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 I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 1 Calculational Linear Algebra.
 2 Wavelet Analysis.
 3 Finite element method.
 4 Construction of approximation spaces.
 5 Time discretization.
 6 Variational inequalities.
 A. Stationary variational inequalities.
 B. Evolutionary variational inequalities.
 a. Strong and variational formulations for evolutionary problem.
 b. Existence and uniqueness for evolutionary problem.
 c. Penalized evolutionary problem.
 d. Proof of existence for evolutionary problem.
 VIII. Bibliography
 Notation. Index. Contents.

## Strong and variational formulations for evolutionary problem.

roblem

(Evolutionary variational inequality problem) For a bounded set with smooth boundary, time interval and given functions , find a function satisfying the relationships where the operation is given by the definition ( Bilinear form B 2 ) and the class of functions is defined by We introduce

Problem

(Strong formulation of evolutionary problem) For a bounded set with smooth boundary, time interval and given functions , find a function satisfying the relationships in and where the operator is defined by the formula ( Operator L 2 ).

Condition

(Symmetric principal part) We assume that

 Notation. Index. Contents.