About Me

About Me

MSc Student of EECS at ETH Zurich

Introdction to Partial Differential Equations

Undergraduate course, ETH Zurich, Department of Mathematics, 2022

I was a teaching assistant responsible for holding weekly exercise sessions.
The course is instructed by Prof. Dr. Mikaela Iacobelli.

Content

The course provides a general overview of first and second order PDEs, with a focus on the solution of quasilinear first order PDEs with the method of characteristics, and on the study of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation, and the wave equation.

My role

I taught and led a class of 40 engineering students weekly throughout the semester in the weekly exercise sessions.
I also designed weekly exercise sheets and corrected handed-in exercises by students.

My sessions

DateTopicSlidesHomework & Solution
30.09.2022Introduction, classification of PDEs (order, linearity, quasilinearity, homogeneity), examples, associated conditions to obtain a unique solution.[Preliminary] [Annotated]Homework 1
Solution 1
07.10.2022First order equations, quasilinear equations, Method of Characteristics, examples.[Preliminary] [Annotated]Homework 2
Solution 2
14.10.2022Examples of the characteristics method, and the existence and uniqueness theorem.[Preliminary] [Annotated]Homework 3
Solution 3
21.10.2022Conservation laws and shock waves.[Preliminary] [Annotated]Homework 4
Solution 4
28.10.2022Shock waves: the Rankine-Hugoniot condition, and the entropy condition. Classification of second order linear PDEs.[Preliminary] [Annotated]Homework 5
Solution 5
04.11.2022The one-dimensional wave equation, canonical form and general solution. The Cauchy problem and d’Alembert formula.[Preliminary] [Annotated]Homework 6
Solution 6
11.11.2022Domain of dependence. The non-homogeneous one-dimensional wave equation. Nonhomogeneous d’Alembert formula. Separation of variables.[Preliminary] [Annotated]Homework 7
Solution 7
18.11.2022Separation of variables for the heat and wave equation, homogeneous problems. Dirichlet and Neumann boundary conditions.[Preliminary] [Annotated]Homework 8
Solution 8
25.11.2022Separation of variables for non-homogeneous equations. Resonance. The energy method for the wave and heat equation, and uniqueness of solutions.[Preliminary] [Annotated]Homework 9
Solution 9
02.12.2022Elliptic equations. The weak maximum principle. The mean value principle. The strong maximum principle.[Preliminary] [Annotated]Homework 10
Solution 10
09.12.2022Applications of maximum principle (uniqueness). The maximum principle for the heat equation. Separation of variables for elliptic problems.[Preliminary] [Annotated]Homework 11
Solution 11
16.12.2022Separation of variables in rectangles, Dirichlet and Neumann compatibility conditions. The Laplace equation in circular domains[Preliminary] [Annotated]Homework 12
Solution 12
23.12.2022The Laplace equation in circular domains: annulus and sectors.[Preliminary] [Annotated]Homework 13
Solution 13