Course content

Complex numbers and the complex exponential function. Second order linear differential equations. Systems of linear equations, Gauss-Jordan elimination, reduced Echelon form, matrix algebra, determinants. Vector spaces, subspaces, linear dependence and independence. Inner products, orthogonality, orthogonal projections, Gram-Schmidt orthogonalization, and the method of least squares. Eigenvalues and eigenvectors, diagonalization, symmetric matrices and quadratic forms. First order systems of differential equations. Examples, exercises, midterm and exam problems adapted to the relevant program of study.

Learning outcome

The aim of the course is to give an introduction to linear differential equations and basic linear algebra, and moreover illustrate the theory with concrete applications within technological sciences.

Learning methods and activities

Lectures and compulsory exercises. Letter grade based 100% from final written examination. Retake of examination may be given as an oral examination. The course may be lectured in English.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course is based on TMA4100 Calculus 1 or equivalent.

Course materials

Will be announced at the semester start.

Credit reductions