# textbook/mathews

```file	chap2.f
for	Chapter 2.  The Solution of Nonlinear Equations f(x) = 0
,	Algorithm 2.1  Fixed point iteration
,	Algorithm 2.2  Bisection method
,	Algorithm 2.3  False position or Regula Falsi method
,	Algorithm 2.4  Approximate location of roots
,	Algorithm 2.5  Newton-Raphson iteration
,	Algorithm 2.6  Secant method
,	Algorithm 2.7  Steffensen's acceleration
,	Algorithm 2.8  Muller's method
,	Algorithm 2.9  Nonlinear Seidel iteration
,	Algorithm 2.10  Newton-Raphson method in 2-dimensions

file	chap3.f
for	Chapter 3.  The Solution of Linear Systems  AX = B
,	Algorithm 3.1  Back substitution
,	Algorithm 3.2  Upper-triangularization followed
,	by back substitution
,	Algorithm 3.3  PA = LU factorization with pivoting
,	Algorithm 3.4  Jacobi iteration
,	Algorithm 3.5  Gauss-Seidel iteration

file	chap4.f
for	Chapter 4.  Interpolation and Polynomial Approximation
,	Algorithm 4.1  Evaluation of a Taylor series
,	Algorithm 4.2  Polynomial calculus
,	Algorithm 4.3  Lagrange approximation
,	Algorithm 4.4  Nested multiplication with multiple centers
,	Algorithm 4.5  Newton interpolation polynomial
,	Algorithm 4.6  Chebyshev approximation

file	chap5.f
for	Chapter 5.  Curve Fitting
,	Algorithm 5.1  Least squares line
,	Algorithm 5.2  Least squares polynomial
,	Algorithm 5.3  Non-linear curve fitting
,	Algorithm 5.4  Cubic splines
,	Algorithm 5.5  Trigonometric polynomials

file	chap6.f
for	Chapter 6.  Numerical Differentiation
,	Algorithm 6.1  Differentiation using limits
,	Algorithm 6.2  Differentiation using extrapolation
,	Algorithm 6.3  Differentiation based on N+1 nodes

file	chap7.f
for	Chapter 7.  Numerical Integration
,	Algorithm 7.1  Composite trapezoidal rule
,	Algorithm 7.2  Composite Simpson's rule
,	Algorithm 7.3  Recursive trapezoidal rule
,	Algorithm 7.4  Romberg integration

file	chap8.f
for	Chapter 8.  Numerical Optimization
,	Algorithm 8.1  Golden search for a minimum
,	Algorithm 8.2  Nelder-Mead's minimization method
,	Algorithm 8.3  Local minimum search using
,	Algorithm 8.4  Steepest descent or gradient method

file	chap9.f
for	Chapter 9.  Solution of Differential Equations
,	Algorithm 9.1  Euler's method
,	Algorithm 9.2  Heun's method
,	Algorithm 9.3  Taylor's method of order four
,	Algorithm 9.4  Runge-Kutta method of order four
,	Algorithm 9.5  Runge-Kutta-Fehlberg method RKF45
,	Algorithm 9.7  Milne-Simpson method
,	Algorithm 9.8  Hamming's method
,	Algorithm 9.9  Linear shooting method
,	Algorithm 9.10  Finite difference method

file	chap10.f
for	Chapter 10.  Solution of Partial Differential Equations
,	Algorithm 10.1  Finite difference solution for the wave equation
,	Algorithm 10.2  Forward difference method for the heat equation
,	Algorithm 10.3  Crank-Nicholson method for the heat equation
,	Algorithm 10.4  Dirichlet method for Laplace's equation

file	chap11.f
for	Chapter 11.  Eigenvalues and Eigenvectors
,	Algorithm 11.1  Power method
,	Algorithm 11.2  Shifted inverse power method
,	Algorithm 11.3  Jacobi iteration for eigenvalues and eigenvectors
,	Algorithm 11.4  Reduction to tridiagonal form
,	Algorithm 11.5  The QL method with shifts