Syllabus, Bachelor's level, 1MA211
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 8 March 2012
- Responsible department
- Department of Mathematics
Several Variable Analysis or Geometry and Analysis III, and Linear Algebra II.
On completion of the course, the student should be able to
- account for basic concepts and theorems within the Fourier analysis;
- demonstrate basic numeracy skill concerning the concepts in the previous point;
- use the numeracy skill at the solution of mathematical and physical problems formulated as ordinary or partial differential equations.
Fourier series in complex and trigonometric form. Pointwise and uniform convergence. The Dirichlet kernel. The Cesàro summability and the Fejér kernel. L2-theory: Orthogonality, completeness, ON systems. Applications to partial differential equations. Separation of variables. Something about Sturm-Liouville theory and eigenfunction expansions.
The Fourier transform and its properties. Convolution. The inversion formula. The Plancherel theorem.
The Laplace transform and its properties. Convolution. Applications to initial value problems and
Lessons in large and small groups.
Written examination at the end of the course.
The course may not be included in higher education qualification together with Fourier Analysis (1MA035), 5 credits.