Mathematics 2B

Sequences, series and power series.
Taylor series, Maclaurin series, Taylor's formula with remainder term.
Functions of several variables. Partial derivatives.
Maximum and minimum values for functions of several variables.
Lagrange multiplier.
Vector spaces, subspaces, linear dependence and independence.
Scalar product (inner product) and orthogonality.
Eigenvalues and eigenvectors, diagonalization, symmetric matrices and quadratic forms.
Difference equations.
First-order systems of differential equations. Use of eigenvalues and eigenvectors.
Fourier series.

Learning outcomes - Knowledge:
The candidate has
- a scientific basis and understanding of mathematics to be built on by other topics
- thorough knowledge of core areas of differential equations
- has good knowledge of functions of several variables
- thorough knowledge of core areas of matrices
- good knowledge of power series
- good knowledge of difference equations
- good knowledge of Fourier series

Learning outcomes - Skills:
The candidate
- knows relevant mathematical symbols and formulas
- can manipulate symbols and formulas
- is able to reason mathematically
- can formulate technical engineering problems in mathematical language
- can use mathematical methods and tools relevant to their field
- can identify connections between mathematics and scientific engineering applications
- can assess the results of mathematical calculations

Learning outcomes - Expertise:
The candidate
- is able to use mathematics to communicate about engineering issues
- is able to understand that change per unit of measurement can be measured, calculated, summarized and included in equations
- is able to understand the level of accuracy of mathematical language, making it suitable for structuring technical engineering problems
- has a mathematical understanding which provides a basis for lifelong learning.

Pedagogical methods:
Lectures and exercises   

Compulsory requirements:
Compulsory exercises and/or compulsory submissions must be approved to get admission to the exam.