http://mech.spbstu.ru/?title=Calculus_of_Variations_and_Integral_Equations&feed=atom&action=history Calculus of Variations and Integral Equations - Revision history 2024-03-29T15:56:52Z Revision history for this page on the wiki MediaWiki 1.27.3 http://mech.spbstu.ru/?title=Calculus_of_Variations_and_Integral_Equations&diff=6353&oldid=prev Vakulinaa at 17:44, 15 November 2015 2015-11-15T17:44:35Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 17:44, 15 November 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10" >Line 10:</td> <td colspan="2" class="diff-lineno">Line 10:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>back to [[IMDP| International MSc program &quot;<del class="diffchange diffchange-inline">Advanced Dynamics of Discrete </del>and <del class="diffchange diffchange-inline">Continuum Systems</del>&quot;]]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>back to [[IMDP| International MSc program &quot;<ins class="diffchange diffchange-inline">Mechanics </ins>and <ins class="diffchange diffchange-inline">Mathematical Modeling</ins>&quot;]]</div></td></tr> <!-- diff cache key wikidb-mech_:diff:version:1.11a:oldid:1459:newid:6353 --> </table> Vakulinaa http://mech.spbstu.ru/?title=Calculus_of_Variations_and_Integral_Equations&diff=1459&oldid=prev Галина Крохалева: Created page with "The objectives of the discipline ''Calculus of Variations and Integral Equations'' is to develop knowledge of the basic tenets of the theory of integral equations and mastery of ..." 2014-06-04T09:46:51Z <p>Created page with &quot;The objectives of the discipline &#039;&#039;Calculus of Variations and Integral Equations&#039;&#039; is to develop knowledge of the basic tenets of the theory of integral equations and mastery of ...&quot;</p> <p><b>New page</b></p><div>The objectives of the discipline ''Calculus of Variations and Integral Equations'' is to develop knowledge of the basic tenets of the theory of integral equations and mastery of the respective solutions of problems and exercises, knowledge of the main provisions of the calculus of variations and the ability to use the concepts and methods of the theory in solving problems arising in theoretical and mathematical physics.<br /> <br /> '''Content:'''<br /> <br /> 1. Integral equations<br /> Classification of integral equations. Methods of solving Volterra integral equations of both the first and the second kind. Some approaches to solutions of Fredholm integral equations (degenerative kernels, Fredholm resolvent, continuous kernels). Theory of Fredholm integral equations with symmetric kernels. Hilbert-Schmidt theorem. Application to Sturm-Liouville problem. Green function.<br /> <br /> 2. Calculus of variations<br /> Functionals and proximity of functions. Lagrange’s lemma. Necessary condition for an extremum. Increment of a functional and its variation. Transversality conditions. Functionals of several dependent variables. Functionals dependent on higher derivatives. Functionals dependent on functions of several independent variables. Conditional extremum. Isoperimetric problem. Sturm-Liouville systems as variational problems. Lagrange problem. Direct methods for solving variational problems (Ritz’s, Galerkin’s and Kantorovich’s methods)<br /> <br /> <br /> back to [[IMDP| International MSc program &quot;Advanced Dynamics of Discrete and Continuum Systems&quot;]]</div> Галина Крохалева