MU:MU02037 Partial Differential Eq. I - Course Information

MU02037 Partial Differential Equations I

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Jana Kopfová, Ph.D. (lecturer)
doc. RNDr. Jana Kopfová, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Jana Kopfová, Ph.D.
Mathematical Institute in Opava

Timetable

Wed 9:45–11:20 RZ

• Timetable of Seminar Groups:

MU02037/01: Wed 11:25–13:00 RZ, J. Kopfová

Prerequisites (in Czech)

TYP_STUDIA(N)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Geometry and Global Analysis (programme MU, NMgr-M)
• Mathematical Analysis (programme MU, NMgr-M)
• Mathematical Modelling (programme MU, NMgr-M)

Course objectives (in Czech)

PDR jsou v jistém smyslu vyvrcholením matematické analýzy, uplatňují se tu výsledky z integrálního a diferenciálního počtu, algebry, geometrie, komplexní analýzy. Přednáška je přehledem klasických výsledků a metod o PDR, budeme se zabývat rovnicemi prvního a druhého řádu.

Syllabus

• 1. Basic notations and definitions. Some known equations. Well posed problems. Short history of PDEs.
  2. PDE's of first order, method of characteristics. Linear, quasilinear and nonlinear equations of first order.
  3. Cauchy initial problem, Cauchy-Kowalevska theorem.
  4. Classification of equations of second order, reduction to the canonical form.
  5. Parabolic equations. Derivation of the physical model. Cauchy problem, fundamental solution, properties of solutions of parabolic PDE's, Maximum principle.
  6. Fourier's method for parabolic and hyperbolic equations. The Laplace equation on a circle.
  7. Hyperbolic equations. Method of characteristics. D'Alembert formula. Hyperbolic equations on a halfline. Three and two-dimensional wave equation. Riemann's method.
  8. Elliptic equations. Physical motivation, Harmonic functions. Symmetric solutions, Maximum principle. Potentials: volume potential, simple layer potential, double layer potential. Green's formulas. Dirichlet problem and Neumann problem,
  Poisson's formula.

Literature

required literature
• Jan Franců. Parciální diferenciální rovnice. Brno, 1998. info
• M. Renardy, R. C. Rogers. An introduction to partial differential equations. New York, 1993. info

recommended literature
• V. I. Averbuch. Partial differential equations. MÚ SU, Opava. info
• L. C. Evans. Partial diferential equations. 1998. info

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course can also be completed outside the examination period.

Teacher's information

Written exams: 3 written exams during the term, all together for 100 points
For zápočet minumum of 75 points is needed.
Exam: Written exam, oral exam. Student with 90 points or more from the exams during the term has only oral exam.

• Enrolment Statistics (Summer 2023, recent)
  
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