Partial Differential Equations
General data
Course ID:  360MS22RRC2a 
Erasmus code / ISCED: 
11.105

Course title:  Partial Differential Equations 
Name in Polish:  Partial Differential Equations 
Organizational unit:  Faculty of Mathematics 
Course groups:  
ECTS credit allocation (and other scores): 
5.00

Language:  English 
Type of course:  obligatory courses 
Prerequisites (description):  Student should know basic methods from onedimensional and multidimensional mathematical analysis and ordinary differential equations. 
Short description: 
Course profile: academic Form of study: stationary Academic discipline: Mathematics, field of study in science: mathematics Prerequisities: Mathematical Analysis, Ordinary Differential Equations lecture 30 h. exercise class 30 h. ECTS credits: 5 
Full description: 
Course is devoted to classical theory of partial differential equations. After course students should know basic, classical methods of solving the first and the second order PDEs, especcialy equations of mathematical physics such as heat equation, wave equation and Laplace equation. 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. Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. 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 
Bibliography: 
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 
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. 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 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.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 
Assessment methods and assessment criteria: 
The overall form of credit for the course: final exam 
Classes in period "Academic year 2022/2023" (past)
Time span:  20221001  20230630 
Navigate to timetable
MO TU W TH FR 
Type of class: 
Class, 30 hours
Lecture, 30 hours


Coordinators:  Tomasz Czyżycki, Aneta Sliżewska  
Group instructors:  (unknown)  
Students list:  (inaccessible to you)  
Examination: 
Course 
Examination
Class  Grading 

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

Bibliography: 
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 
Copyright by University of Bialystok.