Calculus 1 TechCompanion Mathematica Function Index

*    A    B    C    D    E    F    I    J    L    M    N    P    R    S    T

*

!  factorial

• 1.4 Graphing with Calculators and Computers

%  shorthand for last output

• 2.2 Limit of a Function and Limit Laws
• Direction
  • 2.4 One-Sided Limits

=. (Unset)  remove definition

• 2.2 Limit of a Function and Limit Laws

//  postfix

• A.1 Real Numbers and the Real Line
• 1.4 Graphing with Calculators and Computers
• 2.1 Rates of Change and Tangents to Curves

/; (Condition)  evaluate code conditionally

• 2.5 Continuity
• 1.4 Graphing with Calculators and Computers
• 2.1 Rates of Change and Tangents to Curves

@@ (Apply)  replace the head of expression

• 5.1 Area and Estimating with Finite Sums

[[ ]] (Part)  index into list

• 3.7 Implicit Differentiation

A

Abs  absolute value

• A.1 Real Numbers and the Real Line

anonymous function (f[#]&)

• 2.5 Continuity

Apart  partial fractions decomposition

• 2.6 Limits Involving Infinity; Asymptotes of Graphs
• 8.4 Integration of Rational Functions by Partial Fractions

ArcCos  arccos

• 7.6 Inverse Trigonometric Functions

ArcCosh  inverse hyperbolic cosine

• 7.7 Hyperbolic Functions

ArcCot  arccot

• 7.6 Inverse Trigonometric Functions

ArcCoth  inverse hyperbolic cotangent

• 7.7 Hyperbolic Functions

ArcCsc  arccsc

• 7.6 Inverse Trigonometric Functions

ArcCsch  inverse hyperbolic cosecant

• 7.7 Hyperbolic Functions

ArcSec  arcsec

• 7.6 Inverse Trigonometric Functions

ArcSech  inverse hyperbolic secant

• 7.7 Hyperbolic Functions

ArcSin  arcsin

• 7.6 Inverse Trigonometric Functions

ArcSinh  inverse hyperbolic sine

• 7.7 Hyperbolic Functions

ArcTan  arctan

• 7.6 Inverse Trigonometric Functions

ArcTanh  inverse hyperbolic tangent

• 7.7 Hyperbolic Functions

Assuming  impose assumptions

• 8.2 Trigonometric Integrals

B

Blank (_)  placeholder

• 1.1 Functions and Their Graphs

C

Ceiling  least integer function

• 2.4 One-Sided Limits

ContourPlot  plot level curves

• 3.7 Implicit Differentiation

Cos  cosine

• 1.3 Trigonometric Functions

Cosh  hyperbolic cosine

• 7.7 Hyperbolic Functions

Cot  cotangent

Coth  hyperbolic cotangent

• 7.7 Hyperbolic Functions

Csc  cosecant

• 1.4 Graphing with Calculators and Computers

Csch  hyperbolic cosecant

• 7.7 Hyperbolic Functions

D

D  symbolic differentiation

• 3.3 Differentiation Rules

DSolve  solve differential system symbolically

• 4.7 Antiderivatives
• 7.4 Exponential Change and Separable Differential Equations

E

Exp  natural exponential function

• 2.1 Rates of Change and Tangents to Curves
• 7.3 Exponential Functions

F

FindMinimum  find minimum of function

• 4.1 Extreme Values of Functions

FindRoot  find zero of function

• 2.5 Continuity

First  first list element

• 8.6 Numerical Integration

Flatten  flatten list

• 3.1 Tangent and the Derivative at a Point

Floor  greatest integer function

• 2.4 One-Sided Limits

I

Integrate  compute integral symbolically

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

InverseFunction  functional inverse

• 7.1 Inverse Functions and Their Derivatives

J

Join  join lists

• 2.2 Limit of a Function and Limit Laws

L

Last  last list element

• 8.6 Numerical Integration

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

Log  natural logarithm

• 7.2 Natural Logarithms

Log10  common logarithm

• 7.2 Natural Logarithms

M

Map  map function over list

• 8.6 Numerical Integration

Module  block code with local variable

• 2.5 Continuity
• 8.6 Numerical Integration

N

N  arbitrary precision numerical approximation

• 1.4 Graphing with Calculators and Computers

Needs  load package

• 1.3 Trigonometric Functions

Nest  apply function iteratively

• 4.6 Newton's Method

NestList  apply function iteratively and collect intermediate results

• 4.6 Newton's Method

NIntegrate  numerically approximate integral

• 5.3 The Definite Integral
• 8.6 Numerical Integration
• 8.7 Improper Integrals

Normal  convert to normal expression

• 3.9 Linearization and Differentials

NumberQ  determine whether argument is a number

• 2.5 Continuity

NumericQ  determine whether argument is numeric

• 2.5 Continuity

P

Pi  mathematical constant $\pi$

• 1.4 Graphing with Calculators and Computers

Piecewise  construct piecewise-defined function

• 1.1 Functions and Their Graphs

Plot  basic 2D plotting command

• 1.1 Functions and Their Graphs
•  
• AspectRatio plot option for controlling aspect ratio
  • 3.1 Tangents and the Derivative at a Point
• AxesLabel plot option for adding labels to axes
  • 3.1 Tangents and the Derivative at a Point
• DisplayFunction 
  • 3.7 Implicit Differentiation
• Exclusions plot option for excluding points or regions
  • 1.4 Graphing with Calculators and Computers
• PlotLegend create a plot legend
  • 1.3 Trigonometric Functions
• PlotRange set viewing window
  • 1.4 Graphing with Calculators and Computers
• PlotStyle specify line styles and colors
  • 1.3 Trigonometric Functions

Plus  addition

• 5.1 Area and Estimating with Finite Sums

PolynomialQuotientRemainder  polynomial long division

• 2.6 Limits Involving Infinity; Asymptotes of Graphs

Print  print string

• 2.5 Continuity

R

Random  generate pseudorandom numbers

• 2.2 Limit of a Functions and Limit Laws

ReplaceAll (/.)  apply replacement rule(s) to an expression

• 1.1 Functions and Their Graphs

Return  exit function and return value

• 2.5 Continuity

S

Sec  secant

Sech  hyperbolic secant

• 7.7 Hyperbolic Functions

Series  compute series expansion

• 3.9 Linearization and Differentials

Set (=)  assignment operator

• 1.1 Functions and Their Graphs

SetDelayed (:=)  delayed assignment operator

• 1.1 Functions and Their Graphs

Show  display graphics

• 2.1 Rates of Change and Tangents to Curves

Sign  signum function

• 2.5 Continuity

Simplify  simplify expression

• A.1 Real Numbers and the Real Line

Sin  sine

• 1.3 Trigonometric Functions

Sinh  hyperbolic sine

• 7.7 Hyperbolic Functions

Solve  solve algebraic system

• 3.4 The Derivative as a Rate of Change

Sum  summation

• 5.2 Sigma Notation and Limits of Finite Sums

T

Table  create an ordered list

• 2.1 Rates of Change and Tangents to Curves

Tan  tangent

Tanh  hyperbolic tangent

• 7.7 Hyperbolic Functions