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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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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.
A. Change of variables for parabolic equation.
a. Change of spacial variable for evolution equation.
b. Multiplicative change of unknown function for evolution equation.
c. Orthogonal transformation for evolution equation.
B. Discontinuous Galerkin technique.
C. Laplace quadrature.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Change of spacial variable for evolution equation.

e are making the change MATH Thus

MATH MATH The LHS of the equation ( Generic parabolic PDE ) takes the form MATH Therefore, we arrive to a new equation of the form MATH MATH

Note that the expression MATH has the same structure as the original equation. It is important to note that we do not have to inherit boundary conditions of original problem when considering $y_{k}$ . In particular, separation of variables might become applicable.

Notation. Index. Contents.

Copyright 2007