Calculus and Linear Algebra

MAT10 Calculus and Linear Algebra

Autumn 2023

  • Topics

    Analysis: Trigonometric functions and Fourier decomposition of cyclic functions, complex numbers, integration methods, smoothing of irregular functions, spline interpolation and Taylor's formula.

    Linear Algebra: Vectors, matrices, determinants, linear systems of equations, linear transformations, eigenvalues and eigenvectors.

  • Learning outcome

    Upon completion of the course the students can


    • Understand basic concepts of calculus and linear algebra.


    • Use tools from analysis: trigonometric and inverse trigonometric functions.
    • Construct the Fourier decomposition of a cyclic function.
    • Understand what a complex number is and what they mean in practice.
    • Use integration by parts and substitution to solve integrals.
    • Be able to smooth an irregular function.
    • Be able to construct a spline interpolation.
    • Be able to find the Taylor polynomial of a function and asses the error term.
    • Master basic tools of linear algebra: vectors, matrices, Gauss-elimination in systems of linear equations, determinants, Cramer's formula, inverse matrices.
    • Understand and analyze linear transformations, eigenvalues and eigenvectors.

    General competence

    • Learn new mathematical tools, which have many applications in economics courses and serve as a background for more specialized mathematical courses.

  • Teaching

    Plenary sessions, 8 sessions of collaborative learning, oracle.

  • Credit reduction due to overlap

    Full overlap with MAT010.

  • Compulsory Activity

    Participation in at least 6 out of 8 sessions of collaborative learning.

  • Assessment

    5 hour individual home exam.

  • Grading Scale

    A - F

  • Computer tools

    Some examples are carried out in Mathematica, but use of this software is not required.

  • Literature


    "Emner i matematisk analyse" can be downloaded from Canvas or bought in the bookstore.

    David C. Lay, Steven R. Lay, and Judi J. McDonald: Linear Algebra and Its Applications, 6. edition, Pearson.


ECTS Credits
Teaching language

Spring. Offered Spring 2023.

Course responsible

Professor Jan Ubøe, Department of Business and Management Science.