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
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)
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