Section 1.1 1.1.1
Applying Rates and Distance Section 1.2 1.2.1
Piecewise
–
Defined Functions and Continuity 1.2.2
End Behavior and Asymptotes 1.2.3
Holes, Vertical Asymptotes, and Approach Statements 1.2.4
Composite Functions and Inverse Functions 1.2.5
Attributes of Even and Odd Functions 1.2.6
Design a Flag Section 1.3 1.3.1
Finite
Differences 1.3.2
Slope Statements and Finite Differences of Non
–
Polynomials 1.3.3
The Slope Walk Section 1.4 1.4.1
Distance and Velocity 1.4.2
Averag
e Velocity on a Position Graph 1.4.3
Average Velocity on a Velocity Graph 1.4.4
Acceleration Section 1.5 1.5.1
Area and Slope
Chapter 2: Rates, Sums, Limits, and Continuity
Section 2.1 2.1.1
Area Under a Curve Using Trapezoids 2.1.2
Methods to Calculate Area Under a Curve 2.1.3
Area Under a Curve as a
Riemann Sum Section 2.2 2.2.1
Introduction to Limits as Predictions 2.2.2
Intuitive
I
deas of Continuity 2.2.3
Definition of Continuity 2.2.4
Evaluating Limits Section 2.3 2.3.1
Ramp Lab 2.3.2
Sudden Impact 2.3.3
Local
Linearity Section 2.4 2.4.1
Improving Approximation
Chapter 3: Slope and Curve Analysis
Section 3.1 3.1.1
The Power Rule 3.1.2
Secants to Tangents, AROC to IROC Section 3.2 3.2.1
Definition of a Derivative 3.2.2
Derivatives Using Multiple Strategies 3.2.3
Derivatives of Sine and Cosine Section 3.3 3.3.1
Curve Constructor: Part One 3.3.2
The Shape of a Curve 3.3.3
Curve Sketching: Derivatives 3.3.4
Ways to Describe
f
′
and
f
′
′ Section 3.4 3.4.1
Conditions for Differentiability 3.4.2
Curve Constructor: Part Two 3.4.3
Differentiability of Specific Functions 3.4.4
Intersection of Tangents
Chapter 4: The Fundamental Theorem of Calculus
Section 4.1 4.1.1
Definite Integrals 4.1.2
Properties
of Definite Integrals 4.1.3
More
Properties of Definite Integrals Section
4.2 4.2.1
Deriving “Area Functions” 4.2.2
Indefinite and Definite Integrals 4.2.3
The Fundamental Theorem of
Calculus 4.2.4
The Fundamental Theorem of Calculus 4.2.5
Integrals as Accumulators Section 4.3 4.3.1
Fast Times: Parts
One
& Two 4.3.2
Fast Times: Parts
Three & Four 4.3.3
Fast Times: Part
Five Section 4.4 4.4.1
Area
Between Curves 4.4.2
More Area Between Curves 4.4.3
Multiple Methods for Calculating Area Between Curves Section 4.5 4.5.1
Newton’s Method
Chapter 5: Derivative Tools and Applications
Section 5.1 5.1.1
Distance, Velocity, and
Acceleration Functions 5.1.2
Optimization 5.1.3
Using the
Frist
and
Second
Derivatives 5.1.4
Applying the First and Second Derivative Tests Section 5.2 5.2.1
The Product Rule 5.2.2
The Chain Rule and Application: Part
One 5.2.3
The Chain Rule and Application: Part
Two 5.2.4
The Quotient Rule 5.2.5
More Trigonometric Derivatives Section 5.3 5.3.1
Optimization Problems: Part One 5.3.2
Optimization Problems: Part Two 5.3.3
Optimization
Problems: Part
Three Section 5.4 5.4.1
Chain Rule Extension of the Fundamental Theorem of Calculus Section 5.5 5.5.1
Evaluating Limits of Indeterminate Forms 5.5.2
Using l’Hôpital’s Rule
Chapter 6: More Tools and Theorems
Section 6.1 6.1.1
Exponential Functions 6.1.2
Derivatives of Exponential Functions 6.1.3
Derivatives Using Multiple Tools 6.1.4
Integrals of Exponential Functions Section 6.2 6.2.1
Implicit Differentiation 6.2.2
Implicit Differentiation Practice Section 6.3 6.3.1
Inverse Trigonometric Derivatives 6.3.2
Derivatives of Natural Logarithms 6.3.3
Derivatives of Inverse Functions Section 6.4 6.4.1
Mean Value 6.4.2
Mean Value Theorem 6.4.3
Mean Value Theorem: Applications Section 6.5 6.5.1
Improper Integral
Chapter 7: Related Rates and Integration Tools
Section 7.1 7.1.1
Related Rates Introduction 7.1.2
Related Rates Applications: The Pythagorean Theorem 7.1.3
Related Rates Applications:
Similar Triangles 7.1.4
Related Rates Applications: Choosing the Best Formula 7.1.5
Related Rates Applications: Trigonometry Section 7.2 7.2.1
Undoing the Chain Rule 7.2.2
Integration with
u
–
Substitution 7.2.3
Definite Integrals and
u
–
Substitution 7.2.
