MAT10 Calculus and Linear Algebra

• 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, 6 sessions of collaborative learning, oracle.

  It will be possible to follow the course digitally.

• Credit reduction due to overlap

  Full overlap with MAT010.

• Compulsory Activity

  Participation in at least 4 out of 6 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.

  K. Sydsæter og B. Øksendal: "Lineær algebra".