470-4112/02 – Equations of Mathematical Physics (RMFPM)
Gurantor department | Department of Applied Mathematics | Credits | 6 |
Subject guarantor | prof. RNDr. René Kalus, Ph.D. | Subject version guarantor | prof. RNDr. René Kalus, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | winter |
| | Study language | English |
Year of introduction | 2015/2016 | Year of cancellation | |
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:
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:
Assigned home tasks.
Conditions for the credit:
At least 10 points gained.
E-learning
Other requirements
There are not defined other requirements for student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction