Analysis III Autumn 2019

Francesca Da Lio
Stefano D'Alesio

- Monday, 24 February 2020, 8:15-9:45 in room HG G 19.1
- Tuesday, 3 March 2020, 17:15-18:30 in room HG G 19.1
- Monday, 13 January 2020, 10:00-11:30 in room HG G 19.1
- Monday, 20 January 2020, 13:00-14:30 in room HG G 19.1.
Thursday 13-15, in HG F 7 and video transmission in HG F 5.
The lectures will be recorded and they are available on
First lecture on 26.09
Exercise classes
Thursday 15-16.
First exercise classes on 26.09
Study Center MAVT
Monday 16-18 in ML H 41.1.
(according to the lecture times in Zentrum: 16:15 - 18:00)
Study Center MATL
Wednesday 15-17 in HCP E 47.3.
(according to the lecture times in Hönggerberg: 14:45 - 16:30)

Course contents

Introduction 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 transform, Fourier series, Fourier transform, separation of variables.

Detailed program

Laplace transform
Laplace transform, inverse Laplace transform, linearity, s-shifting. Transforms of derivatives and integrals, application to 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 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 Summaries

The detailed program of each lecture and the notes from the lectures are published weekly on the webpage ~fdalio/ANALYSISIIIDMAVTDMATLHS19 under "Class content".

Written session examination, 120 minutes, English.

Allowed aids:
20 pages (=10 sheets) DIN A4 summary. The students are encouraged to write their personal summary. However, non personal summaries provided by the Amiv or other students are allowed as well. English <-> German dictionary.

NOT allowed:
Electronic devices (such as, but not limited to, smartphones, calculators, tablets, laptops, etc.) are NOT allowed to use during the exam.
In order to make sure, that everyone has the same information about the exam only what is written about the exam here or in the VVZ is legally binding for the exam.

In the exam, we will not ask about the transformation of a PDE in a canonical form but the classification (linear, homogeneous, degree, elliptic, parabolic, hyperbolic) of a PDE may be asked. Furthermore, we will ask explicitly if one has to describe the steps of the method of separation of variables or take a formula for given.

The Amiv ( provides a large collection of exams from previous semesters. More recent exams can be downloaded here (, and the most recents (HS 18) are available on the webpage of last year (

Winter 2020 - Exam and solutions

Exam Winter 2020 Solutions Winter 2020
Exam Summer 2020 Solutions Summer 2020

The exercise classes take place every week, starting from the first week of lectures (23-27 September). The problems are on the topics treated in the lecture held on Thursday.
However, the exercise sheets will be published already at the beginning of the week, so that you can start having a look at them.
We expect you to do that, in order to be able to ask your questions in the exercise classes.

After the exercise class you have one week to hand in your solutions, either in your assistant's box (next to the office HG F 27.3), or directly to your assistant in the following exercise class.
Your solutions will then be corrected and handed in back to you in the second exercise class to come (or left in the box if you're not there in the class).
Written solutions will be published in the day you hand in your exercises. We encourage you to actively participate in the classes.

Bonus exercises: some exercises are denoted by "Bonus exercise". They are not necessary in preparation for the exam.

Serie # Discussed on Hand in by Solutions
Serie 1 - Warm up - - Solutions 1
Serie 2 26 Sep 3 Oct Solutions 2
Serie 3 3 Oct 10 Oct Solutions 3
Serie 4 10 Oct 17 Oct Solutions 4
Serie 5 17 Oct 24 Oct Solutions 5
Serie 6 24 Oct 31 Oct Solutions 6
Serie 7 31 Oct 7 Nov Solutions 7
Serie 8 7 Nov 14 Nov Solutions 8
Serie 9 14 Nov 21 Nov Solutions 9
Serie 10 21 Nov 28 Nov Solutions 10
Serie 11 28 Nov 5 Dec Solutions 11
Serie 12 5 Dec 12 Dec Solutions 12
Serie 13 12 Dec - Solutions 13
Serie 14 19 Dec - Solutions 14
Serie 15 - Ferienserie - - Solutions 15
It's important that you give us feedback on the exercise classes through your teaching assistant.

Please enroll in an exercise class as soon as you can via myStudies and spread as evenly as possible. Only the tutor you are enrolled with is obliged to correct your exercises.

Thursday 15-16CHN D 46Lars BeglingerGerman
Thursday 15-16HG E 1.1Lena EgliGerman
Thursday 15-16CLA E 4Shady Elshater MohamedEnglish
Thursday 15-16ETZ F 91Jacob Euler-RolleGerman
Thursday 15-16CAB G 59Daniel Flavián BlascoGerman
Thursday 15-16HG E 21Sarah HodelGerman
Thursday 15-16ML E 12Florian HuwylerGerman
Thursday 15-16HG E 33.5Raamadaas KrishnadasGerman
Thursday 15-16HG G 26.3Thomas-Julien MendozaGerman
Thursday 15-16HG G 26.5Marco SemeraroGerman
Thursday 15-16LEE D 105Eric StrauchGerman
Thursday 15-16LFW C 4Bhavya SukhijaGerman
Thursday 15-16ML F 38Michael SzalaiGerman
Thursday 15-16ML J 37.1Vullnet UseiniGerman
Thursday 15-16NO C 6Chantal WoodtliGerman
Lecture notes by Alessandra Iozzi: last version (June 2019) Analysis III MAVT-MATL
Lecture notes by Alessandro Sisto / Martin Larson for the section on the Laplace transform: available at the webpage of the course Analysis III 2017 D-BAUG

E. 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:
Ingenieur-Analysis by Christian Blatter (available at ~Blatter).

Interactive learning
Since during the lectures we will work with EduApp, we encourage the students to download it: EduApp