Category: Uncategorized
Selected Lecture Materials – Selected Topics 2020-2021
Selected Lecture Materials
Some open problems in the dynamics
Name | Amy Novick-Cohen |
Date | 19.1.20 |
Faculty | Mathematics |
Title | Some open problems in the dynamics |
Web page | www2.math.technion.ac.il/~amync |
amync@technion.ac.il | |
Study materials | Amy Novick-Cohen 19.1.20 |
Dynamics of recurrent networks with low-rank perturbations
Name | Omri Barak |
Date | 12.1.20 |
Faculty | Medicine |
Title | Dynamics of recurrent networks with low-rank perturbations |
Web page | https://barak.net.technion.ac.il/ |
omri.barak@gmail.com | |
Study materials | Omri Barak 12.01.20 |
Mathematical Models for Air and Water Quality through Wireless Distributed Sensor Networks
Name | Barak Fishbain |
Date | 29.12.19 |
Faculty | CEE |
Title | Mathematical Models for Air and Water Quality through Wireless Distributed Sensor Networks |
Web page | https://fishbain.net.technion.ac.il/ |
fishbain@technion.ac.il | |
Study materials | Barak Fishbain 29.12.19 |
Flow, deformation and, reaction in porous media: The preferential flow case
Name | Yaniv Edery |
Date | 5.1.20 |
Faculty | CEE |
Title | Flow, deformation and, reaction in porous media: The preferential flow case |
Web page | https://sites.google.com/view/pmvlab |
ysnivedery@technion.ac.il | |
Study materials | Yaniv Edery 5.1.20 |
Analytical methods in differential equations – Syllabus
Strum Theory. Proof of existence of eigenvalues of the Strum-Liouville problem, and properties of these eigenvalues. Properties of the Eigen functions of the Strum-Liouville Problem. The adjoint operator, and the self-adjoint operator. The Fredholm Alternative theorem. Solvability conditions. Bessd Functions. The Legendre Polynomials. Other special functions such as the gamma Function, the Beta Functions. The Hilbert-Schmidt theorem. Convergence theorems for series of Eigen functions. The Rayleigh-Ritz theorem. The Fourier Transform. The Laplace Transform. Application of all the above to PDEs (with 2 or 3 special variables, as well as time).
At the end of the course the student will be able to
- Obtain solvability conditions for a non-homogeneous ODE with boundary conditions.
- Obtain and use the Green function for ODEs and PDEs
- Obtain solutions to PDEs using generalized Fourier series and special functions.
- Obtain solutions to ODEs and PDEs using integral transforms special functions.
Analytical methods in differential equations – Mandatory prerequisite
- Single variable and multi variable calculus
- A first course in ODEs (mandatory)
- A first course in PDEs (recommended)
- Complex functions
Analytical methods in differential equations – Technical details
- A four-hour lecture course which provides four academic points.
- A weekly homework assignment will be provided.
- There will be a final exam.
- One of the questions at the final exam will be similar to one of the questions in the homework.
- The lecturer will prepare formula sheets for use at the final exam. These formula sheets will be available on the course website throughout the semester.
- A large collection of old exam will be available for students on the course website.