4
Varied Integration Techniques Section 7.3 7.3.1
Solving Differential Equations 7.
3
.2
Newton’s Law of Cooling 7.
3
.3
Solving Separable Differential Equations 7.
3
.4
Slope Fields with
Parallel Tangents 7.
3
.5
Plotting Slope Efficiently 7.
3
.
6
Differential Equation
and Slope Field Applications Section 7.4 7.
4.1
Euler’s Method 7.4.2
Integration By Parts 7.4.3
Integration By Parts with Substitution 7.4.4
Integration by Partial Fraction
Chapter 8: Volume
Section 8.1 8.1.1
Volumes by Slicing 8.1.2
The Disk Method 8.1.3
The Washer Method 8.1.4
Revolution About Horizontal and Vertical Lines 8.1.5
Changing the Axis of Rotation 8.1.6
Disk and Washer Problems Section 8.2 8.2.1
Shell Lab 8.2.2
Comparing the Disk and Shell Methods 8.2.3
Using an Appropriate Method to Calculate Volume Section 8.3 8.
3
.1
Cross
–
Sections Lab: General Case 8.
3
.2
Cross
–
Sections Lab:
Functions Given 8.3.3
Cross
–
Section Problems Section 8.4 8.4.1
Arc Length
Chapter 9: Pre-Calculus Review
Section 9.1 9.1.1
Infinite Geometric Series 9.1.2
More Infinite Geometric Series 9.1.3
Convergence and Divergence Section 9.2 9.2.1
Parametric Equations 9.2.2
Converting Between Parametric and Rectilinear Form Section 9.3 9.3.1
Introduction to Vectors 9.3.2
Vector Operations Section 9.4 9.
4
.1
Graphs
of Polar Equations 9.
4
.2
Converting Between Polar and Rectilinear Form 9.4.3
Polar Families
Chapter 10: Convergence of Series
Section 10.1 10.1.1
Convergence of Series 10.1.2
The Divergence Test 10.1.3
The Alternating
Series Test 10.1.4
The Integral Test 10.1.
5
The
p
–
Series Test 10.1.6
The Comparison Test 10.1.7
The Limit Comparison Test 10.1.8
The Ratio Test Section 10.2 10.2.1
The Cootie Lab 10.2.2
More Logistic Differential
Equations Section 10.3 10.
3
.1
Power Series Convergence 10.
3
.2
Using Polynomials to Approximate Curves Section 10.4 10.
4
.1
Absolute Convergence 10.4.2
Regrouping and Rearranging
Serie
Chapter 11: Polar and Parametric Functions
Section 11.1 11.1.1
Area Bounded by a Polar Curve 11.1.2
More Polar Area 11.1.3
Area Between Polar Curves Section 11.2 11.2.1
Applied Calculus in Component Form 11.2.2
Second Derivatives in Component Form 11.2.3
Tot
al Distance and Arc Length Section 11.3 11.
3
.1
Slopes of Polar Curves 11.3.2
More Slopes of Polar Curves Section 11.4 11.4.1
Battling Robot
Chapter 12: Approximating Functions and Error
Section 12.1 12.1.1
Approximating
with Polynomial Functions 1
2
.1.2
Taylor Polynomials About
x
= 0 1
2
.1.3
Taylor Polynomials About
x
=
c 1
2
.1.
4
Taylor Series 1
2
.1.
5
Building Taylor Series Using Substitution Section 12.2 12.2.1
Interval of Convergence
Using
Technology 1
2
.2.2
Interval of Convergence Analytically Section 12.3 12.3.1
Error Bound for Alternating Taylor Polynomials 12.3.2
Lagrange Error Bound Section 12.4 12.4.1
Evaluating Indeterminate Forms
U
sing Taylor Serie
