Calculus and Fundamentals

1. Calculus
2. Mean Value Theorem
3. Fundamental Theorem of Calculus
4. Fundamental Theorem of Algebra
5. Big "O" Truncation Error
6. Complex Numbers
7. Roots of Cubic Equation
8. Roots of Quartic Equations
9. 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. Halley's Method
9. Nonlinear Systems
10. Horner's Method
11. Lin-Bairstow Method
12. Brent's Method
13. Broyden's Method
14. Graeffe's Method
15. Jenkins-Traub Method
16. Laguerre'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. Hilbert Matrix
6. LU Factorization
7. Cholesky, Doolittle and Crout Factorizations
8. Jacobi and Gauss-Seidel Iteration
9. Ill-Conditioned Linear Systems
10. Successive Over Relaxation - SOR
11. Pivoting Methods
12. Iterative Refinement
13. Row Reduced Echelon Form
14. Homogeneous Linear Systems
15. Kirchoff's Law
16. Leontief Model
17. Linear Programming

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 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. Orthogonal Polynomials
13. Legendre Polynomials
14. Computation of Pi
15. Catenary

Curve Fitting

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

Numerical Differentiation

1. Numerical Differentiation 
2. Richardson Extrapolation
3. Automatic Differentiation

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. Romberg Integration
7. Adaptive Simpson's Rule
8. Gauss-Legendre Quadrature  
9. Gauss-Kronrod Quadrature
10. Monte Carlo Pi
11. Monte Carlo Integration
12. Chebyshev Quadrature
13. Gauss-Laguerre Quadrature

Solution of Differential Equations

1. Euler's Method for O. D. E.'s
2. Taylor Series Method for D.E.'s
3. Runge-Kutta Method
4. Runge-Kutta-Fehlberg Method
5. Adams-Bashforth-Moulton Method
6. Milne-Simpson's Method
7. Predictor-Corrector Methods for O.D.E.'s
8. Shooting Methods for O.D.E.'s
9. Finite Difference Method for O.D.E.'s
10. Galerkin's Method
11. Lotka-Volterra Model
12. Pendulum
13. Projectile Motion
14. Lorenz Attractor
15. Duffing Equation
16. van der Pol System
17. Harvesting Model
18. Spring Mass Oscillations
19. Stiff Differential Equations
20. Painlevé Property
21. Picard Iteration
22. Difference Equations
23. Cobweb Models

Solution of Partial Differential Equations

1. Finite Difference Method
2. Crank-Nicolson Method
3. Elliptic PDE's
4. Vibrating Drum
5. Vibrating String
6. Dirichlet Problem
7. Harmonic Functions

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
11. Wielandt Deflation
12. Eigenfaces
13. Principal Axis
14. The Jordan Form

Numerical Optimization

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

Ordinary Differential Equations  

1. Series Solutions & Frobenius Method
2. Airy Functions
3. Bessel Functions
4. Exact Differential Equations
5. Homogeneous Linear Differential Equations
6. Separable Differential Equations
7. Variation of Parameters
8. Autonomous Systems
9. Belousov-Zhabotinskii Model
10. Hodgkin-Huxley Model
11. Michaelis-Menten Model

Return to Numerical Methods - Numerical Analysis

(c) John H. Mathews 2005