Glossary for Multivariable Calculus with MATLAB

This web page contains a list of MATLAB commands and options which you may find useful in working on topics and problems in the book. The descriptions of the comands are purposely kept very short. Except when stated, all commands are part of MATLAB itself or the Symbolic Math Toolbox (for symbolic operations). For more information on the commands, see the MATLAB documentation. Better still, download the attached Live Script and run or modify the sample commands in it to see what the various commands do.

MATLAB Punctuation

@

Creates a function handle or anonymous function

&

Logical AND operator

|

Logical OR operator

~

Logical NOT operator

=

Assignment operator

==

Operator for representing a symbolic equation

%

Introduces a comment (not to be executed)

:

Range operator

,

Separates commands without suppressing output

;

Suppresses output and can also be used to separate commands

'

Used to deliminate a string

+

Addition operator, works on vectors also

-

Subtraction operator, works on vectors also

*

Multiplication operator

.*

Vectorized multiplication operator

/

Division operator

./

Vectorized division operator

^

Exponentiation operator

.^

Vectorized exponentiation operator

.

Decimal point, also operator for accessing fields of a structure array

...

Line continuation operator (used to split a command over more than one line)

MATLAB Constants

pi

π

i

The imaginary unit, if not overwritten by a variable name

inf

∞

MATLAB Commands

abs

The absolute value function

acos

The inverse cosine function

asin

The inverse sine function

assume

Set assumptions on a symbolic variable (e.g., real, positive, integer)

atan

The inverse tangent function

atan2

Finds the polar coordinate θ in terms of y and x

axis

Selects the ranges of x and y (also z if a 3D plot) to show in a plot

clear

Clears values and definitions for variables and functions. If you specify one or more variables, then only those variables are cleared.

conj

Complex conjugation

copyobj

Copy a graphics object

cos

The cosine function

cosh

The hyperbolic cosine function (e^x + e^-x)/2

cross

The cross product of two vectors

curl

The curl of a vector field

det

Computes the determinant of a square matrix

diff

Computes the derivative

disp

Displays the value of a variable or string. Useful for formatting output

divergence

The divergence of a vector field

dot

The dot product of two vectors

double

Converts the (possibly symbolic) expression for a number to a numerical (double-precision) value

dsolve

Symbolic differential equation solver

edit

Opens a script in the Editor

eig

Computes the eigenvalues of a square matrix

erf

The error function (integral of a Gaussian)

exp

The exponential function e^x

ezpolar

Easy plotter in polar coordinates

fcontour

Plots the contour curves of a symbolic expression f(x,y)

figure

Start a new graphic

fimplicit

Produces a plot of an implicit equation f(x,y)=0

fimplicit3

Plots a contour surface of a symbolic expression f(x,y,z)

fmesh

Easy 3D mesh surface plotter

fminbnd

Find minimum of single-variable function on fixed interval

fminsearch

Searches numerically for a minimum of a function of a single (possibly vector) variable

fminunc

In the Optimization Toolbox. Searches for an unconstrained minimum of a function of several variables

format

Changes the format for displaying numbers

fplot

Easy function plotter

fplot3

Easy 3D plotter for curves in 3-space

fsurf

Easy 3D surface plotter

fzero

Finds (numerically) a zero of a function near a given starting value

gca

Get current axes

gcf

Get current figure

heaviside

A step function that is +1 for x > 0 and 0 for x < 0

hold on

Retain current figure; combine new graph with previous one

hold off

Returns to the default where new figures overwrite old ones

int

Computes the integral (symbolically)

integral

Integrates numerically

integral2

Computes a numerical integral in two variables

integral3

Computes a numerical integral in three variables

jacobian

Finds the gradient of a function of several variables. When applied to the symbolic expression for the gradient, can be used to compute the Hessian

laplacian

Computes the Laplacian of a scalar field

legend

Attaches a legend to a combination of plots

length

Gets the dimension (number of entries) of a vector

limit

Computes the limit

linspace

Generates a linearly spaced vector

log

The natural logarithm

loglog

Log-log plotter

logspace

Generates a logarithmically spaced vector

matlabFunction

Converts a symbolic expression to a vectorized numerical function

max

Computes the maximum of the entries of a vector

meshgrid

Returns grid coordinates. Needed for quiver

min

Computes the minimum of the entries of a vector

norm

Norm of a vector or matrix

ode45

Numerical differential equation solver

odeset

Sets options for ode45

ones

Creates a matrix of all ones

plot

Basic plotting command for numerical data

plot3

Basic plotting command in 3D for numerical data

polarplot

Plots a curve in polar coordinates

potential

Computes a potential for a conservative vector field

pretty

Displays a symbolic expression in mathematical style

quiver

Plots vector field based on grid coordinates supplied by meshgrid

rand

Generates a matrix of uniformly distributed random numbers

real

Follows syms to insure variables are real. Also gets the real part of a complex number

series

Computes a series expansion

simplify

Used to simplify a symbolic expression

sin

The sine function

sinh

The hyperbolic sine function (e^x - e^-x)/2

size

Gets the dimensions of a matrix

solve

Symbolic equation solver

sqrt

Square root function

struct

Creates a structure array

subs

Substitute for a variable in an expression

syms

Set up one or more symbolic variables

symsum

Finds the (symbolic) sum of a series

tan

The tangent function

tanh

The hyperbolic tangent function (e^x - e^-x)/(e^x + e^-x)

taylor

Computes the Taylor polynomial; use the optional argument Order to reset the order. Compare series, which is similar but allows expansions involving negative and fractional exponents.

title

Puts a title on a figure

trace

Sum of the diagonal elements of a matrix

transpose

Computes the transpose of a symbolic matrix

vectorPotential

Computes a vector potential for a divergence-free vector field

view

Specifies a point from which to view a 3D graph

vpasolve

Finds numerical solutions to symbolic equations

zeros

Creates a matrix of all zeros

Options to MATLAB Commands

AbsTol, RelTol

Control error tolerances in numerical commands like integral or ode45

LevelList

Specifies the contour levels for fcontour

LineColor

Specifies color of curves in a graph

LineWidth

Controls thickness of curves or contours in a graph

MarkerSize

Controls size of points in a graph

MaxDegree

An option to solve, giving the maximum degree of polynomials for which MATLAB will try to find explicit solution formulas

MaxFunEvals

Sets maximum number of function evaluations allowed in a computation or process

Order

An option to taylor and series, specifying the number of terms to take in the series

Steps

An option to simplify, specifying the number of simplification steps to try

WayPoints

Specifies specific points for evaluation of the function in integral