Partial Differential Equations
General data
Course ID:  0600MS22RRC2  Erasmus code / ISCED:  11.105 / (0541) Mathematics 
Course title:  Partial Differential Equations  Name in Polish:  Równania różniczkowe cząstkowe 
Department:  (in Polish) Instytut Matematyki  
Course groups: 
(in Polish) 2L stac. II st. studia matematyki  przedmioty obowiązkowe 

ECTS credit allocation (and other scores): 
5.00 view allocation of credits 

Language:  Polish  
Type of course:  obligatory courses 

Short description: 
Course objectives: Knowledge of fundamenta notions and theorems: 1. CauchyKowalewska theorem. 2. Integration of first order quasilinear and linear PDEs. First integrals. Hamiltonian systems. 3. Classification of second order PDEs. 4. Boundary value problems of different kinds. Wellposed 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. 

Full description: 
Course profile: academic Form of study: stationary Course type: obligatory Academic discipline: Mathematics, field of study in the arts and science: mathematics Year: 2, semester: 3 Prerequisities: Differential Geometry, Functional Analysis lecture 30 h. exercise class 30 h. Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. ECTS credits: 5 Balance of student workload: attending lectures15x2h = 30h attending exercise classes 15x2h = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x2h = 14h consultations 12x1h = 12h the final examination: preparation.and take 12h + 3h = 15h control works: repeating the material and preparation 3x4h = 12h Quantitative description Direct interaction with the teacher: 75 h., 3 ECTS Practical exercises: 77 h., 3 ECTS 

Learning outcomes: 
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.K_W02, K_W03, K_U01, K_U06 Student knows classification of first order PDEs and boudary value problems of different kinds; knows a notion of wellposed 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.K_W02, K_W05, K_W07, K_U06, K_U10 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.K_W02, K_W07, K_U06 Student knows fundamental solution of Laplace equation, properties of harmonic functions, notion of Green function and its applications.K_W02, K_W03, K_U01, K_U06 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.K_W02, K_W05, K_W07, K_U06, K_U10 Student obtains basic practice in creative development of theory of differential equations.K_K01, K_K02, K_K07 

Assessment methods and assessment criteria: 
The overall form of credit for the course: final exam 
Classes in period "Academic year 2017/2018" (past)
Time span:  20171001  20180630 
see course schedule 
Type of class: 
Individual Classes more information 

Coordinators:  Małgorzata Zdanowicz  
Group instructors:  Małgorzata Zdanowicz  
Students list:  (inaccessible to you)  
Examination:  Examination 
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