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

SemesterAutumn Semester 2017
LecturersF. Da Lio
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-0373-00 VMathematics III: Partial Differential Equations2 hrs
Thu09:45-11:30HCI J 6 »
F. Da Lio
401-0373-00 UMathematics III: Partial Differential Equations1 hrs
Thu08:45-09:30HCI D 6 »
08:45-09:30HCI D 8 »
08:45-09:30HCI J 6 »
11:45-12:30HCI D 8 »
11:45-12:30HIL F 10.3 »
F. Da Lio

Catalogue data

AbstractExamples of partial differential equations. Linear partial differential equations. Introduction to Separation of Variables method. Fourier Series, Fourier Transform, Laplace Transform and applications to the resolution to some partial differential equations (Laplace Equation, Heat Equation, Wave Equation).
ObjectiveThe main objective is that the students get a basic knowledge of the classical tools to solve explicitly linear partial differential equations.
Content## Examples of partial differential equations
- Classification of PDEs
- Superposition principle

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

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

## Separation of variables
- Resolution of wave and heat equation
- Homogeneous and inhomogeneous boundary conditions, Dirichlet and Neumann boundary conditions

## Laplace equation
- Resolution of the Laplace equation on rectangle, disk and annulus
- Poisson formula
- Mean value theorem and maximum principle

## Fourier transform
- Derivation and Definition
- Inverse Fourier transformation and inversion formula
- Interpretation and properties of the Fourier transform
- Resolution of the heat equation

## Laplace transform
- Definition, motivation and properties
- Inverse Laplace transform of rational functions
- Application to ordinary differential equations
Lecture notesThere are available some Lecture Notes in English and also in German of the Professor. These can be found following the links provided under the tab 'Lernmaterialien'.
The Professor will use also the following book:
S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY.
Literature1) N. Hungerbühler, Einführung in partielle Differentialgleichungen für Ingenieure, Chemiker und Naturwissenschaftler, vdf Hochschulverlag, 1997.

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

3) E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons (only Chapters 1,2,6,11)

4) T. Westermann: Partielle Differentialgleichungen, Mathematik für Ingenieure mit Maple, Springer-Lehrbuch 1997.
Prerequisites / NoticeIt is required a minimal background of: 1) multivariables
functions (Riemann integrals in two or three variables, change of variables in the integrals through the Jacobian, partial derivatives, differentiability, Jacobian) 2) numerical and functional sequences and series, 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 Chemistry 2005; Version 27.03.2018 (Examination Block I)
Bachelor's Degree Programme in Interdisciplinary Sciences 2010; Version 27.03.2018 (Examination Block)
ECTS credits4 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
Additional information on mode of examinationThe exam is offered in English and in German. / Die Prüfung wird auf Deutsch und auf Englisch angeboten.
Written aids20 A4 pages summary and formulary. No pocket calculator. / 20 A4-Seiten Zusammenfassung und Formelsammlung. 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 linkCourse Homepage
Additional linksLink zur Homepage Mathematik III von F. Da Lio mit Skripten und Literatur
Only public learning materials are listed.

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

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