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.

• Requirements for course approval

  Course approval is given based on 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".