MAT10 Calculus and Linear Algebra
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.
Upon completion of the course the students can
- Understand basic concepts of calculus and linear algebra.
- 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.
- Learn new mathematical tools, which have many applications in economics courses and serve as a background for more specialized mathematical courses.
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.
5 hour individual home exam.
Some examples are carried out in Mathematica, but use of this software is not required.
"Emner i matematisk analyse" can be downloaded from Canvas or bought in the bookstore.
K. Sydsæter og B. Øksendal: "Lineær algebra".
- ECTS Credits
- Teaching language
Spring. Offered Spring 2021.
Exam each semester.
Professor Jan Ubøe, Department of Business and Management Science.