# Course: AP Calculus AB & BC • Prep Plus 2019-2020

• Part 1 The Basics
• Chapter 1 Inside the AP Calculus AB Exam
• Chapter 2 Strategies for Success
• Chapter 3 Calculator Basics
• Part 2 Fundamental Concepts
• Big Idea 1 Limits
• Chapter 4 Basic Limits
• 4.1 Evaluating Limits Graphically
• 4.2 Evaluating Limits Algebraically
• 4.3 Limits of Composite Functions
• 4.4 Limits That Don’t Exist
• Chapter 5 More Advanced Limits
• 5.1 Infinite Limits
• 5.2 Limits at Infinity
• 5.3 Horizontal and Vertical Asymptotes
• 5.4 Limits Involving Trig Functions
• 5.5 L’Hopital’s Rule
• Chapter 6 Continuity
• 6.1 Continuity and Limits
• 6.2 Types of Discontinuities
• 6.3 Piecewise Functions
• 6.4 The Intermediate Value, Extreme Value, and Mean Value Theorems
• Big Idea 2 Derivatives
• Chapter 7 Derivatives—The Basics
• 7.1 The Limit Definition of the Derivative
• 7.2 Estimating Derivatives from Graphs and Tables
• 7.3 The Power Rule
• 7.4 The Product and Quotient Rules
• 7.5 The Chain Rule
• 7.6 Derivatives of Logarithmic and Exponential Functions
• Chapter 8 More Advanced Derivatives
• 8.1 Derivatives of Trig Functions
• 8.2 Derivatives of Inverse Trig Functions
• 8.3 Higher Order Derivatives
• 8.4 Implicit Differentiation
• 8.5 Derivatives of Inverse Functions
• Chapter 9 Applications of the Derivative
• 9.1 The Slope of a Curve at a Point
• 9.2 Tangent Lines and Normal Lines
• 9.3 Local Linear Approximations
• 9.4 Derivatives as Rates of Change
• 9.5 First Derivatives and Curve Sketching
• 9.6 Second Derivatives and Curve Sketching
• Chapter 10 More Advanced Applications
• 10.1 The Relationship between Differentiability and Continuity
• 10.2 Using the Graphs of 𝑓, 𝑓′ and 𝑓′′
• 10.3 Optimization
• 10.4 Rectilinear Motion
• 10.5 Related Rates
• Big Idea 3 Integrals and the Fundamental Theorem of Calculus
• Chapter 11 Integration—The Basics
• 11.1 Antiderivatives and the Indefinite Integral
• 11.2 Antiderivatives Subject to an Initial Condition
• 11.3 U-Substitution and Algebraic Functions
• 11.4 Trig Functions
• 11.5 Exponential and Logarithmic Functions
• Chapter 12 The Definite Integral
• 12.1 The Fundamental Theorems of Calculus
• 12.2 Reimann Sums and Definite Integrals
• 12.3 Properties of Definite Integrals
• 12.4 U-Substitution and Definite Integrals
• 12.5 Equivalent Forms of Definite Integrals
• Chapter 13 Geometric Applications of Integration
• 13.1 Area Under a Curve
• 13.2 Area between or Bounded by Curves
• 13.3 Volumes of Solids with Known Cross Sections
• 13.4 Volume of Solids of Revolution
• Chapter 14 Further Applications of Integration
• 14.1 Average Value of a Function
• 14.2 Net Change over an Interval
• 14.3 Motion along a Line
• 14.4 Differential Equations
• 14.5 Exponential Growth and Decay
• 14.6 Slope Fields
• Part 3 Graphing Calculators and Free Response Questions
• Chapter 15 Problems That Require Graphing Calculators
• 15.1 Graphing Functions and Finding Critical Points
• 15.2 Finding a Derivative at a Point
• 15.3 Evaluating a Definite Integral
• Chapter 16 Answering Free Response Questions
• Part 4 Calculus BC Topics
• Chapter 17 Parametric, Polar, and Vector Functions
• 17.1 Define and Graph Parametric Functions
• 17.2 Differentiate and Integrate Parametric Functions
• 17.3 Define and Graph Polar Functions
• 17.4 Differentiate and Integrate Polar Functions
• 17.5 Define and Graph Vector Functions
• 17.6 Differentiate and Integrate Vector Functions
• Chapter 18 Additional Techniques of Differentiation and Integration
• 18.1 Solve Differential Equations via Euler’s Method
• 18.2 Apply Integration by Parts to Integrands with Two Functions
• 18.3 Evaluate Fractional Integrands Using Simple Partial Fractions
• 18.4 Perform Antidifferentiation of Improper Integrals
• 18.5 Solve Logistic Differential Equations and Use Them in Modeling
• Chapter 19 Series
• 19.1 Evaluate the Limits of Series Using Partial Sums
• 19.2 Define Convergence in a Series and Identify Geometric and Harmonic Series
• 19.3 Apply the Integral Test and Determine Convergence in 𝑝-Series
• 19.4 Determine Convergence with the Comparison Test and the Ratio Test
• 19.5 Evaluate Alternating Series for Convergence and Estimate Their Limit
• Chapter 20 Power Series
• 20.1 Find the Radius and Interval of Convergence of Functions Defined by Power Series
• 20.2 Use Taylor Polynomial Expansion to Approximate Nonpolynomial Functions
• 20.3 Apply the Maclaurin Series of Special Functions to More Complex Functions
• 20.4 Find the Lagrange Error Bound for Taylor Polynomials
• Part 5 Practice Exams

Use Nagwa in conjunction with your preferred textbook. The recommended lessons from Nagwa for each section of this textbook are provided below. This course is not affiliated with, sponsored by, or endorsed by the publisher of the referenced textbook. Nagwa is a registered trademark of Nagwa Limited. All other trademarks and registered trademarks are the property of their respective owners.