Calculus for AP 1st edition

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• Chapter 1: Limits and Their Properties
  • 1.1: A Preview of Calculus
  • 1.2: Finding Limits Graphically and Numerically
  • 1.3: Evaluating Limits Analytically
  • 1.4: Continuity and One-Sided Limits
  • 1.5: Infinite Limits
  • 1.6: Limits at Infinity
  • 1: Review Exercises
  • 1: AP^® Exam Practice Questions
  
  
• Chapter 2: Differentiation
  • 2.1: The Derivative and the Tangent Line Problem
  • 2.2: Basic Differentiation Rules and Rates of Change
  • 2.3: Product and Quotient Rules and Higher-Order Derivatives
  • 2.4: The Chain Rule
  • 2.5: Implicit Differentiation
  • 2.6: Derivatives of Inverse Functions
  • 2.7: Related Rates
  • 2.8: Newton's Method
  • 2: Review Exercises
  • 2: AP^® Exam Practice Questions
  
  
• Chapter 3: Applications of Differentiation
  • 3.1: Extrema on an Interval
  • 3.2: Rolle's Theorem and the Mean Value Theorem
  • 3.3: Increasing and Decreasing Functions and the First Derivative Test
  • 3.4: Concavity and the Second Derivative Test
  • 3.5: A Summary of Curve Sketching
  • 3.6: Optimization Problems
  • 3.7: Differentials
  • 3: Review Exercises
  • 3: AP^® Exam Practice Questions
  
  
• Chapter 4: Integration
  • 4.1: Antiderivatives and Indefinite Integration
  • 4.2: Area
  • 4.3: Riemann Sums and Definite Integrals
  • 4.4: The Fundamental Theorem of Calculus
  • 4.5: Integration by Substitution
  • 4.6: The Natural Logarithmic Function: Integration
  • 4.7: Inverse Trigonometric Functions: Integration
  • 4: Review Exercises
  • 4: AP^® Exam Practice Questions
  
  
• Chapter 5: Differential Equations
  • 5.1: Slope Fields and Euler's Method
  • 5.2: Growth and Decay
  • 5.3: Separation of Variables
  • 5.4: The Logistic Equation
  • 5: Review Exercises
  • 5: AP^® Exam Practice Questions
  
  
• Chapter 6: Applications of Integration
  • 6.1: Area of a Region Between Two Curves
  • 6.2: Volume: The Disk and Washer Methods
  • 6.3: Volume: The Shell Method
  • 6.4: Arc Length and Surfaces of Revolution
  • 6: Review Exercises
  • 6: AP^® Exam Practice Questions
  
  
• Chapter 7: Integration Techniques, L'Hôpital's Rule, and Improper Integrals
  • 7.1: Basic Integration Rules
  • 7.2: Integration by Parts
  • 7.3: Trigonometric Integrals
  • 7.4: Trigonometric Substitution
  • 7.5: Partial Fractions
  • 7.6: Integration by Tables and Other Integration Techniques
  • 7.7: Indeterminate Forms and L'Hôpital's Rule
  • 7.8: Improper Integrals
  • 7: Review Exercises
  • 7: AP^® Exam Practice Questions
  
  
• Chapter 8: Infinite Series
  • 8.1: Sequences
  • 8.2: Series and Convergence
  • 8.3: The Integral Test and p-Series
  • 8.4: Comparisons of Series
  • 8.5: Alternating Series
  • 8.6: The Ratio and Root Tests
  • 8.7: Taylor Polynomials and Approximations
  • 8.8: Power Series
  • 8.9: Representation of Functions by Power Series
  • 8.10: Taylor and Maclaurin Series
  • 8: Review Exercises
  • 8: AP^® Exam Practice Questions
  
  
• Chapter 9: Parametric Equations, Polar Coordinates, and Vectors
  • 9.1: Conics and Calculus
  • 9.2: Plane Curves and Parametric Equations
  • 9.3: Parametric Equations and Calculus
  • 9.4: Polar Coordinates and Polar Graphs
  • 9.5: Area and Arc Length in Polar Coordinates
  • 9.6: Vectors in the Plane
  • 9.7: Vector-Valued Functions
  • 9.8: Velocity and Acceleration
  • 9: Review Exercises
  • 9: AP^® Exam Practice Questions
  
  
• Chapter 0: Preparation for Calculus
  • 0.1: Graphs and Models
  • 0.2: Linear Models and Rates of Change
  • 0.3: Functions and Their Graphs
  • 0.4: Inverse Functions
  • 0.5: Exponential and Logarithmic Functions
  • 0: Review Exercises
  
  
• Chapter A: Appendices
  • A.A: Proofs of Selected Theorems
  • A.B: Integration Tables
  • A.C: Precalculus Review
  • A.D: Algebra Review
  • A.E: Rotation and the General Second-Degree Equation (Online)*
  • A.F: Complex Numbers (Online)*
  • A.G: Business and Economic Applications (Online)*
  
  
• Chapter QP: Quick Prep Topics
  • QP.1: Definition and Representations of Functions
  • QP.2: Working with Representations of Functions
  • QP.3: Function Notation
  • QP.4: Domain and Range of a Function
  • QP.5: Solving Linear Equations
  • QP.6: Linear Functions
  • QP.7: Parabolas
  • QP.8: Factoring Quadratic Equations and Finding x-intercepts of a Quadratic Function
  • QP.9: Polynomials
  • QP.10: More about Factoring Polynomials
  • QP.11: Finding Roots
  • QP.12: Dividing Polynomials
  • QP.13: Rational Functions
  • QP.14: Root Functions
  • QP.15: Rationalizing the Numerator or Denominator
  • QP.16: Exponential Functions
  • QP.17: Logarithmic Functions
  • QP.18: Trigonometric Functions and the Unit Circle
  • QP.19: Graphs of Trigonometric Functions
  • QP.20: Trigonometric Identities
  • QP.21: Special Functions
  • QP.22: Algebraic Combinations of Functions
  • QP.23: Composition of Functions
  • QP.24: Transformations of Functions
  • QP.25: Inverse Functions
  
  
• Chapter FT5: Fast Track to a 5: Preparing for the AP^® Calculus AB and Calculus BC Examinations
  • FT5.ABDT: AB Diagnostic Test
  • FT5.BCDT: BC Diagnostic Test
  • FT5.1: Limits and Continuity
  • FT5.2: Differentiation: Definition and Fundamental Properties
  • FT5.3: Differentiation: Composite, Implicit, and Inverse Functions
  • FT5.4: Contextual Applications of Derivatives
  • FT5.5: Analytical Applications of Derivatives
  • FT5.6: Integration and Accumulation of Change
  • FT5.7: Differential Equations
  • FT5.8: Applications of Integration
  • FT5.9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
  • FT5.10: Infinite Sequences and Series
  • FT5.ABT1: AB Practice Test 1
  • FT5.ABT2: AB Practice Test 2
  • FT5.BCT1: BC Practice Test 1
  • FT5.BCT2: BC Practice Test 2