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

 Semester Autumn Semester 2019 Lecturers T. Ilmanen, C. Busch Periodicity yearly recurring course Language of instruction English

### Courses

NumberTitleHoursLecturers
401-0373-00 VMathematics III: Partial Differential Equations2 hrs
 Thu 09:45-11:30 HCI J 7 » 19.09. 09:45-11:30 HCI 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
 Thu 08:45-09:30 HCI D 8 » 08:45-09:30 HCI J 7 » 08:45-09:30 HIT J 53 » 11:45-12:30 HCI D 8 »
T. Ilmanen, C. Busch

### Catalogue data

 Abstract Examples 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). Objective Classical tools to solve the most common linear partial differential equations. Content 1) Examples of partial differential equations - Classification of PDEs - Superposition principle2) One-dimensional wave equation- D'Alembert's formula - Duhamel's principle3) Fourier series - Representation of piecewise continuous functions via Fourier series - Examples and applications4) 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 principle6) Fourier transform - Derivation and definition - Inverse Fourier transformation and inversion formula- Interpretation and properties of the Fourier transform - Solution of the heat equation7) Laplace transform (if time allows)- Definition, motivation and properties- Inverse Laplace transform of rational functions - Application to ordinary differential equations Lecture notes See the course web site (linked under Lernmaterialien) Literature 1) S.J. Farlow, Partial Differential Equations for Scientists andEngineers, Dover Books on Mathematics, NY.2) N. Hungerbühler, Einführung in partielle Differentialgleichungenfür Ingenieure, Chemiker und Naturwissenschaftler, vdfHochschulverlag, 1997.Additional books:3) T. Westermann: Partielle Differentialgleichungen, Mathematik fürIngenieure mit Maple, Band 2, Springer-Lehrbuch, 1997 (chaptersXIII,XIV,XV,XII)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 / Notice Required background:1) Multivariate functions: partial derivatives, differentiability, Jacobian matrix, Jacobian determinant2) Multiple integrals: Riemann integrals in two or three variables, change of variables2) Sequences and series of numbers and of functions3) 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 for Bachelor'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 credits 4 credits Examiners T. Ilmanen, C. Busch Type session examination Language of examination English Repetition The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. Mode of examination written 120 minutes Additional information on mode of examination The exam will actually be offered in both English and German. / Die Prüfung wird sowohl auf Deutsch als auch auf Englisch angeboten. Written aids 10 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 link Information Only public learning materials are listed.

### Groups

401-0373-00 UMathematics III: Partial Differential Equations
GroupsG-01
 Thu 08:45-09:30 HCI D 8 »
G-02
 Thu 08:45-09:30 HCI J 7 »
G-03
 Thu 08:45-09:30 HIT J 53 »
G-04
 Thu 11:45-12:30 HCI D 8 »

### Restrictions

 There are no additional restrictions for the registration.

### Offered in

ProgrammeSectionType
Chemistry BachelorCompulsory Subjects Examination Block IO
Chemistry BachelorCompulsory Subjects Examination Block IO
Chemical Engineering BachelorCompulsory Subjects Examination Block IO
Chemical Engineering BachelorExamination Block IO
Interdisciplinary Sciences BachelorCompulsory Subjects Examination BlockW
Interdisciplinary Sciences BachelorExamination Block IO
Interdisciplinary Sciences BachelorElectivesW