Home Teaching

Advanced Topics in Ordinary Differential Equations

(Formerly Methods of Applied Mathematics 1)

Fall 2021. Reception Hours: Monday, 16:10 - 17:00, on ZOOM. In better times: Room 123b, Schreiber building


The survey lecture, 2021, is the last lecture of the semester to take place on 09/01-2022, ON ZOOM

In the fall of 2021 due to the pandemic the exam is replaced with a home task, which will be available on 13/01-2022.

The work should be submitted by 10/02-2022.


Short Syllabus Preliminary Detailed Syllabus

Literature:

Arnold V.I. "Ordinary differential equations"
Birkhoff G., Rota G.-C.
"Ordinary differential equations"
Boyce W.E.,
DiPrima R.C. "Elementary differential equations and boundary value problems"

Additional literature: Coddington E.A., Levinson N. "Theory of ordinary differential equations"

Linear systems with constant coefficients: method of undetermined coefficients, real numbers' case


Chosen problems from previous exams, including exams on ODE1 and ODE2 UPDATED 09.01.2022. Problems 19, 20 are not relevant for the years 2008-2022

In Hebrew In English


Lectures taught in the Fall of 2021

Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13


Exercises:

The following problems were given in other courses, where also the corresponding solutions were given.

Theorem of existence and uniquiness: 1-4(solution); Dependence on parameters: 1,2 (solution);

Newton equation: 1-3 (part.solution);  Liouville theorem: 1-3 (solution); Matrix exponent: 3(solution);

Comparison theorems: 1-4(solution); Sturm theorems: 1-4(solution); Critical points in plane: 1-11(solution);

Stability theory: 1-6(solution); stability region: 1,2,3(solution) ; region of attraction, region of convergence: 1,2(solution);

Boundary value problems: 2,3(solution); Green function, Sturm-Liouville problem: 1-4(solutions a, b);

NEW (2021): Solution of ODE by means of power series, remainder evaluation: 4 (solution)

Not included in 2008-2021: non-homogeneous irregular boundary problems (solution)


Test 2006, moed a

Exam conditions

There are 5 questions, each student has to choose 4 exactly to solve.

One may take with him 2 sheets of paper A4 filled from both sides by hand with formulas. Calculators are allowed, but not needed