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 then be downloaded.
Chapter 1: Introduction | ||
horner_symbolic | 3 | Manipulation of Horner polynomial |
sin_plot | 18-19 | Graph of Taylor series partial sums sin(x) |
taylor_series | 22 | Taylor series expansion of functions |
sqrt_approx | 27 | Taylor series expansion of square roots | Chapter 2: Number Representation and Errors |
convert | 51 | Converting numbers |
loss_of_significance | 78 | Loss of significance in subtraction |
accuracy | 81 | Computations with various accuracy |
Chapter 3: Locating Roots of Equations | ||
fcn_roots | 97 | Roots of functions |
newt | 107-108 | Newton's method example |
poly_roots | 128 | Roots of a 5th degree polynomial |
Chapter 4: Interpolation and Numerical Differentiation | ||
newton_interp | 145,152,176 | Newton interpolation polynomial |
runge_fun | 170-171 | Polynomial interpolation for Runge function |
derivative | 186 | Symbolic and numerical derivative |
Chapter 5: Numerical Integration | ||
num_integ1 | 201 | Numerical integration of exp(-x*x) |
trapezoid_rule | 208 | Trapezoid rule for an integral |
comp_trap_rule | 212 | Composite Trapezoid rule for an integral | Chapter 6: More on Numerical Integration |
num_integ2 | 242 | Numerical integration of cos(2*x)/exp(x) |
Chapter 7: Systems of Linear Equations | ||
gauss_elim1 | 266 | Gaussian elimination first example |
gauss_elim2 | 289-290 | Gaussian elimination second example |
band | 303 | Banded linear system example |
penta | 305 | Pentadiagonal example |
pentasym | 305 | Pentadiagonal symmetric example |
Chapter 8: More on Systems of Linear Equations | ||
lu | 325,328 | LU decomposition |
lufactor | 328-329 | LU factorization |
cp8-2-8 | 356 | Computer Problem 8.2.8 |
char | 358 | Eigenvalues via characteristic polynomial |
null | 359 | Null space, eigenvalues/eigenvectors |
eigen | 360 | Eivenvalues/eigenvectors (LinearAlgebra) |
Schur | 362-363 | Schur decomposition (Linear Algebra) |
Svd | 366 | Singular value decomposition (linalg) |
sng_val_decomp | 367 | Singular value decomposition (LinearAlgebra) |
Chapter 9: Approximation by Spline Functions | ||
cubic_spline1 | 402 | Plot of natural cubic spline curve |
cubic_spline2 | 407 | Generate and plot cubic spline curve |
bernstein_poly | 432 | Graph of few Bernstein polynomials |
ctrl_pt_curve | 433 | Generating curves using control points |
Chapter 10: Ordinary Differential Equations | ||
ode0 | 443 | Numerical solution of an IVP: example 0 |
ode1 | 444 | Numerical solution of an IVP: example 1 |
euler | 449 | Euler's method for solving an ODE |
ode2 | 452 | Numerical solution of an IVP: example 2 |
ode3 | 453 | Taylor series method (order 4) solving ODE: example 3 |
ode4 | 463 | Numerical solution of an IVP: example 4 |
adams_mlt_coef | 477 | Adams-Moulton formulas |
Chapter 11: Systems of Ordinary Differential Equations | ||
ode_sys1 | 488,494 | Analytic/numerical solution systems of ODE | ode_2nd_order | 501 | Second order IVP |
ode_sys2 | 514 | Analytic/numerical solution systems of ODE |
Chapter 12: Smoothing of Data and the Method of Least Squares | ||
lstsq1 | 524 | Linear least squares example |
lstsq2 | 524 | Linear least squares example |
lstsq3 | 526 | Nonpolynomial least squares example |
minimal_sol | 551-552 | Minimal solution random matrix A/vector b |
svd_penrose_sol | 553 | Penrose properties for pseudomatrix |
Chapter 13: Monte Carlo Methods and Simulation | ||
rand_num | 563 | Generating random numbers |
rand | 563 | Generating random integers |
Chapter 14: Boundary Value Problems for Ordinary Differential Equations | ||
bvp | 607 | Solving broundary value problems |
Chapter 15: Partial Differential Equations | ||
heat | 623 | Parabolic PDE: heat equation |
wave | 631-632 | Hyperbolic PDE: wave equation |
ell | 645 | Elliptic PDE |
Chapter 16: Minimization of Functions | ||
grad_hessian | 674 | Calculate gradient vector and Hessian matrix |
Chapter 17: Linear Programming | ||
lin_prog1 | 693 | Maximize subject to inequality constraints |
lin_prog2 | 697 | Minimize subject to inequality constraints |
lin_prog3 | 712-713 | 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/
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