The Readable Calculus Project (AB version)
Table of Contents
Introduction: General Overview of Calculus [pdf Intro]
Chapter 1: Derivatives [2021-22 Chapter 1 pdf]
Overview: Review of Derivatives Rules
1.1: The Power and Exponential Rules
1.2: Composite Functions and the Chain Rule
1.3: Trig, Trig Inverse, and Log Rules
1.4: Local Linearity and Approximations
1.5: Product Rule
1.6: Quotient Rules
1.7: Higher Order Derivatives
Chapter 1 Practice Test
Chapter 2: Indefinite Integrals [2021-22 Chapter 2 pdf]
Overview: The Operations of Calculus
2.1: The Power and Transcendental Rules
2.2: Integration by Substitution: Reversing the Chain Rule
2.3: Integration by Substitution and the Transcendental Functions
2.4: Separable Differential Equations
2.5: Slope Fields
Chapter 2 Practice Test
Chapter 3: Definite Integrals [2021-22 Chapter 3 pdf]
Overview:
3.1: Definite Integrals and the Fundamental Theorem of Calculus
3.2: Integration by U-Substitution
3.3: Approximate Integration – Riemann Sums
3.4: Context: Area, Displacement, and Net Change
3.5: Intro to AP: Accumulation of Rates
3.6: Intro to AP: Table Problems
Chapter 3 Test
Chapter 3 Answer Key
Chapter 4 Applications of the Derivative I--Graphing [2021-22 Chapter 4 pdf]
Overview:
4.1: Extremes and the Derivative Tests
4.2 The Mean Value Theorem
4.3: Optimization
4.4: The Second Derivative, Points of Inflection, and Concavity
4.5: Graphing with Derivatives
4.6: Graphical Analysis I
4.7: Intro to AP: Graphical Analysis II
Chapter 4 Test
Chapter 4 Answer Key
Chapter 5: Applications of the Derivative II—Rates of Change [2021-22 Chapter 5 pdf]
Overview:
5.1: Motion
5.2: Implicit Differentiation
5.3: Related Rates
5.4: Logistic Growth
Chapter 5 Test
Chapter 5 Answer Key
Chapter 6: Applications of Integrals [2021-22 Chapter 6 pdf]
Overview:
6.1: Area between Two Curves
6.2: Arc Length
6.3: Volume by Cross-section Method
6.4: Volume by Rotation about an Axis
6.5: Volume by Rotation about a Line not an Axis
6.6: Volume by Shell Method
Chapter 6 Test
Chapter 7: Limits, Continuity and Differentiability [2021-22 Chapter 7 pdf]
Overview: Introduction to Limits
7.1: Limits and L’Hopital’s Rule
7.2: The Limit Definitions of a Derivative
7.3: One-sided Limits
7.4: Continuity
7.5: Differentiability and Smoothness
7.6: Limits at Infinity and End Behavior
Chapter 3 Test
Chapter 8: AP Calculus AB Review [2021-22 Chapter 8]
Overview:
8.1: Accumulation of Rates
8.2: Rectilinear Motion
8.3: Graphical Analysis
8.4: Tabular Data Problems
8.5: Differential Equations
8.6: Area & Volume
8.7: Implicit Differentiation and Related Rates
8.8: Miscellaneous Topics
Appendix A: Reminders from PreCalculus
A.1: PreCalculus Basics
A.2: Important Facts for Calculus
A.3: Factoring Review
A.4: Sign Patterns
- Project Manager/Lead Writer: Kevin Quattrin
- Associate Writer: Paul Maychrowitz
- Associate Writer: Najla (nee Fawal) Abrao
- Chief Editor: Elizabeth Regalia
Table of Contents
Introduction: General Overview of Calculus [pdf Intro]
Chapter 1: Derivatives [2021-22 Chapter 1 pdf]
Overview: Review of Derivatives Rules
1.1: The Power and Exponential Rules
1.2: Composite Functions and the Chain Rule
1.3: Trig, Trig Inverse, and Log Rules
1.4: Local Linearity and Approximations
1.5: Product Rule
1.6: Quotient Rules
1.7: Higher Order Derivatives
Chapter 1 Practice Test
Chapter 2: Indefinite Integrals [2021-22 Chapter 2 pdf]
Overview: The Operations of Calculus
2.1: The Power and Transcendental Rules
2.2: Integration by Substitution: Reversing the Chain Rule
2.3: Integration by Substitution and the Transcendental Functions
2.4: Separable Differential Equations
2.5: Slope Fields
Chapter 2 Practice Test
Chapter 3: Definite Integrals [2021-22 Chapter 3 pdf]
Overview:
3.1: Definite Integrals and the Fundamental Theorem of Calculus
3.2: Integration by U-Substitution
3.3: Approximate Integration – Riemann Sums
3.4: Context: Area, Displacement, and Net Change
3.5: Intro to AP: Accumulation of Rates
3.6: Intro to AP: Table Problems
Chapter 3 Test
Chapter 3 Answer Key
Chapter 4 Applications of the Derivative I--Graphing [2021-22 Chapter 4 pdf]
Overview:
4.1: Extremes and the Derivative Tests
4.2 The Mean Value Theorem
4.3: Optimization
4.4: The Second Derivative, Points of Inflection, and Concavity
4.5: Graphing with Derivatives
4.6: Graphical Analysis I
4.7: Intro to AP: Graphical Analysis II
Chapter 4 Test
Chapter 4 Answer Key
Chapter 5: Applications of the Derivative II—Rates of Change [2021-22 Chapter 5 pdf]
Overview:
5.1: Motion
5.2: Implicit Differentiation
5.3: Related Rates
5.4: Logistic Growth
Chapter 5 Test
Chapter 5 Answer Key
Chapter 6: Applications of Integrals [2021-22 Chapter 6 pdf]
Overview:
6.1: Area between Two Curves
6.2: Arc Length
6.3: Volume by Cross-section Method
6.4: Volume by Rotation about an Axis
6.5: Volume by Rotation about a Line not an Axis
6.6: Volume by Shell Method
Chapter 6 Test
Chapter 7: Limits, Continuity and Differentiability [2021-22 Chapter 7 pdf]
Overview: Introduction to Limits
7.1: Limits and L’Hopital’s Rule
7.2: The Limit Definitions of a Derivative
7.3: One-sided Limits
7.4: Continuity
7.5: Differentiability and Smoothness
7.6: Limits at Infinity and End Behavior
Chapter 3 Test
Chapter 8: AP Calculus AB Review [2021-22 Chapter 8]
Overview:
8.1: Accumulation of Rates
8.2: Rectilinear Motion
8.3: Graphical Analysis
8.4: Tabular Data Problems
8.5: Differential Equations
8.6: Area & Volume
8.7: Implicit Differentiation and Related Rates
8.8: Miscellaneous Topics
Appendix A: Reminders from PreCalculus
A.1: PreCalculus Basics
A.2: Important Facts for Calculus
A.3: Factoring Review
A.4: Sign Patterns