401-0363-10L  Analysis III

SemesterAutumn Semester 2022
LecturersA. Iozzi
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-0363-10 VAnalysis III
Lectures in HG F7 with video transmission to HG F5.
Starts in the second week of the semester.
2 hrs
Thu14:15-16:00HG F 5 »
14:15-16:00HG F 7 »
A. Iozzi
401-0363-10 UAnalysis III
Groups are selected in myStudies.
Many of the exercise classes are offered in German.

Zusätzlich wird montags 18-20 ab der 3. Semesterwoche im HG F 7 das Study Center angeboten, wo die Möglichkeit des betreuten Lernens angeboten wird. Im Study Center können Studierende Vorlesungsstoff vor- oder nachbereiten und Übungen lösen.
1 hrs
Thu/216:15-17:00CAB G 59 »
Thu/116:15-17:00CAB G 59 »
16:15-17:00CLA E 4 »
Thu/216:15-17:00CLA E 4 »
16:15-17:00HG G 26.3 »
Thu/116:15-17:00HG G 26.3 »
16:15-17:00HG G 26.5 »
Thu/216:15-17:00HG G 26.5 »
Thu/116:15-17:00LEE C 114 »
Thu/216:15-17:00LEE C 114 »
Thu/116:15-17:00LFW B 3 »
Thu/216:15-17:00LFW B 3 »
16:15-17:00LFW E 13 »
Thu/116:15-17:00LFW E 13 »
Thu/216:15-17:00ML F 40 »
Thu/116:15-17:00ML F 40 »
16:15-17:00ML J 34.1 »
Thu/216:15-17:00ML J 34.1 »
17:15-18:00CAB G 59 »
Thu/117:15-18:00CAB G 59 »
Thu/217:15-18:00CLA E 4 »
Thu/117:15-18:00CLA E 4 »
17:15-18:00HG G 26.3 »
Thu/217:15-18:00HG G 26.3 »
Thu/117:15-18:00HG G 26.5 »
Thu/217:15-18:00HG G 26.5 »
17:15-18:00LEE C 114 »
Thu/117:15-18:00LEE C 114 »
Thu/217:15-18:00LFW B 3 »
Thu/117:15-18:00LFW B 3 »
17:15-18:00LFW E 13 »
Thu/217:15-18:00LFW E 13 »
17:15-18:00ML F 40 »
Thu/117:15-18:00ML F 40 »
17:15-18:00ML J 34.1 »
Thu/217:15-18:00ML J 34.1 »
A. Iozzi

Catalogue data

AbstractIntroduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.
ObjectiveMathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations.
ContentLaplace Transforms:
- Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting
- Transforms of Derivatives and Integrals, ODEs
- Unit Step Function, t-Shifting
- Short Impulses, Dirac's Delta Function, Partial Fractions
- Convolution, Integral Equations
- Differentiation and Integration of Transforms

Fourier Series, Integrals and Transforms:
- Fourier Series
- Functions of Any Period p=2L
- Even and Odd Functions, Half-Range Expansions
- Forced Oscillations
- Approximation by Trigonometric Polynomials
- Fourier Integral
- Fourier Cosine and Sine Transform

Partial Differential Equations:
- Basic Concepts
- Modeling: Vibrating String, Wave Equation
- Solution by separation of variables; use of Fourier series
- D'Alembert Solution of Wave Equation, Characteristics
- Heat Equation: Solution by Fourier Series
- Heat Equation: Solutions by Fourier Integrals and Transforms
- Modeling Membrane: Two Dimensional Wave Equation
- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series
- Solution of PDEs by Laplace Transform
Lecture notesLecture notes by Prof. Dr. Alessandra Iozzi:
Link
LiteratureE. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011

C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.

S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY.

G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003.

Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005

For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis
Link

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
In examination block forBachelor's Degree Programme in Materials Science 2017; Version 28.01.2020 (Examination Block 2)
Bachelor's Degree Programme in Materials Science 2020 (Examination Block 1)
Bachelor's Degree Programme in Mechanical Engineering 2010; Version 24.02.2022 (Examination Block 1)
Bachelor's Degree Programme in Mechanical Engineering 2022 (Examination Block 1)
ECTS credits3 credits
ExaminersA. Iozzi
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 120 minutes
Written aids20 pages (=10 sheets) DIN A4 handwritten or typed personal summary. English <-> German dictionary. No further aids (in particular, no pocket calculator).
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkMoodle course
Only public learning materials are listed.

Groups

401-0363-10 UAnalysis III
GroupsG-01A
Thu/116:15-17:00LFW B 3 »
Thu/217:15-18:00LFW B 3 »
G-01B
Thu/216:15-17:00LFW B 3 »
Thu/117:15-18:00LFW B 3 »
G-02A
Thu/116:15-17:00LEE C 114 »
Thu/217:15-18:00LEE C 114 »
G-02B
Thu/216:15-17:00LEE C 114 »
Thu/117:15-18:00LEE C 114 »
G-03A
Thu/116:15-17:00CAB G 59 »
Thu/217:15-18:00CAB G 59 »
G-03B
Thu/216:15-17:00CAB G 59 »
Thu/117:15-18:00CAB G 59 »
G-04A
Thu/116:15-17:00CLA E 4 »
Thu/217:15-18:00CLA E 4 »
G-04B
Thu/216:15-17:00CLA E 4 »
Thu/117:15-18:00CLA E 4 »
G-05A
Thu/116:15-17:00LFW E 13 »
Thu/217:15-18:00LFW E 13 »
G-05B
Thu/216:15-17:00LFW E 13 »
Thu/117:15-18:00LFW E 13 »
G-06A
Thu/116:15-17:00HG G 26.5 »
Thu/217:15-18:00HG G 26.5 »
G-06B
Thu/216:15-17:00HG G 26.5 »
Thu/117:15-18:00HG G 26.5 »
G-07A
Thu/116:15-17:00ML F 40 »
Thu/217:15-18:00ML F 40 »
G-07B
Thu/216:15-17:00ML F 40 »
Thu/117:15-18:00ML F 40 »
G-08A
Thu/116:15-17:00ML J 34.1 »
Thu/217:15-18:00ML J 34.1 »
G-08B
Thu/216:15-17:00ML J 34.1 »
Thu/117:15-18:00ML J 34.1 »
G-09A
Thu/216:15-17:00HG G 26.3 »
Thu/116:15-17:00HG G 26.3 »
G-09B
Thu/117:15-18:00HG G 26.3 »
Thu/217:15-18:00HG G 26.3 »

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Mechanical Engineering BachelorExamination Block 1OInformation
Materials Science BachelorExamination Block 1OInformation