Numerical Analysis - Numerical Methods

Modules

 

Calculus and Fundamentals
  1. Calculus Review
  2. Big "O" Truncation Error
  3. Complex Numbers
  4. Complex Functions
  5. Using MATLAB for Numerical Analysis

The Solution of Nonlinear Equations f(x) = 0

  1. Fixed Point Iteration
  2. Bisection Method
  3. False Position or Regula Falsi Method
  4. Newton-Raphson Method
  5. Secant Method
  6. Muller's Method
  7. Aitken's Method & Steffensen's Acceleration
  8. Accelerated & Modified Newton-Raphson
  9. Improved Newton Method
  10. Halley's Method
  11. Horner's Method
  12. Lin-Bairstow Method
  13. Brent's Method
  14. Graeffe's Method
  15. Nonlinear Systems
  16. Broyden's Method

The Solution of Linear Systems AX = B

  1. Triangular Systems and Back Substitution
  2. Gauss-Jordan Elimination and Pivoting
  3. Tri-Diagonal Matrices
  4. Inverse Matrix
  5. LU Factorization
  6. Cholesky, Doolittle and Crout Factorizations
  7. Jacobi and Gauss-Seidel Iteration
  8. Successive Over Relaxation - SOR
  9. Pivoting Methods
  10. Iterative Refinement
  11. Row Reduced Echelon Form
  12. Homogeneous Linear Systems
  13. Kirchoff's Law
  14. Leontief Model
  15. Linear Programming-Simplex Method

Interpolation and Polynomial Approximation

  1. Maclaurin and Taylor Series
  2. Lagrange Polynomial Interpolation and Approximation
  3. Newton Interpolation Polynomial
  4. Hermite Polynomial Interpolation
  5. Cubic Splines
  6. B-Splines
  7. Bézier Curves Bézier Curves
  8. Chebyshev Approximation Polynomial
  9. Pade Approximation
  10. Rational Approximation
  11. Aitken's and Neville's Interpolation
  12. Legendre Polynomials
  13. The Tangent Parabola
  14. Catenary

Curve Fitting

  1. Least Squares Lines
  2. Least Squares Polynomials
  3. Nonlinear Curve Fitting
  4. Logistic Curve
  5. FFT and Trigonometric Polynomials 
  6. Conic Fit
  7. Circle of Curvature

Numerical Differentiation

  1. Numerical Differentiation 
  2. Richardson Extrapolation
  3. Derive Numerical Differentiation Formulae

Numerical Integration

  1. Riemann Sums
  2. Midpoint Rule
  3. Newton-Cotes Integration
  4. Trapezoidal Rule for Numerical Integration
  5. Simpson's Rule for Numerical Integration
  6. Simpson's 3/8 Rule for Numerical Integration
  7. Boole's Rule
  8. Romberg Integration
  9. Adaptive Simpson's Rule
  10. Gauss-Legendre Quadrature
  11. Cubic Spline Quadrature  
  12. Monte Carlo Pi
  13. Monte Carlo Integration
  14. 2D Trapezoidal and Simpson Rules

Solution of Differential Equations

  1. Euler's Method for ODE's
  2. Taylor Series Method for ODE's
  3. Runge-Kutta Method
  4. Runge-Kutta-Fehlberg Method
  5. Adams-Bashforth-Moulton Method
  6. Milne-Simpson's Method
  7. Predictor-Corrector Methods
  8. Shooting Methods for ODE's
  9. Finite Difference Method for ODE's
  10. Galerkin's Method
  11. Painleve Property
  12. Lotka-Volterra Model
  13. Pendulum
  14. Projectile Motion
  15. Lorenz Attractor
  16. van der Pol System
  17. Harvesting Model
  18. Frobenius Series Solution
  19. Picard Iteration
  20. Spring-Mass Systems

Solution of Partial Differential Equations

  1. Finite Difference Method
  2. Crank-Nicolson Method
  3. Elliptic PDE's

Eigenvalues and Eigenvectors

  1. Eigenvalues and Eigenvectors
  2. Power method
  3. Jacobi method
  4. Householder Transformations
  5. QR method
  6. Compartment Model
  7. Earthquake Model
  8. Matrix Exponential
  9. Faddeev-Leverrier Method 
  10. Hessenberg Factorization

Numerical Optimization

  1. Golden Ratio Search
  2. Fibonacci Search
  3. Quadratic Interpolative Search
  4. Nelder Mead Method
  5. Powell's Method
  6. Steepest Descent - Gradient Search
  7. Newton's Search Method

Return to Numerical Methods - Numerical Analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

(c) John H. Mathews 2005