2011 - Žádost o prodlouženàplatnosti akreditace bakalářského ...
2011 - Žádost o prodlouženàplatnosti akreditace bakalářského ...
2011 - Žádost o prodlouženàplatnosti akreditace bakalářského ...
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SLEZSKÁ UNIVERZITA V OPAV!<br />
01.09.<strong>2011</strong><br />
35 / 80<br />
P!EDM"TY - AKREDITA#NÍ SESTAVA<br />
<strong>2011</strong>/12<br />
MU/02027<br />
Parciální diferenciální rovnice I<br />
Partial Differential Equations I<br />
Statut:<br />
Po"et kredit#:<br />
Forma výuky:<br />
Rozsah výuky:<br />
Ukon"ení:<br />
Garant:<br />
Povinný<br />
6<br />
P!ednáška,Cvi$ení<br />
2 HOD/TYD + 2 HOD/TYD<br />
Zkouška<br />
Doc. RNDr. Jana KOPFOVÁ, Ph.D.<br />
Cíle:<br />
PDR sú v istom zmysle vyvrcholením matematickej analýzy, uplat'ujú sa tu<br />
výsledky z integrálneho a diferenciálneho po$tu, algebry, geometrie, komplexnej<br />
analýzy.<br />
Prednáška je preh)adom klasických výsledkov a metód z PDR, budeme sa zaobera*<br />
rovnicami prvého a druhého rádu.<br />
Obsah:<br />
1.Basic notations and definitions. Some known equations. Well posed problems.<br />
Generalized solutions. Short history of PDEs<br />
2.PDE's of first order. Cauchy problem. Characteristic ordinary differential<br />
equations. Homogenized linear equations of first order . Quasilinear equations.<br />
Nonlinear equations of first order. Plane elements. Monge cone<br />
3.Cauchy initial problem. Cauchy-Kowalewska theorem. Generalized Cauchy problem.<br />
Characteristics<br />
4.Classification of equations of second order. Linear PDE's with constant<br />
coefficients. Linear PDE's of second order: reduction to the canonical form<br />
5.Parabolic equations. Derivation of the physical model. Correctly stated<br />
boundary value problems. Cauchy problem: fundamental solution; existence and<br />
uniqueness theorem. Maximum principle<br />
Fourier method. Boundary value problems for parabolic equations. Hyperbolic<br />
equations. The Laplace equation on a circle<br />
6.Hyperbolic equations. Method of characteristics. D'Alembert formula.<br />
Hyperbolic equations on a halfline and on a finite interval. Three-dimensional<br />
wave equation. Riemann method for the Cauchy problem. Riemann formula<br />
7.Elliptic equations. Laplace equation. Poisson equation. Physical motivation.<br />
Harmonic functions. Symmetric solutions. Maximum principle. Uniqueness of<br />
solutions<br />
Literatura:<br />
Jan Franc#: Parciální diferenciální rovnice, Brno 1998<br />
L. C. Evans: Partial diferential equations 1998<br />
M. Renardy, R. C. Rogers: An introduction to partial differential equations, New<br />
York 1993<br />
V. I. Averbuch: Partial differential equations, MÚ SU, Opava
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