A

absolute convergence
5.5 Alternating Series

absolute error
3.6 Numerical Integration

air resistance
4.5 First-order Linear Equations

Airy’s equation
6.4 Working with Taylor Series

algebraic function
3.1 Integration by Parts

alternating series
5.5 Alternating Series

alternating series test
5.5 Alternating Series

angular coordinate
7.3 Polar Coordinates

annuities
6.2 Properties of Power Series

annuity payments
6 Review Exercises

arc length
2.4 Arc Length of a Curve and Surface Area

Archimedean spiral
7.3 Polar Coordinates

Archimedes
1.1 Approximating Areas

*area density*2.5 Physical Applications

area under the curve
1.1 Approximating Areas

arithmetic sequence
5.1 Sequences

asymptotically semi-stable solution
4.2 Direction Fields and Numerical Methods

asymptotically stable solution
4.2 Direction Fields and Numerical Methods

asymptotically unstable solution
4.2 Direction Fields and Numerical Methods

autonomous differential equation
4.3 Separable Equations

average value of the function
1.2 The Definite Integral

B

binomial series
6.4 Working with Taylor Series

bounded above
5.1 Sequences

bounded below
5.1 Sequences

bounded sequence
5.1 Sequences

C

carbon dating
2.8 Exponential Growth and Decay

cardioid
7.3 Polar Coordinates

carrying capacity
4.4 The Logistic Equation

center of mass
2.6 Moments and Centers of Mass

centroid
2.6 Moments and Centers of Mass

change of variables
1.5 Substitution

*cissoid of Diocles*7.4 Area and Arc Length in Polar Coordinates

comparison test
5.4 Comparison Tests

compound interest
2.8 Exponential Growth and Decay

computer algebra systems (CAS)
3.5 Other Strategies for Integration

conditional convergence
5.5 Alternating Series

conic section
7.5 Conic Sections

convergence of a series
5.2 Infinite Series

convergent sequence
5.1 Sequences

*coupon collector’s problem*5.3 The Divergence and Integral Tests

cross-section
2.2 Determining Volumes by Slicing

curtate cycloid
7.1 Parametric Equations

cusps
7.1 Parametric Equations

cycloid
7.1 Parametric Equations

D

deceleration
1.4 Integration Formulas and the Net Change Theorem

definite integral
1.2 The Definite Integral

density function
2.5 Physical Applications

differential equation
4.1 Basics of Differential Equations

direction field (slope field)
4.2 Direction Fields and Numerical Methods

directrix
7.5 Conic Sections

discriminant
7.5 Conic Sections

disease epidemics
4.2 Direction Fields and Numerical Methods

disk method
2.2 Determining Volumes by Slicing

divergence of a series
5.2 Infinite Series

divergence test
5.3 The Divergence and Integral Tests

divergent sequence
5.1 Sequences

doubling time
2.8 Exponential Growth and Decay

drugs in the bloodstream
4.3 Separable Equations

E

Earth’s orbit
7.1 Parametric Equations

eccentricity
7.5 Conic Sections

elliptic integral
6.4 Working with Taylor Series

*epitrochoid*7.1 Parametric Equations

equilibrium solution
4.2 Direction Fields and Numerical Methods

*Euler transform*5.5 Alternating Series

Euler’s constant
5.2 Infinite Series

Euler’s formula
6 Review Exercises

Euler’s Method
4.2 Direction Fields and Numerical Methods

evaluation theorem
1.3 The Fundamental Theorem of Calculus

even function
1.4 Integration Formulas and the Net Change Theorem

explicit formulas
5.1 Sequences

exponential decay
2.8 Exponential Growth and Decay

exponential growth
2.8 Exponential Growth and Decay

F

federal income tax
1.4 Integration Formulas and the Net Change Theorem

Fibonacci numbers
5.1 Sequences

focal parameter
7.5 Conic Sections

focus
7.5 Conic Sections

Fresnel integrals
6.4 Working with Taylor Series

Fundamental Theorem of Calculus
1.3 The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus, Part 1
1.3 The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus, Part 2
1.3 The Fundamental Theorem of Calculus

