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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
MVE535 - Calculus, part 1  
Matematisk analys, del 1
Syllabus adopted 2019-02-21 by Head of Programme (or corresponding)
Owner: TIDAL
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Major subject: Mathematics

Teaching language: Swedish
Application code: 62112
Open for exchange students: No
Maximum participants: 125
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0117 Examination 7,5c Grading: TH   7,5c   18 Mar 2021 pm L,  10 Jun 2021 pm L,  24 Aug 2021 pm L

In programs



Sonja Radosavljevic

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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

Elementary knowledge in algebra corresponding to the course LMA212 Algebra.


The course should, in a coherent way, give basic knowledge of calculus. The course will also facilitate mathematical treatment of technical problems in the profession and provide basic knowledge for further studies.

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

  • define the concepts of limit and continuity and compute limits
  • define the concepts of derivative and differentiation and use the definition of derivative to calculate the derivatives of elementary functions and the fundamental rules of differentiation
  • outline the elementary functions and account for their properties
  • define the concepts of increasing (decreasing) function and local maximum (minimum) value
  • construct graphs of functions and calculate the absolute maximum (minimum) value of a function
  • define the concept of inverse function, calculate inverse functions and their derivatives


Theory of sets
Algebraic equations
Algebraic simplifications
Absolute value
The circle and the ellipse
The concept of a function
Exponential- and logarithmic functions
Derivative, rules of differentiation
Implicit differentiation
Tangent and normal
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


The course includes lectures, tutorials, quizzes and homework.


James Stewart: Calculus Early Transcendentals, Brooks/Cole

Examination including compulsory elements

The learning outcomes are assessed continuously by quizzes and a final exam.

Page manager Published: Thu 04 Feb 2021.