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Differential calculus 7.5 credits

First cycle, M0047M
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
First cycle
Grade scale
G U 3 4 5
Subject group (SCB)

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language + Swedish upper secondary school courses Physics 2, Chemistry 1, Mathematics 4 (specifik entry A9). Or: Swedish upper secondary school courses Physics B, Chemistry A, Mathematics E (specifik entry 9)

More information about English language requirements


The selection is based on final school grades or Swedish Scholastic Aptitude Test.

Course Aim
After completed course, the students should be able to:
  • explain and use mathematical reasoning and notation.
  • use sets and logic in mathematical proofs.
  • use key concepts and methods in the calculus of one variable on extreme value calculations, graphing, limit calculations, analysis of functions and expressions, inverse functions, approximations of functions and other applied problems.
  • prove central theorems in the field of differential calculus in one variable.
  • manage and prove key properties of elementary functions and their inverses.
  • derive methods for numerical solution of equations in one variable.

This course treats basic principles in differential calculus, separated into the following four main categories:
  1. Basics: Logic, sets, equation solving, proofs, functions, graphs, trigonometry.
  2. Differential calculus: limits, continuity, tangent, derivative, differentiation rules, mean value theorem.
  3. Differentiation: higher-order derivatives, implicit differentiation, elementary functions, inverse function.
  4. Applications: Graphing, asymptotes, extreme values, related rates, Newton’s method, linear approximation, taylor polynomials.

Students use the computer software MATLAB to solve and analyze mathematical problems connected to this course.

Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
Teaching and learning are achieved through lectures (in classroom or online), problem solving, home studies (mainly problem solving) and computer tasks carried out in groups of 1-3 students.

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
The course aims are examined by a written individual exam and compulsary computer tasks. Grading according to the scale G U 3 4 5.

Transition terms
The course replaces M0029M

Johan Byström

Literature. Valid from Autumn 2021 Sp 1 (May change until 10 weeks before course start)
Adams Robert A, Essex C: Calculus, A Complete Course. Pearson, latest edition.
Dunkels A, m fl: Derivator, integraler och sånt... Studentlitteratur, latest edition.
Jönsson, Per: MATLAB – beräkningar inom teknik och naturvetenskap. Studentlitteratur, fjärde upplagan. (Note: voluntary)

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleCrStatusFrom periodTitle
0002LaborationU G#1.50MandatoryA19
0003Written examG U 3 4 56.00MandatoryA21

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
by Niklas Lehto 15 Feb 2019

Last revised
by Head Faculty Programme Director Niklas Lehto 17 Feb 2021