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

    Knowledge

    • Understand basic concepts of calculus and linear algebra.

    Skills

    • 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

    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.

Overview

ECTS Credits
7.5
Teaching language
Norwegian
Semester

Spring. Offered Spring 2023.

Course responsible

Professor Jan Ubøe, Department of Business and Management Science.