Numerical Analysis (Numana)

Code for Numerical Analysis.

Setup

conda install -c conda-forge matplotlib numpy pytest rich sympy

Check List

Chapter 0 Fundamentals

• [x] 0.1 Evaluating a Polynomial
• [x] 0.2 Binary Numbers
• [x] 0.3 Floating Point Representation of Real Numbers
• [x] 0.4 Loss of Significance
• [x] 0.5 Review of Calculus

Chapter 1 Solving Equations

• [x] 1.1 The Bisection Method
• [x] 1.2 Fixed-Point Iteration
• [x] 1.3 Limits of Accuracy
• [x] 1.4 Newton’s Method
• [x] 1.5 Root-Finding without Derivatives

Chapter 2 Systems of Equations

• [x] 2.1 Gaussian Elimination
• [x] 2.2 The LU Factorization
• [ ] 2.3 Sources of Error
• [ ] 2.4 The $PA = LU$ Factorization
• [ ] 2.5 Iterative Methods
• [ ] 2.6 Methods for symmetric positive-definite matrices
• [ ] 2.7 Nonlinear Systems of Equations

Chapter 3 Interpolation

• [x] 3.1 Data and Interpolating Functions
• [x] 3.2 Interpolation Error
• [ ] 3.3 Chebyshev Interpolation
• [x] 3.4 Cubic Splines
• [x] 3.5 Bézier Curves

Chapter 4 Least Squares

• [x] 4.1 Least Squares and the Normal Equations
• [ ] 4.2 A Survey of Models
• [ ] 4.3 QR Factorization
• [ ] 4.4 Generalized Minimum Residual (GMRES) Method
• [ ] 4.5 Nonlinear Least Squares

Chapter 5 Numerical Differentiation and Integration

• [x] 5.1 Numerical Differentiation
• [x] 5.2 Newton–Cotes Formulas for Numerical Integration
• [x] 5.3 Romberg Integration
• [ ] 5.4 Adaptive Quadrature
• [x] 5.5 Gaussian Quadrature

Chapter 6 Ordinary Differential Equations

• [ ] 6.1 Initial Value Problems
• [ ] 6.2 Analysis of IVP Solvers
• [ ] 6.3 Systems of Ordinary Differential Equations
• [ ] 6.4 Runge–Kutta Methods and Applications
• [ ] 6.5 Variable Step-Size Methods
• [ ] 6.6 Implicit Methods and Stiff Equations
• [ ] 6.7 Multistep Methods

Chapter 7 Boundary Value Problems

• [ ] 7.1 Shooting Method
• [ ] 7.2 Finite Difference Methods
• [ ] 7.3 Collocation and the Finite Element Method

Chapter 8 Partial Differential Equations

• [ ] 8.1 Parabolic Equations
• [ ] 8.2 Hyperbolic Equations
• [ ] 8.3 Elliptic Equations
• [ ] 8.4 Nonlinear Partial Differential Equations

Chapter 9 Random Numbers and Applications

• [ ] 9.1 Random Numbers
• [ ] 9.2 Monte Carlo Simulation
• [ ] 9.3 Discrete and Continuous Brownian Motion
• [ ] 9.4 Stochastic Differential Equations

Chapter 10 Trigonometric Interpolation and the FFT

• [ ] 10.1 The Fourier Transform
• [ ] 10.2 Trigonometric Interpolation
• [ ] 10.3 The FFT and Signal Processing

Chapter 11 Compression

• [ ] 11.1 The Discrete Cosine Transform
• [ ] 11.2 Two-Dimensional DCT and Image Compression
• [ ] 11.3 Huffman Coding
• [ ] 11.4 Modified DCT and Audio Compression

Chapter 12 Eigenvalues and Singular Values

• [ ] 12.1 Power Iteration Methods
• [ ] 12.2 QR Algorithm
• [ ] 12.3 Singular Value Decomposition
• [ ] 12.4 Applications of the SVD

Chapter 13 Optimization

• [ ] 13.1 Unconstrained Optimization without Derivatives
• [ ] 13.2 Unconstrained Optimization with Derivatives