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, 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 school exam (pen and paper).

• 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. 

  Support literature: Arne Hole: "Kalkulus og lineær algebra", 1. ed., Universitetsforlaget. 

• Permitted Support Material

  All written support material permitted (category III) 

  Calculator 

  One bilingual dictionary (Category I) 

  All in accordance with Supplementary provisions to the Regulations for Full-time Study Programmes at the Norwegian School of Economics Ch.4 Permitted support material https://www.nhh.no/en/for-students/regulations/https://www.nhh.no/en/for-students/regulations/ and https://www.nhh.no/en/for-students/examinations/examination-support-materials/https://www.nhh.no/en/for-students/examinations/examination-support-materials/