MAT10 Calculus and Linear Algebra
Autumn 2022Spring 2023
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.
Participation in at least 4 out of 6 sessions of collaborative learning.
5 hour individual home exam.
A - F
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 2022.
Exam each semester.
Professor Jan Ubøe, Department of Business and Management Science.