Numerical Mathematics and Computing, 6th Ed. - Sample Mathematica Codes

# Numerical Mathematics and Computing Sixth Edition Ward Cheney & David Kincaid Sample Mathematica Codes

In the following table, each line/entry contains the code file name and a brief description. Click on the program name to display the source code, which can be downloaded.
 Chapter 1: Introduction sineplot Plots of partial series for sin(x) sin Sine series expansion and plot series Taylor series expansions Chapter 2: Number Representation and Errors numbers Examples of numbers in different bases precision Machine precision and accuracy Chapter 3: Locating Roots of Equations bisect Bisection example newt Newton's method example newt_sys Newton's method for system of equations secant Examples associated with Secant Chapter 4: Interpolation and Numerical Differentiation newt_interp1 Newton interpolation polynomial example (5 data points) newt_interp2 Newton interpolation polynomial example (4 data points) newt_interp_sin Newton interpolation (sin(x) at 10 equidistant ponts) inv_interp Newton inverse interpolation example runge_fcn Newton interpolation Runge function derivative Newton interpolation example 1 Chapter 5: Numerical Integration error_integral1 Numerical integration: error integral sine_integral Numerical integration: sine integral error_integral2 Numerical integration: exp(-x*x) bernoulli Bernoulli polynomials Chapter 6: More on Numerical Integration cos-exp Numerical integration example: cos(2x)/exp(x) cp6-2-8 Computer Problem 6.2.8 Chapter 7: Systems of Linear Equations lin_sys1 Linear system first example lin_sys2 Linear system second example Chapter 8: More on Systems of Linear Equations lu_factor LU factorization char_poly Characteristic polynomial example null Null space example timing Timing example eigen Eigenvalue/eigenvector example schur Schur form example svd Singular Value Decomposition example Chapter 9: Approximation by Spline Functions cubic_spline1 Cubic spline example 1 cubic_spline2 Cubic spline example 2 bezier Bezier polynomial example Chapter 10: Ordinary Differential Equations explicit Explicit solution of an ODE practial Practial ODE example ode1 Numerical solution of an ODE ode2 Numerical solution of an ODE ode3 Numerical solution of an ODE ode4 Numerical solution of an ODE Chapter 11: Systems of Ordinary Differential Equations ode_sys1 Analytic/numerical solution systems of ODE 1 ode_2nd_order Second order IVP ode_high_order High order IVP ode_sys2 Analytic/numerical solution systems of ODE 2 Chapter 12: Smoothing of Data and the Method of Least Squares ls_fit Linear least squares fit for polynomials np_ls_fit Least squares fit of a non-polynomial function cheby Plot of Chebyshev polynomials p_inv1 Minimal solution using pseudo-inverse of matrices p_inv2 Find pseudo-inverse in case of loss in rank Chapter 13: Monte Carlo Methods and Simulation ran_num_exps Examples using random numbers Chapter 14: Boundary Value Problems for Ordinary Differential Equations bvp1 Two-point boundary-value problem example 1 bvp2 Two-point boundary-value problem example 2 Chapter 15: Partial Differential Equations heat Parabolic PDE: solve heat eqn. & plot wave Hyperbolic PDE: solve wave eqn. & plot Chapter 16: Minimization of Functions min_val1 Minimizing multivariate functions min_val2 Find local minimum of a function taylor_series Taylor series in two variables Chapter 17: Linear Programming lin_prog1 Maximize subject to inequality constraints lin_prog2 Minimize subject to inequality constraints lin_prog3 Minimize subject to equality constraints lin_prog4 Minimize subject to inequality constraints

Addditional programs can be found at the textbook's anonymous ftp site:

ftp://ftp.ma.utexas.edu/pub/cheney-kincaid/

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 Last updated: 25/07/2007