Syllabus for Fourier Analysis
A revised version of the syllabus is available.
- 5 credits
- Course code: 1MA211
- Education cycle: First cycle
Main field(s) of study and in-depth level:
Explanation of codes
The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:
- G1N: has only upper-secondary level entry requirements
- G1F: has less than 60 credits in first-cycle course/s as entry requirements
- G1E: contains specially designed degree project for Higher Education Diploma
- G2F: has at least 60 credits in first-cycle course/s as entry requirements
- G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
- GXX: in-depth level of the course cannot be classified
- A1N: has only first-cycle course/s as entry requirements
- A1F: has second-cycle course/s as entry requirements
- A1E: contains degree project for Master of Arts/Master of Science (60 credits)
- A2E: contains degree project for Master of Arts/Master of Science (120 credits)
- AXX: in-depth level of the course cannot be classified
- Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Established: 2012-03-08
- Established by: The Faculty Board of Science and Technology
- Revised: 2012-03-08
- Revised by: The Faculty Board of Science and Technology
- Applies from: Autumn 2012
Several Variable Analysis or Geometry and Analysis III, and Linear Algebra II.
- Responsible department: Department of Mathematics
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.
- Latest syllabus (applies from Autumn 2023)
- Previous syllabus (applies from Autumn 2022, version 2)
- Previous syllabus (applies from Autumn 2022, version 1)
- Previous syllabus (applies from Autumn 2019)
- Previous syllabus (applies from Spring 2019)
- Previous syllabus (applies from Autumn 2012, version 2)
- Previous syllabus (applies from Autumn 2012, version 1)
Applies from: Autumn 2012
Some titles may be available electronically through the University library.
Fourier analysis and its applications
New York: Springer, 2003
Matematiska institutionen, 2010