## Index Index

absolute convergence test, Theorem

alternating harmonic series, Definition

antiderivative, Paragraph Definition

general antiderivative, Definition

antidifferentiation, Paragraph

area, Item Subsection

net area, Item

average value, Definition Theorem

bell curve, Item

comparison test, Theorem

for improper integrals, Theorem

for series, Paragraph

continuous money flow, Paragraph

contour map, Paragraph

convergence, Definition

absolutely, Paragraph Definition

conditionally, Definition

covariance, Paragraph Definition

cumulative distribution, Paragraph

bell-shaped, Paragraph

exponential, Paragraph Definition

joint, Paragraph Definition

uniform, Paragraph Definition

cylindrical shell, Paragraph

definite integral, Definition Paragraph

geometric interpretation, Paragraph

lower limit of integration, Definition

upper limit of integration, Definition

derivative, Paragraph

differential equation, Paragraph Paragraph Definition

Euler's method, Paragraph

first order, Definition

standard form, Paragraph

initial conditions, Definition

initial value problem, Paragraph Definition Example Example Example

integrating factor, Paragraph Definition Subsubsection

linear, Definition Paragraph

constant coefficients, Definition

homogeneous, Definition Paragraph

non-homogeneous, Definition Paragraph

long-term behaviour, Paragraph

non-linear, Definition

numerical methods, Paragraph

order, Definition

separable, Paragraph Definition

separation of variables, Paragraph Subsection

slope field, Paragraph

solution, Definition

specific solution, Paragraph

variation of parameters, Paragraph Subsubsection

discrete probability, Paragraph

disk, Paragraph

disk method, Theorem

divergence, Definition

double integral, Paragraph Definition

dummy variable, Item

Euler's method, Paragraph Subsection

non-uniform, Item

uniform, Item

expected value, Paragraph Paragraph Definition Definition Definition

average, Paragraph

mean, Paragraph

first order differential equation, Definition

first order homogeneous linear equation, Paragraph

first order linear differential equation, Paragraph

function

continuous, Paragraph

multi-variable, Paragraph

single-variable, Paragraph

and chain rule, Paragraph

geometric sequence, Definition

common ratio, Definition

growth and decay

carrying capacity, Paragraph

growth rate constant, Paragraph Subsection Paragraph

logistic, Paragraph Subsection

simple, Paragraph Subsection

harmonic series, Definition

improper integral, Paragraph Definition

comparison test, Theorem

converges, Paragraph Definition

diverges, Paragraph Definition

improper integrals

p-integrals, Paragraph

p-test, Theorem

indefinite integral, Definition Paragraph

index, Definition

initial value problem, Definition

integrable, Item

integral sign, Definition Definition

integral test, Paragraph

integrand, Definition Definition

integrating factor, Paragraph

area, Example

by parts, Paragraph

definite

Riemann sums, Theorem

displacement, Example

products of secant and tangent, Paragraph

products of sine and cosine, Paragraph

rules, Subsection

trapezoid approximation, Paragraph

trigonometric substitution, Paragraph

integration by parts, Paragraph

tabular method, Paragraph

interval of convergence, Item

joint cumulative distribution function, Paragraph Definition

joint probability density function, Paragraph Definition

p-series, Paragraph Definition

partial fraction decomposition, Example

power series, Paragraph Definition

centred at a, Definition

convergence, Subsection

derivative, Item

integral, Item

interval of convergence, Item

radius of convergence, Item

probability, Item Definition

independent, Item

probability density function, Definition

joint, Paragraph Definition

marginal, Item

uniform, Definition

quadratic formula, Paragraph

radius of convergence, Item

random variable, Definition

continuous, Definition

discrete, Definition

random variables

ratio test, Theorem

rational function, Paragraph

Riemann sum, Paragraph Definition Theorem

right hand rule, Item

sequence, Paragraph

bounded, Definition

bounded above, Definition

bounded below, Definition

boundedness, Paragraph

converves, Definition

decreasing, Item

diverges, Definition

geometric, Paragraph

increasing, Item

limit, Theorem

monotonic, Definition

monotonicity, Paragraph

n-th term, Definition

non-decreasing, Item

non-increasing, Item

properties, Theorem

strictly decreasing, Item

strictly increasing, Item

term, Definition

series, Paragraph Paragraph Definition

absolute convergence test, Theorem

alternating harmonic, Paragraph Definition

converges, Definition

diverges, Definition

geometric, Definition

harmonic, Item Example Definition

Maclaurin, Paragraph Definition

p-series, Definition

ratio test, Theorem

sequence of partial sums, Paragraph Definition

Taylor, Paragraph Definition

sigma notation, Paragraph Definition

error bound, Paragraph

single-variable, Paragraph

slope field, Paragraph

family of curves, Item

standard deviation, Paragraph Definition Definition Definition

standard normal distribution, Paragraph

characteristics, Subsubsection

substitution

inverse substitution, Item

trigonometric substitution, Paragraph

substitution rule

guideline for substitution rule, Subsection

summation

formulas, Theorem

notation, Paragraph

properties, Theorem

summation symbol, Definition

surplus, Paragraph

Taylor polynomial, Paragraph Definition

Taylor series, Paragraph Definition

Taylor's Theorem

remainder, Item

error bound, Theorem

trigonometric substitution, Paragraph

guideline for trigonometric substitution, Section

triple integral, Paragraph

variable of integration, Definition Definition

variance, Paragraph Definition Definition Definition

variation of parameters, Paragraph

volume, Paragraph

axis of rotation, Paragraph

cross-section, Definition

cylindrical shell, Paragraph

disk, Paragraph

disk method, Theorem

solid of revolution, Paragraph

volume below a surface, Theorem