G

*Gabriel’s Horn*3.7 Improper Integrals

general form
7.5 Conic Sections

general solution
4.1 Basics of Differential Equations

geometric sequence
5.1 Sequences

geometric series
5.2 Infinite Series

golden ratio
5.1 Sequences

Gompertz equation
4.4 The Logistic Equation

growth of bacteria
1.6 Integrals Involving Exponential and Logarithmic Functions

growth rate
4.4 The Logistic Equation

H

half-life
2.8 Exponential Growth and Decay

hanging cables
2.9 Calculus of the Hyperbolic Functions

harmonic series
5.2 Infinite Series

Hooke’s law
2.5 Physical Applications

Hoover Dam
2.5 Physical Applications

hydrostatic pressure
2.5 Physical Applications

hypocycloid
7.1 Parametric Equations

I

improper integral
3.7 Improper Integrals

indefinite integrals
3.1 Integration by Parts

*index*1.1 Approximating Areas

index variable
5.1 Sequences

infinite sequence
5.1 Sequences

infinite series
5.2 Infinite Series

initial population
4.4 The Logistic Equation

initial value
4.1 Basics of Differential Equations

initial velocity
4.1 Basics of Differential Equations

initial-value problem
4.1 Basics of Differential Equations

integrable function
1.2 The Definite Integral

integral test
5.3 The Divergence and Integral Tests

integrand
1.2 The Definite Integral

integrating factor
4.5 First-order Linear Equations

integration by parts
3.1 Integration by Parts

integration by substitution
1.5 Substitution

integration tables
3.5 Other Strategies for Integration

interval of convergence
6.1 Power Series and Functions

J

K

Koch’s snowflake
5.2 Infinite Series

L

left-endpoint approximation
1.1 Approximating Areas

Leibniz
1.2 The Definite Integral

limaçon
7.3 Polar Coordinates

limit comparison test
5.4 Comparison Tests

limit of the sequence
5.1 Sequences

limits of integration
1.2 The Definite Integral

logarithmic function
3.1 Integration by Parts

logistic differential equation
4.4 The Logistic Equation

lower sum
1.1 Approximating Areas

M

Maclaurin polynomials
6.3 Taylor and Maclaurin Series

Maclaurin series
6.3 Taylor and Maclaurin Series

major axis
7.5 Conic Sections

Mean Value Theorem for Integrals
1.3 The Fundamental Theorem of Calculus

method of cylindrical shells.
2.3 Volumes of Revolution: Cylindrical Shells

*method of equating coefficients*3.4 Partial Fractions

*method of exhaustion*1.1 Approximating Areas

*method of strategic substitution*3.4 Partial Fractions

midpoint rule
3.6 Numerical Integration

minor axis
7.5 Conic Sections

monotone sequence
5.1 Sequences

N

nappes
7.5 Conic Sections

net change theorem
1.4 Integration Formulas and the Net Change Theorem

net signed area
1.2 The Definite Integral

Newton’s second law of motion
4.1 Basics of Differential Equations

nonelementary integral
6.4 Working with Taylor Series

numerical integration
3.6 Numerical Integration

O

odd function
1.4 Integration Formulas and the Net Change Theorem

order of a differential equation
4.1 Basics of Differential Equations

orientation
7.1 Parametric Equations

P

parameter
7.1 Parametric Equations

parameterization of a curve
7.1 Parametric Equations

parametric curve
7.1 Parametric Equations

parametric equations
7.1 Parametric Equations

partial fraction decomposition
3.4 Partial Fractions

partial sum
5.2 Infinite Series

particular solution
4.1 Basics of Differential Equations

partition
1.1 Approximating Areas

Pascal’s principle
2.5 Physical Applications

*pascals*2.5 Physical Applications

*perihelion*1.3 The Fundamental Theorem of Calculus

phase line
4.4 The Logistic Equation

polar axis
7.3 Polar Coordinates

polar coordinate system
7.3 Polar Coordinates

polar equations
7.3 Polar Coordinates

Population growth
2.8 Exponential Growth and Decay

power reduction formulas
3.2 Trigonometric Integrals

power series
6.1 Power Series and Functions

*power-reducing identities*3.2 Trigonometric Integrals

present value
6.2 Properties of Power Series

price–demand function
1.6 Integrals Involving Exponential and Logarithmic Functions

probability
3.7 Improper Integrals

probability density function
3.7 Improper Integrals

prolate cycloid
7.1 Parametric Equations

R

radial coordinate
7.3 Polar Coordinates

*radial density*2.5 Physical Applications

radius of convergence
6.1 Power Series and Functions

Ramanujan
5.6 Ratio and Root Tests

*rate of change*1.4 Integration Formulas and the Net Change Theorem

ratio test
5.6 Ratio and Root Tests

rational functions
3.4 Partial Fractions

*RC circuit*4.5 First-order Linear Equations

regular partition
1.1 Approximating Areas

relative error
3.6 Numerical Integration

remainder estimate
5.3 The Divergence and Integral Tests

Riemann sum
1.1 Approximating Areas

Riemann sums
3.6 Numerical Integration

right-endpoint approximation
1.1 Approximating Areas

root test
5.6 Ratio and Root Tests

S

separable differential equation
4.3 Separable Equations

separation of variables
4.3 Separable Equations

Sierpinski triangle
5.2 Infinite Series

sigma notation
1.1 Approximating Areas

*simple interest*2.8 Exponential Growth and Decay

Simpson’s rule
3.6 Numerical Integration

slicing method
2.2 Determining Volumes by Slicing

solid of revolution
2.2 Determining Volumes by Slicing

solution concentrations
4.3 Separable Equations

solution curve
4.2 Direction Fields and Numerical Methods

solution to a differential equation
4.1 Basics of Differential Equations

space-filling curve
7.3 Polar Coordinates

*space-filling curves*7.1 Parametric Equations

*spring constant*2.5 Physical Applications

summation notation
1.1 Approximating Areas

sums and powers of integers
1.1 Approximating Areas

Surface area
2.4 Arc Length of a Curve and Surface Area

symmetry
7.3 Polar Coordinates

symmetry principle
2.6 Moments and Centers of Mass

T

Taylor polynomials
6.3 Taylor and Maclaurin Series

Taylor series
6.3 Taylor and Maclaurin Series

Taylor’s theorem with remainder
6.3 Taylor and Maclaurin Series

telescoping series
5.2 Infinite Series

term
5.1 Sequences

term-by-term differentiation of a power series
6.2 Properties of Power Series

term-by-term integration of a power series
6.2 Properties of Power Series

theorem of Pappus for volume
2.6 Moments and Centers of Mass

threshold population
4.4 The Logistic Equation

total area
1.2 The Definite Integral

Tour de France
1.4 Integration Formulas and the Net Change Theorem

traffic accidents
3.7 Improper Integrals

trapezoidal rule
3.6 Numerical Integration

trigonometric integrals
3.2 Trigonometric Integrals

trigonometric substitution
3.3 Trigonometric Substitution

V

variable of integration
1.2 The Definite Integral

vertex
7.5 Conic Sections

von Bertalanffy growth
5.2 Infinite Series

W

washer method
2.2 Determining Volumes by Slicing

wingsuits
1.3 The Fundamental Theorem of Calculus

witch of Agnesi
7.1 Parametric Equations