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Contents

Single Variable Calculus

• sgnchng
searches for a sign change in the values of a function
• secgraph
plots the graph of a function along with a collection of secant lines
• tangraph
plots the graph of a function along with a collection of tangent lines
• derlist
computes a list of the first n derivatives of a function
• newt
finds a root of a function and displays a table of the iterates
• newtfn
root found by Newton's Method as a function of the initial guess
• grphnewt
creates a graphical display of the Newton's Method iteration
• leftbox
creates a graphical display of the left-endpoint approximation to the area under a curve
• rightbox
creates a graphical display of the right-endpoint approximation to the area under a curve
• midbox
creates a graphical display of the midpoint approximation to the area under a curve
• trapez
creates a graphical display of the trapezoidal approximation to the area under a curve
• simpson
computes the Simpson's Rule approximation to the integral of a function
• wincheck
a boring utility

### Multivariable Calculus and Optimization

• arrow
plots an arrow to represent a vector in the plane
• showvecs
plots a collection of vectors in the plane
• vpproj
computes the projection of a point in 3D onto a “viewing plane”
• view3d
plots a 3d parametric curve (a “space curve”)
• viewmore
basically the same as view3D; used in
parasurf
• parasurf
plots a 3D parametric surface
• vecfield
plots a 2D vector field (with arrowheads!)
computes the gradient of a function of any number of variables
• div
computes the divergence of a vector field of any number of variables
• curl
computes the curl of a 3D vector field
• laplace
computes the Laplacian of a function of any number of variables
• hessian
computes the hessian matrix (2nd derivative) of a function of any number of variables
evaluates a vector function at a given point
• evalhesn
evaluates a matrix function at a given point
• jacobian
computes the Jacobian matrix of a vector field (or transformation from Rn to Rn)
• newtstep
computes one step of Newton's Method for finding a zero of a vector field (or transformation
from Rn to Rn)
• qapprox
computes the quadratic approximation to a function of any number of variables at a given point
• wincheck

### Linear Algebra

• lufac
computes the LU factorization of a matrix
• lusolve
solves LUx = b
• cholfac
computes the Cholesky factorization LLT of a symmetric, positive definite matrix
• cholsol
solves Ax = b by means of the Cholesky factorization of A, if A is symmetric and positive definite
• nullsp
returns a description of the null space of a matrix
• nullvecs
returns a basis for the null space of a matrix
• eignvals
computes the eigenvalues of a matrix by the least efficient method possible
computes the eigenvector(s) of a matrix corresponding to a particular eigenvalue
• qrfac
computes the QR factorization of a matrix
• qform
decodes the result of qrfac to display Q
• qrsolve
solves Ax = b by means of the QR factorization of A
• gschmidt
orthogonalizes the columns of a matrix

### Differential Equations

• slopefld
plots the slope (direction) field of a differential equation (or pair of equations)
• imeuf, imeug
functions for using the Improved Euler's (a.k.a. Heun's) Method to plot approximate
solutions of a pair of differential equations
• rkstep2
computes one step of 4th-order Runge-Kutta for a pair of differential equations
• ndsolve2
computes an array of points along an approximate solution of a pair of differential
equations (uses rkstep2)
• ndplot2
plots an approximate solution of a pair of differential equations (uses ndsolve2)

### Probability

• bin, cbin
binomial and cumulative binomial probabilities, resp.
• poisson, cpoisson
Poisson and cumulative Poisson probabilities, resp.
• nrml
cumulative probabilities from the standard normal distribution
• nrmlpctl
percentiles of the standard normal distribution (a great application of Newton's Method!)
• zalpha
critical z values associated with tail area
• zcntrl
critical z values associated with central area
• tdist
cumulative probabilities from Student's t-distribution with r degrees of freedom
• tpctl
percentiles of Student's t-distribution with r degrees of freedom
• talpha
critical t values associated with tail area in Student's t-distribution with r degrees of freedom
• tcntrl
critical t values associated with central area in Student's t-distribution with r degrees of freedom
• chi2
cumulative probabilities from the chi-square distribution with r degrees of freedom
• chi2pctl
percentiles of the chi-square distribution with r degrees of freedom
• gauss5
• gauss7
• gauss11
• cmpgauss
composite Gaussian quadrature based on gauss11

### A Few Special Functions

• dblfac
“double factorial” n(n-2)(n-4) ... (2 or 1)
• gamma
the Gamma function. Gamma(x) is defined for all reals except the negative integers.
If n is a positive integer, then Gamma(n) = (n-1)!
• expint1
the “exponential integral” function
• besselj
the Bessel function Jn (“first kind”)
• bessely
the Bessel function Yn (“second kind”)

### General

• circles
draws random circles on the screen
• polygon
plots a triangulated regular polygon
• makelist
computes an array of points (xk, f(xk)), k = 1, ..., n
• nestlist
computes an array of recursively defined points (xk+1,yk+1) = (f(xk,yk), g(xk,yk)), k = 1, .. n
• listplot
creates a piecewise linear graph from an array of points as returned by makelistor nestlist

 This work is dedicated to the numerical analysts at NCSU who corrupted me in grad school.