/Numana

Code for Numerical Analysis.

Primary LanguagePython

Numerical Analysis (Numana)

Code for Numerical Analysis.

Check List

Chapter 0 Fundamentals

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

Chapter 1 Solving Equations

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

Chapter 2 Systems of Equations

  • 2.1 Gaussian Elimination
  • 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

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

Chapter 4 Least Squares

  • 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

  • 5.1 Numerical Differentiation
  • 5.2 Newton–Cotes Formulas for Numerical Integration
  • 5.3 Romberg Integration
  • 5.4 Adaptive Quadrature
  • 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