAB, programming and applications.


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


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.