1-1  Introducing Calculus: Can Change Occur at an Instant?
1-2  Defining Limits and Using Limit Notation
1-3  Estimating Limit Values from Graphs
1-4  Estimating Limit Values from Tables
1-5  Determining Limits Using Algebraic Properties of Limits
1-6  Determining Limits Using Algebraic Manipulation
1-7  Selecting Procedures for Determining Limits
1-8  Determining Limits Using the queeze Theorem
1-9  Connecting Multiple Representations of Limits
1-10  Exploring Types of Discontinuities
1-11  Defining Continuity at a Point
1-12  Confirming Continuity over an Interval
1-13  Removing Discontinuities
1-14  Connecting Infinite Limits and Vertical Asymptotes
1-15  Connecting Limits at Infinity and Horizontal Asymptotes
1-16  Working with the Intermediate Value Theorem (IVT)

2-1  Defining Average and Instantaneous Rates of Change at a Point
2-2  Defining the Derivative of a Function and Using Derivative Notation
2-3  Estimating Derivatives of a Function at a Point
2-4  Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
2-5  Applying the Power Rule
2-6  Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2-7  Derivatives of cos x, sin x, ex, and ln x
2-8  The Product Rule
2-9  The Quotient Rule
2-10  Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

3-1  The Chain Rule
3-2  Implicit Differentiation
3-3  Differentiating Inverse Functions
3-4  Differentiating Inverse Trigonometric Functions
3-5  Selecting Procedures for Calculating Derivatives
3-6  Calculating Higher Order Derivatives

4-1  Interpreting the Meaning of the Derivative in Context
4-2  Straight-Line Motion: Connecting Position, Velocity, and Acceleration
4-3  Rates of Change in Applied Contexts Other Than Motion
4-4  Introduction to Related Rates
4-5  Solving Related Rates Problems
4-6  Approximating Values of a Function Using Local Linearity and Linearization
4-7  Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

5-1  Using the Mean Value Theorem
5-2  Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
5-3  Determining Intervals on Which a Function Is Increasing or Decreasing
5-4  Using the First Derivative Test to Determine Relative (Local) Extrema
5-5  Using the Candidates Test to Determine Absolute (Global) Extrema
5-6  Determining Concavity of Functions over Their Domains
5-7  Using the Second Derivative Test to Determine Extrema
5-8  Sketching Graphs of Functions and Their Derivatives
5-9  Connecting a Function, Its First Derivative, and Its Second Derivative
5-10  Introduction to Optimization Problems
5-11  Solving Optimization Problems
5-12  Exploring Behaviors of Implicit Relations

6-1  Exploring Accumulations of Change
6-2  Approximating Areas 1 with Riemann Sums
6-3  Riemann Sums, Summation Notation, and Definite Integral Notation
6-4  The Fundamental Theorem of Calculus and Accumulation Functions
6-5  Interpreting the Behavior of Accumulation Functions Involving Area
6-6  Applying Properties of Definite Integrals
6- 7 The Fundamental Theorem of Calculus and Definite Integrals
6-8  Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
6-9  Integrating Using Substitution
6-10  Integrating Functions Using Long Division and Completing the Square
6-11  Integrating Using Integration by Parts
6-12  Using Linear Partial Fractions
6-13  Evaluating Improper Integrals
6-14  Selecting Techniques for Antidifferentiation

7-1  Modeling Situations with Differential Equations
7-2  Verifying Solutions for Differential Equations
7-3  Sketching Slope Fields
7-4  Reasoning Using Slope Fields
7-5  Approximating Solutions Using Euler’s Method
7-6  Finding General Solutions Using Separation of Variables
7-7  Finding Particular Solutions Using Initial Conditions and Separation of Variables
7-8  Exponential Models with Differential Equations
7-9  Logistic Models with Differential Equations

8-1  Finding the Average Value of a Function on an Interval
8-2  Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8-3  Using Accumulation Functions and Definite Integrals in Applied Contexts
8-4  Finding the Area Between Curves Expressed as Functions of x
8-5  Finding the Area Between Curves Expressed as Functions of y
8-6  Finding the Area Between Curves that Intersect at More Than Two Points
8-7  Volumes with Cross Sections: Squares and Rectangles
8-8  Volumes with Cross Sections: Triangles and Semicircles
8-9  Volume with Disc Method: Revolving Around the x- or y-Axis
8-10  Volume with Disc Method: Revolving 2 Around Other Axes
8-11  Volume with Washer Method: Revolving 4 Around the x- or y-Axis
8-12  Volume with Washer Method: Revolving 2 Around Other Axes
8-13  The Arc Length of a Smooth, Planar Curve and Distance Traveled

9-1  Defining Convergent and Divergent Infinite
9-2  Working with Geometric Series
9-3  The nth Term Test for Divergence
9-4  Integral Test for Convergence
9-5  Harmonic Series and p-Series
9-6  Comparison Tests for 3 Convergence
9-7  Alternating Series Test for Convergence
9-8  Ratio Test for Convergence
9-9  Determining Absolute or Conditional Convergence
9-10  Alternating Series Error Bound
9-11  Finding Taylor Polynomial Approximations of Functions
9-12  Lagrange Error Bound
9-13  Radius and Interval of Convergence of Power Series
9-14  Finding Taylor or Maclaurin Series for a Function
9-15  Representing Functions as Power Series