Fourier Analysis

5 credits

Syllabus, Bachelor's level, 1MA211

Code
1MA211
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Grading system
Pass with distinction, Pass with credit, Pass, Fail
Finalised by
The Faculty Board of Science and Technology, 9 February 2023
Responsible department
Department of Mathematics

Entry requirements

15 credits in mathematics. Participation in Several Variable Calculus, Several Variable Calculus M or Geometry and Analysis III. Participation in Linear Algebra II.

Learning outcomes

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.

Content

Fourier series in complex and trigonometric form. Pointwise and uniform convergence. The Dirichlet kernel. Summability methods. L^2-theory: Orthogonality, completeness, ON systems. Applications to partial differential equations. Separation of variables. Distributions.

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

integral equations.

Instruction

Lessons in large and small groups.

Assessment

Written examination at the end of the course (5 credits). 

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course cannot be included in the same degree as Fourier Analysis (1MA035), 5 credits.

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