Calculus 1 TechCompanion Octave/MATLAB Function Index

*    A    C    D    E    F    G    H    I    J    L    M    N    P    Q    R    S    T    V    W    X    Y

*

;  output suppression

• 1.1 Functions and Their Graphs

:  array creation

• see colon operator

@  create function handle

• see anonymous functions

%  comment marker

• 1.4 Graphing with Calculators and Computers
• 3.1 Tangents and the Derivative at a Point

'  transpose

• 2.2 Limit of a Function and Limit Laws

.^  elementwise exponentiation

• 1.1 Functions and Their Graphs

./  elementwise division

• 1.1 Functions and Their Graphs

.*  elementwise multiplication

• 1.1 Functions and Their Graphs

&  logical conjunction

• 4.6 Newton's Method

==  equality relation

• 3.7 Implicit Differentiation

A

abs  absolute value

• A.1 Real Numbers and the Real Line

acos  arccos

• 7.6 Inverse Trigonometric Functions

acosh  inverse hyperbolic cosine

• 7.7 Hyperbolic Functions

acot  arccot

• 7.6 Inverse Trigonometric Functions

acoth  inverse hyperbolic cotangent

• 7.7 Hyperbolic Functions

acsc  arccsc

• 7.6 Inverse Trigonometric Functions

acsch  inverse hyperbolic cosecant

• 7.7 Hyperbolic Functions

anonymous functions

• 1.1 Functions and Their Graphs
• 2.5 Continuity
• 4.1 Extreme Values of Functions
• 5.3 The Definite Integral

asec  arcsec

• 7.6 Inverse Trigonometric Functions

asech  inverse hyperbolic secant

• 7.7 Hyperbolic Functions

asin  arcsin

• 7.6 Inverse Trigonometric Functions

asinh  inverse hyperbolic sine

• 7.7 Hyperbolic Functions

atan  arctan

• 7.6 Inverse Trigonometric Functions

atanh  inverse hyperbolic tangent

• 7.7 Hyperbolic Functions

axis  scale axis and set axis style

• 1.4 Graphing with Calculators and Computers

C

ceil  least integer function

• 2.4 One-Sided Limits

colon operator :

• 1.1 Functions and Their Graphs
• without increment specification
  • 2.2 Limit of a Function and Limit Laws

compose  compose symbolic functions

• 7.1 Inverse Functions and Their Derivatives

contour  plot isolines

• 3.7 Implicit Differentiation

cos  cosine

• 1.3 Trigonometric Functions

cosh  hyperbolic cosine

• 7.7 Hyperbolic Functions

cot  cotangent

• 3.5 Derivatives of Trigonometric Functions

coth  hyperbolic cotangent

• 7.7 Hyperbolic Functions

csc  cosecant

• 1.3 Trigonometric Functions
• 1.4 Graphing with Calculators and Computers

csch  hyperbolic cosecant

• 7.7 Hyperbolic Functions

D

deconv  polynomial division

• 2.6 Limits Involving Infinity; Asymptotes of Graphs

diff  compute consecutive differences

• 3.2 The Derivative as a Function

diff (Symbolic toolbox)  compute symbolic derivative

• 3.3 Differentiation Rules
• implicit differentiation
  • 3.7 Implicit Differentiation

disp  display message in terminal window

• 3.1 Tangents and the Derivative at a Point
• 4.6 Newton's Method

double  convert to double precision

• 4.3 Monotonic Functions and the First Derivative Test
• 4.6 Newton's Method

dsolve  solve differential system symbolically

• 4.7 Antiderivatives
• 7.4 Exponential Change and Separable Differential Equations

E

exp  natural exponential function

• 7.2 Natural Logarithms
• 7.3 Exponential Functions

expand  expand polynomials

• 8.4 Integration of Rational Functions by Partial Fractions

ezplot  easy-to-use plotting utility

• 1.3 Trigonometric Functions
• 3.3 Differentiation Rules
• implicitly defined functions
  • 3.7 Implicit Differentiation

F

factorial  

• 1.4 Graphing with Calculators and Computers

feval  evaluate function

• 8.4 Integration of Rational Functions by Partial Fractions

finverse  symbolic functional inverse

• 7.1 Inverse Functions and Their Derivatives

floor  greatest integer function

• 2.4 One-Sided Limits

fminbnd  find function minimum

• 4.1 Extreme Values of Functions

for...end  loop

• 2.1 Rates of Change and Tangents to Curves
• 5.1 Area and Estimating with Finite Sums

format  set display style for numbers

• 2.2 Limit of a Functions and Limit Laws

fzero  numerically approximate zero of a continuous function

• 2.5 Continuity
• 5.6 Substitution and Area Between Curves

G

gcf  get the current figure handle

• 4.5 Applied Optimization

grid  grid lines for plots

• 3.4 The Derivative as a Rate of Change
• 4.5 Applied Optimization

H

handles

• function handles
• 1.1 Functions and Their Graphs
• 2.5 Continuity
• graphics handles
• 3.9 Linearization and Differentials
• 4.5 Applied Optimization

