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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.
A. Elementary definitions of wavelet analysis.
B. Haar functions.
C. Multiresolution analysis.
D. Orthonormal wavelet bases.
E. Discrete wavelet transform.
F. Construction of MRA from scaling filter or auxiliary function.
G. Consequences and conditions for vanishing moments of wavelets.
H. Existence of smooth compactly supported wavelets. Daubechies polynomials.
I. Semi-orthogonal wavelet bases.
J. Construction of (G)MRA and wavelets on an interval.
a. Adapting MRA to the interval [0,1].
b. Adapting wavelets to interval [0,1].
c. Adapting GMRA to interval [0,1].
d. Adapting dual wavelets to interval [0,1].
e. Constructing dual GMRA on [0,1] with boundary conditions.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Constructing dual GMRA on [0,1] with boundary conditions.

ne can construct wavelet bases satisfying homogeneous boundary conditions, such as MATH by starting from linear combinations of the boundary functions $x_{d,L}^{m}$ , MATH , MATH , MATH satisfying such boundary conditions and then repeating procedures of the previous sections. In particular, for the Dirichlet conditions above we simply drop the constant term from the set of initial boundary functions.

Notation. Index. Contents.

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