Syllabus for Fourier Analysis

Fourieranalys

A revised version of the syllabus is available.

Syllabus

  • 5 credits
  • Course code: 1MA211
  • Education cycle: First cycle
  • Main field(s) of study and in-depth level: Mathematics G1F

    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:

    First cycle

    • 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

    Second cycle

    • 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
  • Entry requirements:

    Several Variable Analysis or Geometry and Analysis III, and Linear Algebra II.

  • Responsible department: Department of Mathematics

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. 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

integral equations.

Instruction

Lessons in large and small groups.

Assessment

Written examination at the end of the course.

Other directives

The course may not be included in higher education qualification together with Fourier Analysis (1MA035), 5 credits.

Syllabus Revisions

Reading list

Reading list

Applies from: Autumn 2012

Some titles may be available electronically through the University library.

  • Vretblad, Anders Fourier analysis and its applications

    New York: Springer, 2003

    Find in the library

  • Lindahl, Lars-Åke Fourieranalys

    Matematiska institutionen, 2010

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