Calculus 4M

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

1. Knowledge. The student is able to recognize, understand and apply concepts and methods from the theory of Fourier series, Fourier transformation, 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, 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.

Lectures and compulsory exercises. The cource will be lectured together with TMA4125 Calculus 4N exept for two weeks where numerical methods replace the Laplace transform. Grade based on written final examination. Retake of examination may be given as an oral examination. The lectures may be given in English.