Course content

Partial derivatives. The Laplace transform with applications to solving ordinary differential equations and integral equations. Fourier series and the Fourier transform with applications to solving linear partial differential equations. Discrete Fourier transform. Numerical methods: Interpolation, differentiation, and integration. Methods for solving linear and non-linear equations. Runge-Kutta methods for solving systems of ordinary differential equations. Difference methods for solving partial differential equations. Introduction to computational tools with examples.

Learning outcome

1. Knowledge. The student is able to recognize, understand and apply concepts and methods from the theory of Fourier series, Fourier transformation, Laplace transformation, ordinary and partial differential equations and numerical solution of systems of equations and differential equations.

2. Skills. The student is able to apply his or her knowledge of Fourier theory, ordinary and partial differential equations and numerical methods to formulate and solve problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.

Learning methods and activities

Lectures and compulsory exercises. Grade based on written final examination. Retake of examination may be given as an oral examination. The lectures may be given in English.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course is based on TMA4100/10/15 Calculus 1/3 or equivalent.

Course materials

Will be announced at the start of the semester.

Credit reductions