Numerical Mathematics and Computing, 5th Ed. - Sample Mathematica Codes

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

In the following table, each line/entry contains the code file name, the page number where it can be found in the textbook, and a brief description. Click on the program name to display the source code, which can be downloaded.
 Chapter 1: Introduction sineplot 20 Plots of partial series for sin(x) sin 20 Sine series expansion and plot series 22, 27 Taylor series expansions Chapter 2: Number Representation and Errors numbers 52 Examples of numbers in different bases precision 66, 81 Machine precision and accuracy Chapter 3: Locating Roots of Equations bisect 98-99 Bisection example newt 108-109 Newton's method example newt_sys 115 Newton's method for system of equations secant 128 Examples associated with Secant Chapter 4: Interpolation and Numerical Differentiation newt_interp1 145 Newton interpolation polynomial example (5 data points) newt_interp2 152 Newton interpolation polynomial example (4 data points) newt_interp_sin 155 Newton interpolation (sin(x) at 10 equidistant ponts) inv_interp 157 Newton inverse interpolation example runge_fcn 171-172 Newton interpolation Runge function derivative 186,189 Newton interpolation example 1 Chapter 5: Numerical Integration error_integral1 202 Numerical integration: error integral sine_integral 209 Numerical integration: sine integral error_integral2 213 Numerical integration: exp(-x*x) bernoulli 226 Bernoulli polynomials Chapter 6: More on Numerical Integration cos-exp 240-241 Numerical integration example: cos(2x)/exp(x) cp6-2-8 260 Computer Problem 6.2.8 Chapter 7: Systems of Linear Equations lin_sys1 266 Linear system first example lin_sys2 290 Linear system second example Chapter 8: More on Systems of Linear Equations lu_factor 329 LU factorization char_poly 358 Characteristic polynomial example null 359 Null space example timing 360 Timing example eigen 360 Eigenvalue/eigenvector example schur 363 Schur form example svd 368 Singular Value Decomposition example Chapter 9: Approximation by Spline Functions cubic_spline1 402 Cubic spline example 1 cubic_spline2 408 Cubic spline example 2 bezier 434 Bezier polynomial example Chapter 10: Ordinary Differential Equations explicit 443 Explicit solution of an ODE practial 444 Practial ODE example ode1 450 Numerical solution of an ODE ode2 452 Numerical solution of an ODE ode3 463 Numerical solution of an ODE ode4 476 Numerical solution of an ODE Chapter 11: Systems of Ordinary Differential Equations ode_sys1 488,494 Analytic/numerical solution systems of ODE 1 ode_2nd_order 501 Second order IVP ode_high_order 503 High order IVP ode_sys2 515 Analytic/numerical solution systems of ODE 2 Chapter 12: Smoothing of Data and the Method of Least Squares ls_fit 523-524 Linear least squares fit for polynomials np_ls_fit 526 Least squares fit of a non-polynomial function cheby 532 Plot of Chebyshev polynomials p_inv1 552 Minimal solution using pseudo-inverse of matrices p_inv2 554 Find pseudo-inverse in case of loss in rank Chapter 13: Monte Carlo Methods and Simulation ran_num_exps 564 Examples using random numbers Chapter 14: Boundary Value Problems for Ordinary Differential Equations bvp1 607 Two-point boundary-value problem example 1 bvp2 607-608 Two-point boundary-value problem example 2 Chapter 15: Partial Differential Equations heat 623 Parabolic PDE: solve heat eqn. & plot wave 634-635 Hyperbolic PDE: solve wave eqn. & plot Chapter 16: Minimization of Functions min_val1 658 Minimizing multivariate functions min_val2 659 Find local minimum of a function taylor_series 675 Taylor series in two variables Chapter 17: Linear Programming lin_prog1 694 Maximize subject to inequality constraints lin_prog2 698 Minimize subject to inequality constraints lin_prog3 713 Minimize subject to equality constraints lin_prog4 715 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/

 [Home] [Features] [TOC] [Purchase] [Sample Code] [Web] [Manuals] [Errata] [Links]

 Last updated: 5/20/2003