457-0308/02 – Equations of Mathematical Physics (RMFPM)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | prof. RNDr. Marek Lampart, Ph.D. | Subject version guarantor | prof. RNDr. Marek Lampart, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2003/2004 | Year of cancellation | 2009/2010 |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The main aim of the subject is to formulate classical partial differential equations motivated by physical phenomena and to use classical methods for their solutions.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
This course is devoted to the analytical methods of the solution of the partial differentia equations. All the methods will give us fruitful imagination of the qualitative behavior of the mathematical modeling. This information will be very useful tor the future modeling of more complicated problems. During this course there will be given standard set of the classical partial differential equations and their properties. Also stability and uniqueness will be discussed.
Compulsory literature:
P. Drábek, G. Holubová: Parciální diferenciální rovnice (Úvod do klasické teorie). Skripta ZČU Plzeň, 2001.
J. Franců: Parciální diferenciální rovnice. Skripta VUT Brno, 2000.
S. Míka, A. Kufner: Parciální diferenciální rovnice I. Stacionární rovnice. Edice MVŠT, sešit XX, SNTL Praha, 1983.
J. Barták, L. Herrmann, V. Lovicar, O. Vejvoda: Parciální diferenciální rovnice II. Evoluční rovnice. Edice MVŠT, sešit XXI, SNTL Praha, 1988.
W. A. Strauss: Partial Differential Equations (An Introduction), John Wiley & Sons, Inc., New York 1992.
Recommended literature:
Textbook for students of the PDE.
Way of continuous check of knowledge in the course of semester
Study control:
There will be tests and projects needed for a credit.
Conditions for the credit:
Student will pass a credit if all projects are submitted on time
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Talks:
First order equations, Cauchy problem, characteristic equations.
Cauchy problem for equations of higher degrees.
Classification equations of the second order.
Formulation of the classical equations given by physical phenomenon (formulation boundary and initial conditions) like: heat eq., diffusion eq., wave eq., Laplace and Poisson eq., etc.
Solution by method of characteristic.
Solution by Fourier method.
Solution by integral transformations.
Solution by Green function.
Maximal principle and uniqueness of solution.
Solution by method of potentials.
Seminars:
Examples of solutions of the classical partial differential equations, compare PDE and ODE.
Classification of the equations, reduction to the canonical form.
Formulation of the classical type eq and their boundary and initial conditions.
Solution of several eq. by characteristic method.
Solution of several eq. by Fourier method.
Solution of several eq. by Green functions.
Application of the Green function.
Solution of the uniqueness problem of the eq.
Solution of several eq. using potentials.
Solution of several eq. by using mathematical software.
Projects:
Students will solve standard problems based on typical equations and their applications.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.