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Fourier Analysis, 6 credits
Fourieranalys, 6 hp
TATA77
Main field of study
Mathematics Applied Mathematics Electrical Engineering Applied Physics Biomedical EngineeringCourse level
First cycleCourse type
Programme courseExaminer
Mats AignerDirector of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 62 hRecommended self-study hours: 98 h
ECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6CYYY | Applied Physics and Electrical Engineering, M Sc in Engineering | 5 (Autumn 2017) | 1 | 1 | Swedish | Linköping, Valla | C |
| 6CITE | Information Technology, M Sc in Engineering | 7 (Autumn 2017) | 1 | 1 | Swedish | Linköping, Valla | E |
| 6KMAT | Mathematics | 5 (Autumn 2017) | 1 | 1 | Swedish | Linköping, Valla | C |
Main field of study
Mathematics, Applied Mathematics, Electrical Engineering, Applied Physics, Biomedical EngineeringCourse level
First cycleAdvancement level
G2XCourse offered for
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Mathematics
- Information Technology, M Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Calculus (one and several variables), Linear Algebra and Complex analysis or equivalent.Intended learning outcomes
The course covers Fourier series as well as Fourier, Laplace and z-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. After a completed course, the student will be able to:
- Differentiate, integrate and transform distributions in one variable with particular emphasis on the Dirac distribution and its derivatives.
- Calculate Fourier series for simple periodic functions and distributions and determine convergence properties and estimate approximation errors in the mean.
- Solve linear differential equations with constant coefficients using distributions and Fourier- and Laplace transforms and linear difference equations using z-transforms.
- Using the complex inversion integral, in combination with residue calculus, to calculate inverse Laplace and z-transforms.
Course content
Basic distribution theory in one variable. Basic properties of Fourier series, Fourier, Laplace and z-transforms. Convergence of Fourier series, point wise and in the mean. Parseval's formula. Integrals with a parameter. The Fourier transform. The inversion formula. Rules of manipulation. The convolution formula. Parseval's formula. Inversion formulas and their validity. Convolutions and their transforms. Transforms of distributions. Applications to engineering and science.
Teaching and working methods
Lectures, problem classes.
Examination
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Mats AignerCourse website and other links
http://www.mai.liu.se/und/kurser/index-amne-tm.htmlEducation components
Preliminary scheduled hours: 62 hRecommended self-study hours: 98 h
Course literature
Additional literature
Other
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Other
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
X
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X
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X
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TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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