Computational Science
Illustrating practical examples from computational science, this applications-oriented book teaches students and engineers how to employ mathematical techniques for simulation and data processing using Mathcad.
TABLE OF CONTENTS Computational Science
List of Code Examples
Chapter 1: Data Processing
- Example 1.1: Reading matrices from a data file
- Example 1.2: Computing the mean value and dispersion of a data array
- Example 1.3: Example of preparing data for histograms
- Example 1.4: Interval estimate of the dispersion
- Example 1.5: Test of statistical hypothesis using the Student s distribution
- Example 1.6: Cubic spline interpolation
- Example 1.7: Realization of the algorithm (14 16) of time-space interpolation
- Example 1.8: Generating correlated samples of random data
- Example 1.9: Modeling ray propagation in heterogeneous media
- Example 1.10: The envelope and phase of Gaussian process
- Example 1.11: Fast Fourier transform of FOREX data
- Example 1.12: Direct and inverse FFT of model data
- Example 1.13: Aliasing effect
- Example 1.14: Effect of shifting zero line (Listing 1.12, continued)
- Example 1.15: Computing power spectrum
- Example 1.16: Polynomial regression
- Example 1.17: Running medians smoothing
- Example 1.18: Wavelet transform
Chapter 2: Inverse Problems
- Example 2.1: Example of the direct problem
- Example 2.2: Constructing the discrete form of a direct problem
- Example 2.3: Solving an overdetermined SLAE
- Example 2.4: Regularization method
- Example 2.5: Quasi solution (Listing 2.2, continued)
- Example 2.6: Solving a triangular SLAE
- Example 2.7: LU-decomposition
- Example 2.8: Cholesky decomposition
- Example 2.9: QR decomposition
- Example 2.10: SVD decomposition
- Example 2.11: Linear reduction
Chapter 3: Ordinary Differential Equations Cauchy Problems
- Example 3.1: Solving a logistic equation
- Example 3.2: Model of a two-species competition
- Example 3.3: Solving the system of equations (14)
- Example 3.4: Euler method
- Example 3.5: Backward Euler method (Listing 3.4, continued)
- Example 3.6: Implicit Euler algorithm (Listing 3.4, continued)
- Example...
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