- Project Manager/Lead Writer: Kevin Quattrin
- Associate Writers: Najla (nee Fawal) Abrao and Paul Maychrowitz
- Chief Editor: Elizabeth Regalia
Solution Manual
Table of Contents and Introduction: General Overview of Calculus
Chapter 1: Review of Derivatives [Chapter 1 pdf]
- 1.1: The Power and Exponential Rules with the Chain Rule
- 1.2: Trig, Trig Inverse, and Log Rules
- 1.3: Local Linearity, Euler’s Method, and Approximations
- 1.4: Product and Quotient Rules
- 1.5: Higher Order Derivatives
- 1.6: Implicit
- 1.7: Logarithmic Differentiation
- Chapter 1 Test
- Chapter 1 Answer Key
Chapter 2: Anti-Derivatives [Chapter 2 pdf]
- 2.1: The Power and Transcendental Rules
- 2.2: Integration by Substitution--the Chain Rule
- 2.3: Separable Differential Equations
- 2.4: Integration by Substitution--Back Substitution
- 2.5: Powers of Trig Functions: Sine and Cosine
- 2.6: Powers of Trig Functions: Secant and Tangent
- 2.7: Slope Fields
- Chapter 2 Test
- Chapter 2 Answer Key
Chapter 3: Derivatives and Graphs [Chapter 3 pdf]
- 3.1: Extremes and the Derivative Tests
- 3.2: The Mean Value Theorem
- 3.3: The Second Derivative, Points of Inflection, and Concavity
- 3.4: Graphing with Derivatives
- 3.5: Graphical Analysis I
- 3.6: Motion
- 3.7: Related Rates
- Chapter 3 Test
- Chapter 3 Answer Key
Chapter 4: Integrals [Chapter 4 pdf]
- 4.1: The Fundamental Theorem of Calculus
- 4.2: Definite Integrals and Integration by Substitution
- 4.3: Context: Area, Displacement, and Net Change
- 4.4: Graphical Analysis II
- 4.5: Approximate Integration – Riemann Sums
- 4.6: Accumulation of Rates
- Chapter 4 Test
- Chapter 4 Answer Key
Chapter 5: Applications of Integrals [Chapter 5 pdf]
- 5.1: Area between Two Curves
- 5.2: Arc Length
- 5.3: Volume by Cross-section Method
- 5.4: Volume by Rotation about an Axis
- 5.5: Volume by Rotation about a Line not an Axis
- 5.6: Volume by Shell Method
- Chapter 5 Test
- Chapter 5 Answer Key
Chapter 6: Limits, Continuity and Differentiability [Chapter 6 pdf]
- 6.1: Continuity and One-sided Limits
- 6.2: Differentiability and Smoothness
- 6.3: Limits, L’Hopital’s Rule, and The Limit Definitions of a Derivative
- 6.4: Limits at Infinity and End Behavior
- 6.5: Type I Improper Integrals
- 6.6: Infinite Limits and Type II Improper Integrals
- Chapter 6 Test
- Chapter 6 Answer Key
Chapter 7: Sequences and Numerical Series [Chapter 7 pdf]
- 7.1: Intro to Sequences
- 7.2: Intro to Series
- 7.3: Convergence and Divergence
- 7.4: The Integral Test
- 7.5: The Comparison Tests
- 7.6: The Ratio Test and Nth Root Tests
- 7.7: Alternating Series
- 7.8: General Series Summary
- Chapter 7 Test
- Chapter 7 Answer Key
Chapter 8: Advanced Integration [Chapter 8 pdf]
- 8.1: Integrals of Rational Functions
- 8.2: Partial Fractions I
- 8.3: Logistic Growth
- 8.4: Integration by Parts
- 8.5: Trig Substitution
- 8.6: Partial Fractions II
- 8.7: Partial Fractions III
- 8.8: General Integration
- Chapter 8 Test
- Chapter 8 Answer Key
Chapter 9: Parametric and Polar Coordinates [Chapter 9 pdf]
- 9.1: Parametrics and Motion
- 9.2: Parametrics and Graphing
- 9.3: Polar Graphs and Parametric Conversions
- 9.4: Polar Coordinates, Arc Length, and Simple Area
- 9.5: Area Involving Two Polar Graphs
- 9.6: Derivatives and Polar Graphs
- Chapter 9 Test
- Chapter 9 Answer Key
Chapter 10: Power Series [Chapter 10 pdf]
- 10.1: Taylor and Maclaurin Series
- 10.2: Power Series
- 10.3: Review of Numerical Series
- 10.4: Radius and Intervals of Convergence
- Chapter 10 Test
- Chapter 10 Answer Key
Chapter 11: AP Calculus BC FRQ Review [Chapter 11 pdf]
Overview: The last 10 years
- 11.1 Accumulation of Rates (AB1)
- 11.2 Reasoning from Tabular Data (AB2)
- 11.3 Graphical Analysis (AB3)
- 11.4 Power Series
- 11.5 Differential Equations (AB5)
- 11.6 Parametric Motion
- 11.7 Polar Coordinates
- 11.8 Area and Volume (AB6)
- 11.9 Related Rates (AB7)
- 11.10 Advanced Integration.
- 11.11 Miscellaneous AB Topics
Appendix A: Synthesis of PreCalculus [Chapter A pdf]
- Overview: Functions and Traits
- 0.1: Recognizing and Identifying Graphs, Graphing from Traits
- 0.2: Factoring Review and Zeroes of Functions
- 0.3: Sign Patterns and Domains
- 0.4: Calculator Review
- 0.5: Important Facts for Calculus
Appendix B: The Formula Booklet [Appendix B pdf]