TMA4115 - Calculus 3


Examination arrangement

Examination arrangement: Home examination
Grade: Passed/Failed

Evaluation form Weighting Duration Examination aids Grade deviation
Home examination 100/100 4 hours

Course content

Complex numbers and the complex exponential function. Second order linear differential equations. Systems of linear equations, Gauss-Jordan elimination, reduced echelon form, matrix algebra, determinants. Vector spaces, subspaces, linear dependence and independence. Inner products, orthogonality, orthogonal projections, Gram-Schmidt orthogonalization, and the method of least squares. Eigenvalues and eigenvectors, diagonalization, symmetric matrices and quadratic forms. First order systems of differential equations.

Learning outcome

1. Knowledge. The student is able to recognize, understand and apply concepts and methods from linear algebra in Euclidean spaces and systems of differential equations. 2. Skills. The student is able to apply his or her knowledge of linear algebra and systems of differential equations to formulate and solve problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.

Learning methods and activities

Lectures and compulsory exercises. Grade based on written final written examination. Retake of examination may be given as an oral examination. The lectures may be given in English.

Compulsory assignments

  • Exercises

Further on evaluation

see «Teaching methods and activities».

Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

Course materials

Will be announced at the beginning of the semester.

Credit reductions

Course code Reduction From To
SIF5010 7.5
MA1201 3.0 01.09.2009
MA1202 3.0 01.09.2009
TMA4110 7.5 01.09.2006
MA0003 1.5 01.09.2009
MA6201 3.0 01.09.2012
TMA4101 3.7 01.09.2020
TMA4106 3.7 01.09.2020

Version: 1
Credits:  7.5 SP
Study level: Foundation courses, level I


Term no.: 1
Teaching semester:  SPRING 2021

No.of lecture hours: 4
Lab hours: 2
No.of specialization hours: 6

Language of instruction: English, Norwegian

Location: Trondheim

Subject area(s)
  • Technological subjects
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences



Examination arrangement: Home examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Summer UTS Home examination 100/100 INSPERA
Room Building Number of candidates
Spring ORD Home examination (1) 100/100

Release 2021-06-09

Submission 2021-06-09

Release 09:00

Submission 13:00

Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
  • 1) Merk at eksamensform er endret til hjemmeeksamen som et smittevernstiltak i den pågående koronasituasjonen. Please note that the exam form has changed to home examination as a preventive measure in the ongoing corona situation.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

More on examinations at NTNU