Ordinary differential equations I
General data
Course ID: | 1000-114bRRZIb |
Erasmus code / ISCED: |
11.132
|
Course title: | Ordinary differential equations I |
Name in Polish: | Równania różniczkowe zwyczajne z laboratorium |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: |
Obligatory courses for 2nd grade JSEM Obligatory courses for 2nd grade JSIM (3M+4I) Obligatory courses for 2rd grade Mathematics Obligatory courses for 4th grade JSIM (3I+4M) |
ECTS credit allocation (and other scores): |
7.50
|
Language: | Polish |
Type of course: | obligatory courses |
Prerequisites (description): | (in Polish) Oczekuje się dobrej znajomości zagadnień ujętych w sylabusach przedmiotów Analiza matematyczna I.2 oraz Analiza matematyczna II.1. |
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: |
E. Hairer, S. P. Norsett, G. Wanner "Solving Ordinary Differential Equations", Springer V.I.Arnold, R.Crooke "Ordinary differential equations", Springer Boyce, DiPrima, "Elementary differential equations", Wiley |
Learning outcomes: |
Knowledge and skills: The students:
Competence:
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Assessment methods and assessment criteria: |
(in Polish) Zaliczenie na podstawie kolokwium, prac domowych, aktywności na zajęciach, projektów komputerowych. Egzamin pisemny i w wyjątkowych przypadkach ustny. Ocena końcowa na podstawie punktów z kolokwium, ćwiczeń, laboratorium i egzaminu. |
Classes in period "Summer semester 2023/24" (in progress)
Time span: | 2024-02-19 - 2024-06-16 |
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MO TU LAB
LAB
WYK
W LAB
LAB
LAB
CW
CW
CW
TH LAB
CW
FR |
Type of class: |
Classes, 30 hours
Lab, 15 hours
Lecture, 30 hours
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Coordinators: | Piotr Kowalczyk | |
Group instructors: | Bartosz Bieganowski, Marcin Choiński, Piotr Kowalczyk, Norbert Mokrzański, Magdalena Szafrańska | |
Students list: | (inaccessible to you) | |
Examination: | Examination |
Classes in period "Summer semester 2024/25" (future)
Time span: | 2025-02-17 - 2025-06-08 |
Navigate to timetable
MO TU W TH FR |
Type of class: |
Classes, 30 hours
Lab, 15 hours
Lecture, 30 hours
|
|
Coordinators: | Piotr Kowalczyk | |
Group instructors: | Bartosz Bieganowski, Michał Borowski, Roman Korsak, Piotr Kowalczyk, Norbert Mokrzański | |
Students list: | (inaccessible to you) | |
Examination: | Examination |
Copyright by University of Warsaw.