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Applied Transform Theory, 6 credits
Tillämpad transformteori, 6 hp
TNG032
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Zhuangwei LiuDirector of studies or equivalent
George BaravdishEducation components
Preliminary scheduled hours: 58 hRecommended self-study hours: 102 h
ECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6CKTS | Communication and Transportation Engineering, M Sc in Engineering | 4 (Spring 2017) | 1 | 4 | Swedish | Norrköping, Norrköping | C |
| 6CIEN | Electronics Design Engineering, M Sc in Engineering | 4 (Spring 2017) | 1 | 4 | Swedish | Norrköping, Norrköping | C |
| 6CMEN | Media Technology and Engineering, M Sc in Engineering | 4 (Spring 2017) | 1 | 4 | Swedish | Norrköping, Norrköping | C |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2XCourse offered for
- Electronics Design Engineering, M Sc in Engineering
- Media Technology and Engineering, M Sc in Engineering
- Communication and Transportation Engineering, 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
Single variable calculus, Linear Algebra, Multi variable calculusIntended learning outcomes
To give the students the mathematical background in transformtheory needed in Circuit Theory, Control Theory, Image Processing and Signals and Systems. Students will be expected to be able to do the following after completing this course:
- utilize and determine Fourierseries, use Parsevals identity, use basic convergence results
- transform functions and sequences using Fourier-, Laplace- and Z-transform, have knowledge about what function and sequences can be transformed, and the properties of the transformed function and sequences.
- use transforms and Fourier series to solve e.g. ordinary differential equations, partial differential equations, difference equations, integral equations.
- have the ability to write a technical report in English, give an oral presentation of results, and critically examine and discuss other students' oral and written presentations.
Course content
We will study some important transform methods: Fourier series, Fourier transforms, Laplacetransforms, and z-transforms, together with some of their applications.
One of the laboratory exercises requires a written report, an oral presentation and opposition in English. These learning activities will help students improve language skills, presentation techniques and opposition in English as well as the ability to adapt a presentation to a specific audience.
Teaching and working methods
The course is given in the form of lectures, tutorials and lab exercises.
Examination
| UPG1 | Written report, oral presentation and opposition | 1 credits | U, G |
| KTR1 | Optional written test | 0 credits | U, G |
| LAB3 | Laboratory work | 1 credits | U, G |
| TEN3 | Written examination | 4 credits | U, 3, 4, 5 |
The laboratory part of the course consists of labs chosen from image processing, control techniques and signal processing. The programming language is Matlab. Support, review and feedback will be given by language teachers in conjunction with report writing and oral presentation / opposition in English.
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Institutionen för teknik och naturvetenskapDirector of Studies or equivalent
George BaravdishExaminer
Zhuangwei LiuCourse website and other links
Education components
Preliminary scheduled hours: 58 hRecommended self-study hours: 102 h
Course literature
Fourier and Laplace transforms, Beerends m.fl., Cambridge University Press. Problemsamling Laborationssamling| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Written report, oral presentation and opposition | 1 credits | U, G |
| KTR1 | Optional written test | 0 credits | U, G |
| LAB3 | Laboratory work | 1 credits | U, G |
| TEN3 | Written examination | 4 credits | U, 3, 4, 5 |
The laboratory part of the course consists of labs chosen from image processing, control techniques and signal processing. The programming language is Matlab. Support, review and feedback will be given by language teachers in conjunction with report writing and oral presentation / opposition in English.
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.
Course literature is preliminary.
Fourier and Laplace transforms, Beerends m.fl., Cambridge University Press.
Problemsamling
Laborationssamling
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) |
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X
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| 1.2 Fundamental engineering knowledge (G1X level) |
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X
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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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X
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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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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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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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X
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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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X
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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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