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About Author
Preface
Preparation
About This Book
Python
JupyterLab
Google Colab
Numerical Analysis
1. Numbers and Quantization Errors
1.1. Bits
1.2. Characters
1.3. Integers
1.4. Floating Point Numbers
1.5. Digitization Errors
1.7. Applications
1.8. Problems
2. Functions
2.1. Common Functions in Physics
2.2. Plotting functions
2.3. Applications in Physics
2.3.1. An Overdamped Motion
2.3.2. Quantum Free Falling
2.3.3. Hydrogen Atom
3. Numerical Derivative
3.1. Finite Difference Methods
3.2. Adaptation of step size
3.3. Second order derivative
3.4. Laplacian
3.5. Problems
4. Root Finding
4.1. Roots of Polynomials
4.2. Bisection Method
4.3. Newton-Raphson method
4.4. Application in Physics
4.4.1. Classical Turning Points
4.4.2. The Closest Approach in a Scattering
4.4.3. Ferromagnetic Phase Transition
4.4.4. A Quantum Particle in a Potential Well
5. Numerical Integration
5.1. Piecewise integration
5.2. Milti-dimensional Integrals
5.3. Improper Integrals
5.3.1. Improper Integrals I: Infinite bound
5.3.2. Improper Integrals II: Integrable Singularities
5.4. Applicatins in Physics
5.4.1. Electric Potential by Charge on a Ring
5.4.2. Ideal Fermi/Bose Gases
5.4.3. The Period of Classical Oscillation
5.4.4. Scattering by the Yukawa potential
5.5. Exercise solutions
6. Ordinary Differential Equations
6.1. Initial Value Problems
6.2. Boundary Value Problems
6.3. Eigenvalue Problems
7. Linear Algebrea
8. Fourier Transformation
8.1. Fourier Theorem and Fourier Transformation
8.2. Discrete Fourier Transform
8.3. Fast Fourier Transform
9. Partial Differential Equations
Monte Carlo simulation
10. Random Number Generators
11. Random Walks
12. Metropolis Methods
13. Langevin Equations
14. Optimization
References
Repository
Open issue
.md
.pdf
Preface
Preface
#
To be written
Ryoichi Kawai, July 30, 2022
