Calculus Volume 1

# Index

A
absolute extremum 4.3 Maxima and Minima
absolute maximum 4.3 Maxima and Minima
absolute minimum 4.3 Maxima and Minima
absolute value function 1.1 Review of Functions
algebraic function 1.2 Basic Classes of Functions
antiderivative 4.10 Antiderivatives
area under the curve 5.1 Approximating Areas
average rate of change 3.4 Derivatives as Rates of Change
average value of the function 5.2 The Definite Integral
B
C
chain rule 3.6 The Chain Rule
change of variables 5.5 Substitution
composite function 1.1 Review of Functions
constant function 1.2 Basic Classes of Functions
Constant multiple law for limits 2.3 The Limit Laws
Constant Multiple Rule 3.3 Differentiation Rules
continuity over an interval 2.4 Continuity
continuous at a point 2.4 Continuity
continuous from the left 2.4 Continuity
continuous from the right 2.4 Continuity
critical number 4.3 Maxima and Minima
D
decreasing on the interval II 1.1 Review of Functions
definite integral 5.2 The Definite Integral
density function 6.5 Physical Applications
dependent variable 1.1 Review of Functions
derivative function 3.2 The Derivative as a Function
Difference law for limits 2.3 The Limit Laws
difference quotient 3.1 Defining the Derivative
Difference Rule 3.3 Differentiation Rules
differentiable at aa 3.2 The Derivative as a Function
differentiable function 3.2 The Derivative as a Function
differentiable on SS 3.2 The Derivative as a Function
Differential calculus 2.1 A Preview of Calculus
differentiation 3.1 Defining the Derivative
discontinuous at a point 2.4 Continuity
E
epsilon-delta definition of the limit 2.5 The Precise Definition of a Limit
existential quantifier 2.5 The Precise Definition of a Limit
Extreme Value Theorem 4.3 Maxima and Minima
F
Fermat’s theorem 4.3 Maxima and Minima
folium of Descartes 3.8 Implicit Differentiation
Fundamental Theorem of Calculus 5.3 The Fundamental Theorem of Calculus
Fundamental Theorem of Calculus, Part 1 5.3 The Fundamental Theorem of Calculus
Fundamental Theorem of Calculus, Part 2 5.3 The Fundamental Theorem of Calculus
I
implicit differentiation 3.8 Implicit Differentiation
increasing on the interval II 1.1 Review of Functions
indefinite integral 4.10 Antiderivatives
independent variable 1.1 Review of Functions
indeterminate forms 4.8 L’Hôpital’s Rule
infinite discontinuity 2.4 Continuity
infinite limit at infinity 4.6 Limits at Infinity and Asymptotes
infinite limits 2.2 The Limit of a Function
initial-value problem 4.10 Antiderivatives
instantaneous rate of change 3.1 Defining the Derivative
integrable function 5.2 The Definite Integral
Integral calculus 2.1 A Preview of Calculus
integration by substitution 5.5 Substitution
Intermediate Value Theorem 2.4 Continuity
interval notation 1.1 Review of Functions
intuitive definition of the limit 2.2 The Limit of a Function
inverse function 1.4 Inverse Functions
inverse hyperbolic functions 1.5 Exponential and Logarithmic Functions
inverse trigonometric functions 1.4 Inverse Functions
iterative process 4.9 Newton’s Method
J
jump discontinuity 2.4 Continuity
L
L’Hôpital’s rule 4.8 L’Hôpital’s Rule
leading coefficient 1.2 Basic Classes of Functions
left-endpoint approximation 5.1 Approximating Areas
limit laws 2.3 The Limit Laws
limits of integration 5.2 The Definite Integral
local extremum 4.3 Maxima and Minima
local maximum 4.3 Maxima and Minima
local minimum 4.3 Maxima and Minima
logarithmic function 1.2 Basic Classes of Functions
M
Mandelbrot set 4.9 Newton’s Method
mathematical models 1.2 Basic Classes of Functions
Mean Value Theorem 4.4 The Mean Value Theorem
Mean Value Theorem for Integrals 5.3 The Fundamental Theorem of Calculus
method of cylindrical shells. 6.3 Volumes of Revolution: Cylindrical Shells
method of exhaustion 5.1 Approximating Areas
multivariable calculus 2.1 A Preview of Calculus
Q
quadratic function 1.2 Basic Classes of Functions
Quotient law for limits 2.3 The Limit Laws
R
rational function 1.2 Basic Classes of Functions
Regiomontanus’ problem 4 Review Exercises
regular partition 5.1 Approximating Areas
related rates 4.1 Related Rates
removable discontinuity 2.4 Continuity
restricted domain 1.4 Inverse Functions
right-endpoint approximation 5.1 Approximating Areas
Rolle’s theorem 4.4 The Mean Value Theorem
Root law for limits 2.3 The Limit Laws
S
secant method 4.9 Newton’s Method
sigma notation 5.1 Approximating Areas
slope-intercept form 1.2 Basic Classes of Functions
spring constant 6.5 Physical Applications
squeeze theorem 2.3 The Limit Laws
standard form of a line 1.2 Basic Classes of Functions
Sum law for limits 2.3 The Limit Laws
summation notation 5.1 Approximating Areas
sums and powers of integers 5.1 Approximating Areas
symmetry about the origin 1.1 Review of Functions
symmetry about the y-axis 1.1 Review of Functions
symmetry principle 6.6 Moments and Centers of Mass
T
table of values 1.1 Review of Functions
tangent line approximation 4.2 Linear Approximations and Differentials
Tangent Problem 2.1 A Preview of Calculus
theorem of Pappus for volume 6.6 Moments and Centers of Mass
transcendental functions 1.2 Basic Classes of Functions
transformation of a function 1.2 Basic Classes of Functions
trigonometric functions 1.3 Trigonometric Functions
trigonometric identity 1.3 Trigonometric Functions
V
variable of integration 5.2 The Definite Integral
vertical asymptote 2.2 The Limit of a Function
vertical line test 1.1 Review of Functions
Z
zeroes of functions 4.9 Newton’s Method
zeros of a function 1.1 Review of Functions
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