Uniwersytet w Białymstoku - Centralny System Uwierzytelniania
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Partial Differential Equations 360-MS2-2RRC2a
Ćwiczenia (CW) Rok akademicki 2022/23

Informacje o zajęciach (wspólne dla wszystkich grup)

Liczba godzin: 30
Limit miejsc: (brak limitu)
Zaliczenie: Zaliczenie na ocenę
Literatura: (tylko po angielsku)

1. L. Evans Partial Differential Equations, Springer 1998

2. M. Renardy, R.C.Rogers An introduction to partial differential equations, Springer 1993

3. E.C. Zachmanoglou, D. Thoe Introduction to partial differential equations with applications 1967

4. P. Olver Introduction to partial differential equations, Springer 2013

5. other book of problems for PDEs

Efekty uczenia się: (tylko po angielsku)

Learning outcomes:

Student knows classification of first order partial differential equations (PDE), understands theorem of existence and uniqueness of solutions of Cauchy problem for quasilinear first order PDE. Student knows a notion of first integral; is able to construct general solution of problem for quasilinear first order PDEs by using characteristics. KA7_WG02, KA7_WG03, KA7_UW02, KA7_UW06

Student knows classification of first order PDEs and boudary value problems of different kinds; knows a notion of well-posed problem for mathematical physics equations and understands connection between equations and physical processes, described by them. Student is able to determine the type of PDE with two independent variables.KA7_WG02, KA7_WG04, KA7_WG06, KA7_UW06, KA7_UW10

Student knows a canonical form of hiperbolic PDE, methods of wave propagation, d'Alembert formula and understand Kirchoff formula. Student is able to use these formulas in simple examples. KA7_WG02, KA7_WG06, KA7_UW06

Student knows fundamental solution of Laplace equation, properties of harmonic functions, notion of Green function and its applications.KA7_WG02, KA7_WG03, KA7_UW01, KA7_UW06

Student understands maximum pronciple and uniqueness of solution in boundary value problem for heat equation with two independent variables. Student knows fundamental solution and formula for solutions in Cauchy problem for heat equation.KA7_WG02, KA7_WG04, KA7_WG05, KA7_UW06, KA7_UW10

Student obtains basic practice in creative development of theory of differential equations. KA7_KK01, KA7_KK02, KA7_KK07, KA7_UU01

Metody i kryteria oceniania: (tylko po angielsku)

There will be two written tests based on problems about solving PDEs discussed on classes. Both test must be passed, which means to get al least 51% points.

In case of fail there will be second term to write the test again.

The final mark is accordingly the list:

91%-100% A

81%-90% B

71%-80% C

61%-70% D

51%-60% E

0%-50% F

Zakres tematów: (tylko po angielsku)

1. Cauchy-Kowalewska theorem.

2. Integration of first order quasi-linear and linear PDEs. First integrals. Hamiltonian systems.

3. Classification of second order PDEs.

4. Boundary value problems of different kinds. Well-posed boundary value problems.

5. Hiperbolic equations . Cauchy problem for wave equations. mixed boundary problem for wave equation.

6. Elliptic equations. Properties of harmonic functions. Green function and its properties. Solution of Dirichlet problem.

7. Parabolic equations. Heat equation. Maximum and minimum principles. existence and uniqueness theorem for solutions of Cauchy problem for heat equation.

8. Applications of knowledge to solving theoretical problems as well as to practical ones.

Metody dydaktyczne: (tylko po angielsku)

Teaching methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.

Grupy zajęciowe

zobacz na planie zajęć

Grupa Termin(y) Prowadzący Miejsca Liczba osób w grupie / limit miejsc Akcje
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