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Titlebook: Variational Methods in Mathematics, Science and Engineering; Karel Rektorys Book 1977 Karel Rektorys 1977 Mathematica.applied mathematics.

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11#
發(fā)表于 2025-3-23 12:14:44 | 只看該作者
12#
發(fā)表于 2025-3-23 17:53:56 | 只看該作者
Hilbert Spaceintegrable in the domain ., with the metric as defined in Chap. 3. We could have started earlier with axioms of the Hilbert space and with the investigation of its properties, without first becoming familiar with .(.). However, a different approach has been chosen which is — in our opinion — by far
13#
發(fā)表于 2025-3-23 18:24:47 | 只看該作者
14#
發(fā)表于 2025-3-23 22:58:40 | 只看該作者
Operators and Functionals, especially in Hilbert Spaces a given element (as a rule, a function considered as an element of a Hilbert space, e.g., of the space .(.)), and . is the desired solution. To explain the meaning of equation (8.1) in more detail let us present a simple example.
15#
發(fā)表于 2025-3-24 02:27:30 | 只看該作者
16#
發(fā)表于 2025-3-24 08:58:49 | 只看該作者
Existence of the Minimum of the Functional , in the Space ,. Generalized Solutions if the equation . = . has a solution.) . ∈ ., then the functional . assumes, for this element ., its minimal value among all the elements. ∈ ., and - conversely — if . assumes on . its minimal value for a certain element . ∈ ., then this element is the solution of the equation . = . in .. At the en
17#
發(fā)表于 2025-3-24 14:18:15 | 只看該作者
18#
發(fā)表于 2025-3-24 18:28:43 | 只看該作者
19#
發(fā)表于 2025-3-24 20:13:51 | 只看該作者
The Method of Steepest Descent. Example method is applicable in the case of bounded operators (Def. 8.13, p. 96), therefore not in the case of differential operators. A typical example of equations to the solution of which it is preferable to apply this method are integral equations.
20#
發(fā)表于 2025-3-24 23:26:08 | 只看該作者
Book 1977ollege of Civil Engineering of the Tech- nical University in Prague, from experience gained as supervisor and consultant to graduate students-engineers in the field of applied mathematics, and - last but not least - from frequent consultations with technicians as well as with physicists who have ask
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