Calculus 1 TechCompanion Sage Function Index

A    C    D    E    F    G    I    L    M    N    P    R    S    T    V    X    Y

A

abs  absolute value

• A.1 Real Numbers and the Real Line

append  append to list

• 4.6 Newton's Method

arccos  inverse cosine

arccosh  inverse hyperbolic cosine

arccot  inverse cotangent

arccoth  inverse hyperbolic cotangent

arccsc  inverse cosecant

arccsch  inverse hyperbolic cosecant

arcsec  inverse secant

arcsech  inverse hyperbolic secant

arcsin  inverse sine

arcsinh  inverse hyperbolic sine

arctan  inverse tangent

arctanh  inverse hyperbolic tangent

assume  assert assumption

• 7.1 Inverse Functions and Their Derivatives

C

ceil  least integer function

• 2.4 One-Sided Limits

cos  cosine

cosh  hyperbolic cosine

cot  cotangent

coth  hyperbolic cotangent

csc  cosecant

csch  hyperbolic cosecant

D

def  define Python function

• 1.1 Functions and Their Graphs

derivative  

• 3.2 The Derivative as a Function

desolve  solve differential equation

• 4.7 Antiderivatives
• 7.4 Exponential Change and Separable Differential Equations

diff  

• 3.3 Differentiation Rules

dot_product  

• 8.6 Numerical Integration

E

exp  natural exponential function

• 7.3 Exponential Functions

F

factorial  

• 1.4 Graphing with Calculators and Computers

find_local_maximum  

• 4.1 Extreme Values of Functions

find_local_minimum  

• 4.1 Extreme Values of Functions

find_root  find zero of a function

• 2.5 Continuity

float  

• 8.6 Numerical Integration

floor  greatest integer function

• 2.4 One-Sided Limits

G

graphics_array  

• 2.3 The Precise Definition of a Limit

I

implicit_plot  

• 3.7 Implicit Differentiations

import  load Python module

• 1.2 Combining Functions; Shifting and Scaling Graphs

Infinity  

• 2.6 Limits Involving Infinity; Asymptotes of Graphs
• 8.7 Improper Integrals

integral  compute integral symbolically

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

@interact  interactive animation decorator

• 1.2 Combining Functions; Shifting and Scaling Graphs
• 1.3 Trigonometric Functions
• 2.1 Rates of Change and Tangents to Curves
• 2.3 The Precise Definition of a Limit
• 3.2 The Derivative as a Function (Weierstrass's nowhere differentiable continuous function)
• 3.6 The Chain Rule
• 4.2 The Mean Value Theorem (for derivatives)
• 4.4 Concavity and Curve Sketching
• 4.6 Newton's Method
• 5.4 The Fundamental Theorem of Calculus (Mean value theorem for definite integrals)
• 8.2 Trigonometric Integrals (Fourier sine series)

L

lambda  define anonymous function

• 4.1 Extreme Values of Functions

limit  compute limit symbolically

• 2.4 One-Sided Limits

line  

• 2.3 The Precise Definition of a Limit

ln  

• 7.2 Natural Logarithms

log  

• 7.2 Natural Logarithms

M

maxima  

• 3.7 Implicit Differentiation

maxima_methods  

• 2.6 Limits Involving Infinity; Asymptotes of Graphs

N

n  arbitrary precision numerical approximation

• 1.4 Graphing with Calculators and Computers

numerical_integral  

• 5.3 The Definite Integral
• 8.7 Improper Integrals

P

partial_fraction  

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

Piecewise  

• 8.6 Numerical Integration

plot  basic 2D plotting command

• 1.1 Functions and Their Graphs
• aspect_ratio
  • 3.1 Tangents and the Derivative at a Point
• exclude
  • 1.4 Graphing with Calculators and Computers
• figsize
  set figure size
  • 1.1 Functions and Their Graphs
• get_axes_range
  • 4.6 Newton's Method
• legend_label
  • 3.1 Tangents and the Derivative at a Point
• set_axes_range
  • 2.3 The Precise Definition of a Limit

print  display string

• 1.4 Graphing with Calculators and Computers

R

range  

• 5.1 Area and Estimating with Finite Sums

RealField  arbitrary precision real numbers

• 1.4 Graphing with Calculators and Computers

S

sec  secant

sech  hyperbolic secant

show  display graphics

• 1.2 Combining Functions; Shifting and Scaling Graphs

simplify_full  

• 7.7 Hyperbolic Functions

sin  sine

sinh  hyperbolic sine

solve  solve algebraic equation(s)

• 3.4 The Derivative as a Rate of Change

sqrt  principal square root

sum  

• 3.2 The Derivative as a Function

symbolic_sum  

• 5.2 Sigma Notation and Limits of Finite Sums

T

tan  tangent

taylor  compute Taylor polynomial

• 3.9 Linearization and Differentials

trapezoid  

• 8.6 Numerical Integration

V

var  declare variable

• 3.4 The Derivative as a Rate of Change

vector  

• 8.6 Numerical Integration

X

xmax  plot window right bound

xmin  plot window left bound

Y

ymax  plot window upper bound

ymin  plot window lower bound