401-0363-10L  Analysis III

SemesterAutumn Semester 2019
LecturersF. Da Lio
Periodicityyearly recurring course
Language of instructionEnglish


401-0363-10 VAnalysis III
Lectures in HG F 7 with video transmission in HG F 5.
Starts in the second week of the semester.
2 hrs
Thu13:15-15:00HG F 5 »
13:15-15:00HG F 7 »
F. Da Lio
401-0363-10 UAnalysis III
Groups are selected in myStudies.
Many of the exercise classes are offered in German.

Zusätzlich wird das Study Center angeboten: Montag 16-18 ab der 3. Semesterwoche im ML H 41.1, wo die Möglichkeit des betreuten Lernens angeboten wird. Im Study Center können Studierende Vorlesungsstoff vor- oder nachbereiten und Übungen lösen.
1 hrs
Thu15:15-16:00CAB G 59 »
15:15-16:00CHN D 46 »
15:15-16:00CLA E 4 »
15:15-16:00ETZ F 91 »
15:15-16:00HG E 1.1 »
15:15-16:00HG E 21 »
15:15-16:00HG E 33.5 »
15:15-16:00HG G 26.3 »
15:15-16:00HG G 26.5 »
15:15-16:00LEE D 105 »
15:15-16:00LFW C 4 »
15:15-16:00ML E 12 »
15:15-16:00ML F 38 »
15:15-16:00ML J 37.1 »
15:15-16:00NO C 6 »
F. Da Lio

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:
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

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 Mechanical Engineering 2010; Version 24.02.2022 (Examination Block 1)
Bachelor's Programme in Materials Science 2015; Version 22.08.2017 (Examination Block 2)
ECTS credits3 credits
ExaminersF. Da Lio
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 linkWeb-page at metaphor
Additional linksClass Content
Only public learning materials are listed.


401-0363-10 UAnalysis III
Thu15:15-16:00CHN D 46 »
Thu15:15-16:00HG E 1.1 »
Thu15:15-16:00CLA E 4 »
Thu15:15-16:00ETZ F 91 »
Thu15:15-16:00CAB G 59 »
Thu15:15-16:00HG E 21 »
Thu15:15-16:00ML E 12 »
Thu15:15-16:00HG E 33.5 »
Thu15:15-16:00HG G 26.3 »
Thu15:15-16:00HG G 26.5 »
Thu15:15-16:00LEE D 105 »
Thu15:15-16:00LFW C 4 »
Thu15:15-16:00ML F 38 »
Thu15:15-16:00ML J 37.1 »
Thu15:15-16:00NO C 6 »


There are no additional restrictions for the registration.

Offered in

Mechanical Engineering BachelorExamination Block 1OInformation
Materials Science BachelorExamination Block 2OInformation