Methods of Applied Mathematics 1
Fall 2012. Reception Hours: Sunday, 15:30 - 16:30, Room 320, Schreiber building
SHIUR HAZARA (review lecture): February 17, 2013, 15:10 - 18:00, Schreiber. 007.
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 02.2013. Problems 20, 21 are not relevant for the semesters of the fall 2008, 2009, 2012
The following problems were given in other courses, where also the corresponding solutions were given.
Theorem of existence and uniquity: 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);
Not included in Fall 2008, 2009, 2012: non-homogeneous irregular 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
