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Physics
Applied and Interdisciplinary Physics
Computational Physics
1. Introduction to Computational Physics
2. Mathematical Foundations
3. Programming Fundamentals
4. Computer Arithmetic and Error Analysis
5. Root Finding Methods
6. Numerical Differentiation
7. Numerical Integration
8. Linear Systems
9. Eigenvalue Problems
10. Ordinary Differential Equations
11. Partial Differential Equations
12. Monte Carlo Methods
13. Molecular Dynamics
14. Data Analysis and Visualization
15. Applications in Classical Mechanics
16. Applications in Electromagnetism
17. Applications in Quantum Mechanics
18. Applications in Statistical Mechanics
19. Applications in Fluid Dynamics
20. High-Performance Computing
5.
Root Finding Methods
5.1.
Single Variable Root Finding
5.1.1.
Bisection Method
5.1.2.
Newton-Raphson Method
5.1.3.
Secant Method
5.1.4.
Fixed-Point Iteration
5.1.5.
Brent's Method
5.2.
Convergence Analysis
5.2.1.
Linear Convergence
5.2.2.
Quadratic Convergence
5.2.3.
Convergence Criteria
5.3.
Multidimensional Root Finding
5.3.1.
Newton's Method for Systems
5.3.2.
Quasi-Newton Methods
5.3.3.
Broyden's Method
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4. Computer Arithmetic and Error Analysis
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6. Numerical Differentiation