I

i  imaginary unit

• A.1 Real Numbers and the Real Line

if  conditional

• 4.6 Newton's Method

inf  infinity

• 2.6 Limits Involving Infinity; Asymptotes of Graphs
• 7.8 Related Rates of Growth
• 8.7 Improper Integrals

int  compute symbolic antiderivative

• 4.7 Antiderivatives
• 5.3 The Definite Integral
• 8.5 Integral Tables and Computer Algebra Systems
• 8.7 Improper Integrals

integral  approximate definite integral numerically

• 5.3 The Definite Integral

J

j  imaginary unit

L

legend  create a plot legend

• 1.3 Trigonometric Functions
• 3.4 The Derivative as a Rate of Change

limit  compute limit symbolically

• 2.2 Limit of a Function and Limit Laws
• 2.6 Limits Involving Infinity; Asymptotes of Graphs
• 7.8 Related Rates of Growth
• one-sided
  • 2.4 One-Sided Limits

line  generate polygonal path

• 4.5 Applied Optimization

linspace  generate linearly spaced vectors

• 1.3 Trigonometric Functions

log  natural logarithm

• 7.2 Natural Logarithms
• 7.4 Exponential Change and Separable Differential Equations

log10  common (base 10) logarithm

• 7.2 Natural Logarithms

logical mask

• 4.3 Monotonic Functions and the First Derivative Test

M

matlabFunction  convert symbolic expression to MATLAB function handle

• 3.3 Differentiation Rules

M-files

• 1.1 Functions and Their Graphs
• 2.1 Rates of Change and Tangents to Curves (avgSpeed.m)
• 2.1 Rates of Change and Tangents to Curves (avgSpeedTable.m)
• 2.1 Rates of Change and Tangents to Curves (avgRateOfChange.m)
• 2.1 Rates of Change and Tangents to Curves (secantLine.m)
• 2.5 Continuity
• 3.1 Tangents and the Derivative at a Point (exercise3_2_48.m)
• 4.3 Monotonic Functions and the First Derivative Test (monotonicity.m)
• 4.5 Applied Optimization (ex_4_5_68aGraphic.m)
• 4.6 Newton's Method (newtonsMethod.m)
• 5.1 Area and Estimating with Finite Sums (estimateArea.m)
• 8.6 Numerical Integration (simp.m)

N

NaN  not a number

• 2.6 Limits Involving Infinity; Asymptotes of Graphs
• 5.3 The Definite Integral
• 8.7 Improper Integrals

num2str  convert number to string

• 4.6 Newton's Method

P

partfrac (MuPAD)  partial fraction decomposition

• 8.4 Integration of Rational Functions by Partial Fractions

path  display or alter search path

• 1.1 Functions and Their Graphs

pi  floating-point approximation to $\pi$

• 1.4 Graphing with Calculators and Computers

plot  basic plotting function

• 1.1 Functions and Their Graphs
•  
• line styles, markers and colors
  • 1.3 Trigonometric Functions
  • 4.5 Applied Optimization

pretty  prettyprint format

• 3.7 Implicit Differentiation
• 7.7 Hyperbolic Functions
• 8.4 Integration of Rational Functions by Partial Fractions

Q

quadgk  Gauss-Kronrod quadrature

• 5.6 Substitution and Area Between Curves

R

rand  generate pseudorandom numbers

• 2.2 Limit of a Function and Limit Laws

rat  rational form specifier

• 2.2 Limit of a Function and Limit Laws

residue  find residues, poles and direct terms

• 8.4 Integration of Rational Functions by Partial Fractions

roots  compute roots of a polynomial

• 2.5 Continuity

S

sec  secant

sech  hyperbolic secant

• 7.7 Hyperbolic Functions

set  set graphics properties

• 3.9 Linearization and Differentials
• 4.5 Applied Optimization

simplify  simplify symbolic expression

• 7.7 Hyperbolic Functions

sin  sine

• 1.3 Trigonometric Functions

sinh  hyperbolic sine

• 7.7 Hyperbolic Functions

solve  solve algebraic system

• 3.7 Implicit Differentiation
• 4.5 Applied Optimization

sqrt  principal square root

• 2.2 Limit of a Function and Limit Laws

subs  substitute value(s) for symbol(s)

• 2.2 Limit of a Function and Limit Laws
• 3.7 Implicit Differentiation

sum  sum array elements

• 5.1 Area and Estimating with Finite Sums

sym  create symbolic object

• 5.3 The Definite Integral
• 8.7 Improper Integrals

syms  Symbolic toolbox symbol declaration

• 2.2 Limit of a Function and Limit Laws

symsum  symbolic sum

• 5.2 Sigma Notation and Limits of Finite Sums

T

tan  tangent

• 3.5 Derivatives of Trigonometric Functions

tanh  hyperbolic tangent

• 7.7 Hyperbolic Functions

taylor  compute Taylor polynomial symbolically

• 3.9 Linearization and Differentials

text  add text to graphics

• 4.3 Monotonic Functions and the First Derivative Test

title  set plot title

• 3.1 Tangents and the Derivative at a Point
• 7.5 L'Hôpital's Rule (Part 2)

trapz  trapezoidal approximation to integrals

• 8.6 Numerical Integration

V

vpa  variable precision arithmetic

• 3.7 Implicit Differentiation
• 5.3 The Definite Integral

W

while...end  loop

• 4.6 Newton's Method

X

xlim  set or determine $x$-axis limits

• 7.1 Inverse Functions and Their Derivatives
• 5.6 Substitution and Area Between Curves

Y

ylim  set or determine $x$-axis limits

• 7.1 Inverse Functions and Their Derivatives
• 5.6 Substitution and Area Between Curves