# Analysis III Autumn 2018

Lecturer
Alessandra Iozzi (Iozzi)
Coordinator
Stefano D'Alesio (D'Alesio)
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 transforms, Fourier series, separation of variables, methods of characteristics.

## 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.

## Exam

Exams of the previous years
You can find the previous exams with solutions (until 2016) in the AMIV webpage at this link https://www.amiv.ethz.ch/studium/unterlagen/20 (log in to access it).
You can find the previous exams with solutions (for 2017/2018) in this folder https://polybox.ethz.ch/index.php/s/blX7S0zOQTyXOdf.

Winter 2019 - Exam and solutions

 Exam Winter 2019 Solutions Winter 2019

Summer 2019 - Exam and solutions

 Exam Summer 2019 Solutions Summer 2019

The exercise classes are every Thursday/Friday, starting from the first week of lectures, that is on 27/28 September. The problems are on the arguments treated in the lecture held on Thursday.
However, the exercise sheets will be published already every Monday, 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 class.

After the exercise class you have exactly one week to hand in your solutions, either in your assistant's box in HG F27, 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 weekend after you have handed in your exercises. We encourage you to actively participate to the classes.

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

Exercise sheet Due by Solution
Serie 1 - preliminary exercises - Solutions 1
Serie 2 4/5 October Solutions 2
Serie 3 11/12 October Solutions 3
Serie 4 18/19 October Solutions 4
Serie 5 25/26 October Solutions 5
Serie 6 1/2 November Solutions 6
Serie 7 8/9 November Solutions 7
Serie 8 15/16 November Solutions 8
Serie 9 22/23 November Solutions 9
Serie 10 29/30 November Solutions 10
Serie 11 6/7 December Solutions 11
Serie 12 13/14 December Solutions 12
Serie 13 - Solutions 13
Serie 14 - Solutions 14
Serie 15 - Ferienserie - Solutions 15

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

TimeRoomAssistantLanguage
Th 15-16HG E 33.5Eberhard Harnoncourtde/en
Th 15-16HG G 26.5Sam Bodryde/en
Fr 15-16CHN D 46Carl Philipp Bucholtzde
Fr 15-16CHN D 48Shuaixin Qide/en
Fr 15-16HG D 7.1Lütolf Marcode/en
Fr 15-16HG F 26.3Stefanie Millerde
Fr 15-16HG F 26.5Rafaél Monasterios Gallardode/en
Fr 15-16HG G 26.3Giulia Zobristde/en
Fr 15-16ML J 37.1Felix Frickede/en
Fr 15-16LFW C 11Axel Holligerde/en
Fr 15-16ML F 34Annina Eichenbergerde/en
Fr 15-16ML F 36Eric Sinnerde/en
Fr 15-16ML J 34.1Christoph Germannde
Fr 15-16NO C 44Louisa Hillegaartde/en
Fr 15-16NO C 6Natalija Jovanovicde/en
Fr 15-16NO D 11Nicolas Kaufmannde/en
Fr 15-16NO E 39Victor Klemmde/en
Lecture notes by Prof. Dr. Alessandra Iozzi: notes

Literature
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).