| TATA20 | Fourier Analysis, 7,5 ECTS credits. /Fourieranalys/ |
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Prel. scheduled
hours: 68 |
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Area of Education: Science Subject area: Mathematics |
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| Advancement level
(A-D): C
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| Aim: The course covers Fourier series as well as Fourier and Laplace transforms in a unified treatment based on the foundations of distribution theory and complex analysis. It will give mathematical knowledge fundamental for treatment of problems in system engineering and physics. It is also a preparation for courses in partial differential equations. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) TATM72 Calculus A, TATM73 Calculus B, TATM18 Linear Algebra and TATM57 Complex analysis or equivalent. Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding. |
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| Organisation: Lectures, problem classes and compulsory home assignments. |
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| Course contents: Function series, especially Fourier series. Orthogonality. Bessel's inequality. Completeness. Convergence -- notions and theorems. Rules of manipulation. Convolution formulas. Parseval's formula. Integrals with a parameter. The Fourier transform. The inversion formula. Rules of manipulation. The convolution formula. Parseval's formula. Distributions, especially "Dirac functions" and their derivatives, and transforms of these. The Laplace transform. The area of convergence. The inversion formula. Rules of manipulation. Convolution formulas. Applications to engineering and science. |
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| Course literature: Compendium with exercises supplemented by selected parts from some book listed on the course homepage. |
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| Examination: | |||
| Written examination |
5 p |
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Course language is Swedish. Department offering the course: MAI. Director of Studies: Arne Enqvist Examiner: Kurt Hansson Link to the course homepage at the department Course Syllabus in Swedish |
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