401-0243-00L Analysis III

Semester	Autumn Semester 2021
Lecturers	M. Akka Ginosar
Periodicity	yearly recurring course
Language of instruction	German

Courses

Number

Title

Hours

Lecturers

401-0243-00 V

Analysis III

2 hrs

Tue

09:45-11:30

HPH G 2 »

M. Akka Ginosar

401-0243-00 U

Analysis III

Groups are selected in myStudies.
Mi 9-10 für Studiengang Raumbezogene Ingenieurwissenschaften.
Fr 12-13 oder Fr 13-14 für Studiengang Bauingenieurwissenschaften gemäss Gruppeneinteilung.

Zusätzlich wird das StudyCenter angeboten: weitere Angaben dazu folgen
(ab der zweiten Semesterwoche)

1 hrs

Wed	09:15-10:00	NO C 6 »
Fri	11:45-12:30	HIL E 7 »
	11:45-12:30	HIT F 31.2 »
	12:45-13:30	HIT F 31.2 »
	12:45-13:30	HIT F 32 »
	12:45-13:30	HIT H 42 »

M. Akka Ginosar

Catalogue data

Abstract	We will model and solve scientific problems with partial differential equations. Differential equations which are important in applications will be classified and solved. Elliptic, parabolic and hyperbolic differential equations will be treated. The following mathematical tools will be introduced: Laplace and Fourier transforms, Fourier series, separation of variables, methods of characteristics.
Learning objective	Learning to model scientific problems using partial differential equations and developing a good command of the mathematical methods that can be applied to them. Knowing the formulation of important problems in science and engineering with a view toward civil engineering (when possible). Understanding the properties of the different types of partial differential equations arising in science and in engineering.
Content	Classification of partial differential equations Study of the Heat equation general diffusion/parabolic problems using the following tools through Separation of variables as an introduction to Fourier Series. Systematic treatment of the complex and real Fourier Series Study of the wave equation and general hyperbolic problems using Fourier Series, D'Alembert solution and the method of characteristics. Laplace transform and it's uses to differential equations Study of the Laplace equation and general elliptic problems using similar tools and generalizations of Fourier series. Application of Laplace transform for beam theory will be discussed. Time permitting, we will introduce the Fourier transform.
Lecture notes	Lecture notes will be provided
Literature	large part of the material follow certain chapters of the following first two books quite closely. S.J. Farlow: Partial Differential Equations for Scientists and Engineers, (Dover Books on Mathematics), 1993 E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2001 The course material is taken from the following sources: Stanley J. Farlow - Partial Differential Equations for Scientists and Engineers G. Felder: Partielle Differenzialgleichungen. https://people.math.ethz.ch/~felder/PDG/ Y. Pinchover and J. Rubinstein: An Introduction to Partial Differential Equations, Cambridge University Press, 2005 C.R. Wylie and L. Barrett: Advanced Engineering Mathematics, McGraw-Hill, 6th ed, 1995
Prerequisites / Notice	Analysis I and II, insbesondere, gewöhnliche Differentialgleichungen.

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 Civil Engineering 2014; Version 01.08.2016 (Examination Block 1) Bachelor's Degree Programme in Geospatial Engineering 2018; Version 06.10.2021 (Examination Block 1)
ECTS credits	3 credits
Examiners	M. Akka Ginosar
Type	session examination
Language of examination	German
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	Es werden Lernelemente angeboten. Die aktive Mitarbeit (Schnellübungen) in den Übungen über das Semester wird in einen Notenbonus von 0 bis 0.25 umgerechnet und anschliessend ungerundet zur ungerundeten Note aus der Sessionsprüfung addiert.
Written aids	20 Seiten (=10 Blätter) DIN A4 (210 mm x 297 mm) selbstverfasste Zusammenfassung (handschriftlich oder getippt). Andere Hilfsmittel sind nicht erlaubt (insbesondere keine 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.