Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | doc. RNDr. Marek Lampart, Ph.D. | Subject version guarantor | doc. RNDr. Marek Lampart, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 2 | 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 |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

KRA04 | Mgr. Bohumil Krajc, Ph.D. | ||

LAM05 | doc. RNDr. Marek Lampart, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 2+2 |

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.

Lectures

Individual consultations

Tutorials

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.

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.

Textbook for students of the PDE.

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

Subject has no prerequisities.

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |

Examination | Examination | 70 | 0 |

Exercises evaluation | Credit | 30 (30) | 10 |

1. Písemka | Written test | 15 | 0 |

2. Písemka | Written test | 15 | 0 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2009/2010 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2009/2010 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2008/2009 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2008/2009 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2007/2008 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2007/2008 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2006/2007 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2006/2007 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2005/2006 | (N2646) Information Technology | (1103T021) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2005/2006 | (N2646) Information Technology | (1103T021) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2004/2005 | (N2646) Information Technology | (1103T021) Computational Mathematics | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2004/2005 | (N2646) Information Technology | (1103T021) Computational Mathematics | K | Czech | Ostrava | 2 | Compulsory | study plan |

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