Upon successful completion of the course, the student will
Have knowledge of and will be able to explain the theory of Fourier series
Have knowledge of and will be able to explain the theory of the Fourier transformation.
Have knowledge of and will be able to explain the theory of Schwartz functions and distributions
Be able to use the theories to analyze some (linear) initial-boundary value problems from physics, such as the heat, wave and Schrødinger equations.
Contents
Introduction to the basic theory of both discrete and continuous Fourier analysis and of Schwartz’ theory of test functions and distribution theory. Important examples of applications of Fourier series and Fourier transformations in analysis and solutions of partial differential equations with time and space requirements. Use of distribution theory to treat problems where parameters and solutions are not smooth.
Teaching and learning methods
Lectures, group work, and mandatory hand-ins. Estimated workload of the course is 267 hours.
Examination requirements
Mandatory hand-ins must be approved. See Canvas for details.
Examinations
Individual oral, graded exam.
Student evaluation
The person responsible for the course decides, in cooperation with student representative, the form of student evaluation and whether the course is to have a midway or end of course evaluation in accordance with the quality system for education, chapter 4.1.