IMAG2012 - Mathematics for engineering 2 A


Examination arrangement

Examination arrangement: Aggregate score
Grade: Letter grades

Evaluation Weighting Duration Grade deviation Examination aids
School exam 70/100 4 hours C
Portfolio 30/100

Course content

Basis module. Functions of several variables. Partial differentiation, gradient. Critical points and optimization. Taylor’s theorem with remainder. Introduction to partial differential equations: examples and solutions.

Laplace transform. Computation by hand and computer. Applications of the Laplace transform to differential equations and signal processing.

Programme module. Trigonometric series and Fourier series. Applications to 1D wave equation with separation of variables. Fourier transform. Computation by hand and computer. Applications of Fourier transforms. Spectral analysis (e.g. sound and light waves). Applications to solution of differential equations, including harmonic motion with external periodic forcing.

Learning outcome


The candidate has good knowledge of:

  • Functions of several variables, including partial derivatives and their application to classification of stationary points and optimization.
  • Taylor’s theorem and approximation by Taylor series.
  • Laplace transforms and applications to differential equations and signal processing.
  • Series representations and approximations to functions, particularly Taylor and Fourier series.
  • Fourier transforms and applications to spectral analysis
  • Digital tools for analysis of mathematical problems


The candidate can:

  • Find and interpret the partial derivatives of a function of several variables
  • Approximate functions by Taylor’s theorem and estimate the error with a remainder term.
  • Solve simple optimization problems with several variables.
  • Verify that a given function solves a partial differential equation
  • Laplace transform certain functions with applications to solution of differential equations and signal processing
  • Compute Fourier coefficients of functions
  • Fourier transform certain functions with applications to solution of differential equations and spectral analysis
  • Apply digital tools to analyse mathematical problems.

General competence

The candidate:

  • Has good knowledge of, and can apply a symbolic and formulaic mathematical apparatus that is relevant for communication in engineering sciences
  • Has experience of evaluation of their own and other students scientific work, and with giving precise and technically correct oral feedback.
  • Has experience with applications of mathematical methods and digital tools to problems with their own and related specializations.
  • Can connect mathematical concepts and techniques to models the candidate meets within and outside of their studies.

Learning methods and activities

Lectures, exercises and group work.

Compulsory assignments

The compulsory assignments consist of two parts:

  • Compulsory assignments that are based on both analytical and numerical solution of problems and interpretation of the results. The assignments include tasks to be solved with the help of digital tools.
  • Compulsory group work

Special conditions

Obligatory activities from previous semesters can be accepted by the institute.

Compulsory assignments

  • Compulsory assignments (exercises and group work)

Further on evaluation

The course has two evaluations. A continuation exam is held in August for the written school exam (under supervision). Retake of examination may be given as an oral examination. There is no continuation exam for the portfolio.

If one evaluation is passed, and one is failed, the evaluation that is failed can be retaken if necessary next time the course is lectured ordinary.

Students that want to improve their grade in the course, can choose to retake one of the two evaluations. If the course changes its evaluation forms, the whole course must be retaken.

Continuation exam in August.

Course materials

Recommended course material will be announced at the start of the semester.

Credit reductions

Course code Reduction From To
IMAT2012 7.5 AUTUMN 2023
IMAA2012 7.5 AUTUMN 2023
IMAG2011 7.5 AUTUMN 2023
IMAA2011 7.5 AUTUMN 2023
IMAT2011 7.5 AUTUMN 2023
IMAG2021 2.0 AUTUMN 2023
IMAA2021 2.0 AUTUMN 2023
IMAT2021 2.0 AUTUMN 2023
IMAG2031 2.0 AUTUMN 2023
IMAA2031 2.0 AUTUMN 2023
IMAT2031 2.0 AUTUMN 2023
More on the course

Version: 1
Credits:  7.5 SP
Study level: Intermediate course, level II


Term no.: 1
Teaching semester:  SPRING 2025

Language of instruction: Norwegian

Location: Gjøvik

Subject area(s)
  • Mathematics
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Mathematical Sciences


Examination arrangement: Aggregate score

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Spring ORD School exam 70/100 C INSPERA
Room Building Number of candidates
Spring ORD Portfolio 30/100 INSPERA
Room Building Number of candidates
Summer UTS School exam 70/100 C INSPERA
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.

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

More on examinations at NTNU