401-0373-00L  Mathematics III: Partial Differential Equations

SemesterAutumn Semester 2019
LecturersT. Ilmanen, C. Busch
Periodicityyearly recurring course
Language of instructionEnglish


401-0373-00 VMathematics III: Partial Differential Equations2 hrs
Thu09:45-11:30HCI J 7 »
19.09.09:45-11:30HCI J 7 »
T. Ilmanen, C. Busch
401-0373-00 UMathematics III: Partial Differential Equations
Groups are selected in myStudies.
Exercises Thu 9-10 (alternatively Thu 12-13)
1 hrs
Thu08:45-09:30HCI D 8 »
08:45-09:30HCI J 7 »
08:45-09:30HIT J 53 »
11:45-12:30HCI D 8 »
T. Ilmanen, C. Busch

Catalogue data

AbstractExamples of partial differential equations. Linear partial differential equations. Separation of variables. Fourier series, Fourier transform, Laplace transform. Applications to solving commonly encountered linear partial differential equations (Laplace's Equation, Heat Equation, Wave Equation).
ObjectiveClassical tools to solve the most common linear partial differential equations.
Content1) Examples of partial differential equations
- Classification of PDEs
- Superposition principle

2) One-dimensional wave equation
- D'Alembert's formula
- Duhamel's principle

3) Fourier series
- Representation of piecewise continuous functions via Fourier series
- Examples and applications

4) Separation of variables
- Solution of wave and heat equation
- Homogeneous and inhomogeneous boundary conditions
- Dirichlet and Neumann boundary conditions

5) Laplace equation
- Solution of Laplace's equation on the rectangle, disk and annulus
- Poisson formula
- Mean value theorem and maximum principle

6) Fourier transform
- Derivation and definition
- Inverse Fourier transformation and inversion formula
- Interpretation and properties of the Fourier transform
- Solution of the heat equation

7) Laplace transform (if time allows)
- Definition, motivation and properties
- Inverse Laplace transform of rational functions
- Application to ordinary differential equations
Lecture notesSee the course web site (linked under Lernmaterialien)
Literature1) S.J. Farlow, Partial Differential Equations for Scientists and
Engineers, Dover Books on Mathematics, NY.

2) N. Hungerbühler, Einführung in partielle Differentialgleichungen
für Ingenieure, Chemiker und Naturwissenschaftler, vdf
Hochschulverlag, 1997.

Additional books:

3) T. Westermann: Partielle Differentialgleichungen, Mathematik für
Ingenieure mit Maple, Band 2, Springer-Lehrbuch, 1997 (chapters

4) E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons
(chapters 1,2,11,12,6)

For additional sources, see the course web site (linked under Lernmaterialien)
Prerequisites / NoticeRequired background:

1) Multivariate functions: partial derivatives, differentiability, Jacobian matrix, Jacobian determinant

2) Multiple integrals: Riemann integrals in two or three variables, change of variables

2) Sequences and series of numbers and of functions

3) Basic knowledge of ordinary differential equations

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 Chemical Engineering 2006; Version 27.03.2018 (Examination Block I)
Bachelor's Degree Programme in Chemical Engineering 2018; Version 26.09.2022 (Examination Block I)
Bachelor's Degree Programme in Chemistry 2005; Version 27.03.2018 (Examination Block I)
Bachelor's Degree Programme in Chemistry 2018; Version 26.09.2022 (Examination Block I)
Bachelor's Degree Programme in Interdisciplinary Sciences 2010; Version 27.03.2018 (Examination Block)
Bachelor's Degree Programme in Interdisciplinary Sciences 2018; Version 12.07.2022 (Examination Block)
ECTS credits4 credits
ExaminersT. Ilmanen, C. Busch
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
Additional information on mode of examinationThe exam will actually be offered in both English and German. / Die Prüfung wird sowohl auf Deutsch als auch auf Englisch angeboten.
Written aids10 A4 pages summary in your own handwriting (or 5 A4 pages on both sides)..No pocket calculator. / 10 A4-Seiten Zusammenfassung in eigener Handschrift (oder 5 A4-Blätter beidseitig). Kein Taschenrechner.
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 linkInformation
Only public learning materials are listed.


401-0373-00 UMathematics III: Partial Differential Equations
Thu08:45-09:30HCI D 8 »
Thu08:45-09:30HCI J 7 »
Thu08:45-09:30HIT J 53 »
Thu11:45-12:30HCI D 8 »


There are no additional restrictions for the registration.

Offered in

Chemistry BachelorCompulsory Subjects Examination Block IOInformation
Chemistry BachelorCompulsory Subjects Examination Block IOInformation
Chemical Engineering BachelorCompulsory Subjects Examination Block IOInformation
Chemical Engineering BachelorExamination Block IOInformation
Interdisciplinary Sciences BachelorCompulsory Subjects Examination BlockWInformation
Interdisciplinary Sciences BachelorExamination Block IOInformation
Interdisciplinary Sciences BachelorElectivesWInformation