Ordinary differential equations I

General data

Course ID:	1000-114aRRZI
Erasmus code / ISCED:	11.102 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Ordinary differential equations I
Name in Polish:	Równania różniczkowe zwyczajne I z laboratorium
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	obligatory courses
Short description:	Ordinary differential equations (ODEs), their properties and applications. Solution methods for ODEs: using paper and pencil, and using numerical schemes. Computer lab experiments: numerical and symbolic ODE packages.
Full description:	Differential equation and its solution, first order and higher order equations, systems of differential equations, direction field, solution methods for simple types equations. Simple numerical one- and multistep schemes. Runge-Kutta methods. Explicit and implicit schemes. Ways to derive numerical methods for ODEs. Local existence and uniqueness theorems. Prolongation of the solution. Dependence on a parameter or on the initial condition; differentiability with respect to the parameter. Systems of linear ODEs, the basis of the solutions. The fundamental matrix. Wronskian, Liouville's theorem. Systems with constant coefficients. Exponential of a matrix, nonhomogeneous systems. Higher order linear ODEs with constant coefficients. Difference equations and their properties. Convergence theory for one-step methods. Consistency and stability. Stability and strong stability of multistep methods. Nonlinear ODEs and stability. Lyapunov function. Phase plane and taxonomy of phase curves of autonomous systems. Singular points on a plane. Absolute stability and the region of absolute stability. Stiffness and how to cope with it. Computer lab experiments: numerical and symbolic ODE packages.
Bibliography:	- V.I.Arnold, R.Crooke "Ordinary differential equations", Springer - Boyce, DiPrima, "Elementary differential equations", Wiley

This course is not currently offered.

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