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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
LMA401 - Calculus  
Matematisk analys
Syllabus adopted 2020-02-27 by Head of Programme (or corresponding)
Owner: TIMAL
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Major subject: Mathematics

Students admitted to the program before 2019/20 should contact their UBS before being registered on the course.
Teaching language: Swedish
Application code: 65115
Open for exchange students: No
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0119 Examination 7,5c Grading: TH   7,5c   24 Oct 2020 am L   05 Jan 2021 pm L,  26 Aug 2021 pm L

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Richard Lärkäng

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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



The aim of the course is to give basic knowledge in mathematical analysis. The course will also create qualification for mathematical treatment of technical problems in future profession and supply a good base for further studies.

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

  • account for the properties of the elementary functions.
  • construct function graphs and determine the maximum and minimum value of a function.
  • apply the basic calculation rules for derivatives and integrals.
  • interpret limits, derivatives and integrals geometrically.
  • apply limits, derivatives and integrals to simpler problems related to the chosen engineering subject.
  • present simpler mathematical reasoning.
  • account for the meaning of definitions, theorems and proffs and also be able to carry out simpler proofs.


  • Limits
  • Continuity
  • Derivative, differentiable functions
  • The mean-value theorem
  • Increasing and decreasing functions
  • Local maximum och minimum
  • Extreme-value problems
  • Inverse function
  • The inverse trigonometric functions. 
  • Derivatives of the elementary functions
  • Asymptotes, construction of the graph of a function
  • Growth of exponentials and logarithms
  • Antiderivatives, connection between area and antiderivative
  • Definite and indefinite integral
  • Rules of integration, integration by parts, integration by substitution
  • Integration of rational functions, algebraic functions and certain transcendental functions
  • Improper integrals


The course includes lectures, tutorials, quizzes and homework.


Course literature is announced on the course web page before start.

Examination including compulsory elements

The examination is based on a written exam. Quizzes giving bonus points may be offered. Grades TH. 

Page manager Published: Thu 04 Feb 2021.