Course syllabus

Matematisk analys

FMA645, 13,5 credits, G1 (First Cycle)

Valid for: 2015/16
Decided by: Education Board B
Date of Decision: 2015-04-16

General Information

Compulsory for: IBYA1, IBYI1, IBYV1, IDA1, IEA1
Language of instruction: The course will be given in Swedish


The course aims at giving a basic treatment of one-dimensional calculus. Particular emphasis is put on the role which this plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must



Algebraic computations. Functions, equations, inequalities and modulus of a number. Complex numbers. Powers and logarithms. Trigonometry. Curve sketching: elementary functions and second degree curves.

Calculus 1:

Complex numbers and polynomials. The concept of a function. Properties of the elementary functions: graphs, formulas, limits. Limits with applications: the number e, series. Continuous functions. Derivatives: definition and properties, applications. Differentiation of the elementary functions. Properties of differentiable functions: the mean value theorem with applications. Curve sketching. Local extreme values. Optimization.

Calculus 2:

Primitive functions. Partial integration and change of variable. Partial fractions. Definition of an integral. Methods of integration. Riemann sums. Geometrical and other applications of integrals. Improper integrals. Differential equations of first order: linear and separable with applications. Linear differential equations of second order: solution of homogeneous and certain inhomogeneous equations, with applications. The Taylor and Maclaurin formulae. Power series expansions of the elementary functions, with applications.

Examination details

Grading scale: TH
Assessment: Written tests on all subcourses. The first subcourse is graded as Passed och Not passed. The courses Calculus 1 and 2 are graded on a scale from 3.0 (passed) to 6.0 in steps of 0.1. The final grade is the integer part of the mean of these two grades (at most 5).

Code: 0107. Name: Algebra.
Credits: 3. Grading scale: UG. Assessment: Written test, with grades Passed and Not passed. Some assignments. Contents: See above, Algebra.
Code: 0207. Name: Calculus 1.
Credits: 6. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 1.
Code: 0307. Name: Calculus 2.
Credits: 4,5. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 2.


The number of participants is limited to: No
The course overlaps following course/s: FMA415, FMAA01, FMAA05, FMA410

Reading list

Contact and other information

Director of studies: Studierektor Anders Holst,
Course coordinator: Anders Magnusson,
Course homepage: