Mathematics 2A

Sequences, series and power series.
Taylor series, Maclaurin series, Taylor's formula with remainder term.
Functions of several variables. Partial derivative.
Maximum og minimum values for functions in several variables.
Lagranges' multiplier method.
Vektor spaces, subspaces, linear dependence and independence.
Scalar product (inner product) and orthogonality.
Eigenvalues and eigenvectors, diagonalization, symmetric matrices and quadratic forms.
Difference equations.
Systems of differential equations of the first order. Use of eigenvalues and eigenvectors.
Fourier series.
Laplace transform og solution of ordinary differential equations.

Learning outcome - Knowledge:
The candidate should
- develop a scientific basis and understanding of mathematics that other topics can build on
- thorough knowledge of the core area of differential equations with applications
- good knowledge of functions of several variables
- thorough knowledge of the core area of matrices
- good knowledge of power series
- good knowledge of difference equations
- good knowledge of the Laplace transform and Fourier series

Learning outcome - Skills:
The candidate should
- have a relevant mathematical symbols and formula apparatus
- be able to manipulate symbols and formulas
- be able to reason mathematically
- be able to formulate technical engineering problems on a mathematical language
- be able to use mathematical methods and tools relevant to their field
- be able to identify connections between mathematics and engineering applications
- be able to assess the results of mathematical calculations

Learning outcome - Competence:
The candidate should
- be able to use mathematics to communicate on engineering issues.
- understand that change and change per unit of measurement can be measured, calculated, summarized and included in equations.
- understand that there is a level of precision in the mathematical language that makes it suitable for structuring technical engineering problems and enables solutions.
- have a mathematical understanding that provides a basis for lifelong learning.

Pedagogical methods:

Lectures, obligatory assignments, exercises, action-reflection-learning.