MAT10 Calculus and Linear Algebra

• Topics

  This course provides a comprehensive introduction to key concepts in analysis and linear algebra, with a focus on both theoretical understanding and practical applications.

  In analysis, the course explores trigonometric functions and Fourier decomposition of cyclic functions, complex numbers, various integration techniques, as well as methods for smoothing irregular functions. Additionally, spline interpolation and Taylor's formula are covered, serving as important tools for analyzing and approximating functions.

  In linear algebra, the course introduces fundamental concepts such as vectors, matrices, and determinants, along with solutions to systems of linear equations and an understanding of linear transformations. The course also includes an in-depth study of eigenvalues and eigenvectors, which are essential for many topics in mathematics and applied sciences.

  Through the combination of analysis and linear algebra, students will build a solid foundation for further studies in mathematics and economics, while also developing skills that are crucial for practical applications.

• 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

  The teaching consists of plenary sessions, 8 sessions of collaborative learning, and oracle sessions.

• 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/

• Retake

  Retake in MAT10 will not be offered during the non-teaching semester (autumn). Only mandatory bachelor courses with an individual assessment will have a retake assessment in the non-teaching semester.

  For detailed information regarding the retake policy, please visit our website: https://www.nhh.no/en/for-students/examinations/retake-of-exams/https://www.nhh.no/en/for-students/examinations/retake-of-exams/ (copy url).