Calculus for AP: A Complete Course 2nd edition

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• Chapter 1: Limits and Continuity
  • 1.1: The Tangent and Velocity Problems
  • 1.2: An Introduction to the Limit of a Function
  • 1.3: Calculating Limits Using the Limit Laws
  • 1.4: Limits at Infinity and Horizontal Asymptotes
  • 1.5: Continuity
  • 1.6: The Precise Definition of a Limit
  • 1: Chapter AP^® Review
  • 1: Cumulative Review
  • 1: Extra Problems
  
  
• Chapter 2: Differentiation: Definition and Fundamental Properties
  • 2.1: Derivatives and Rates of Change
  • 2.2: The Derivative as a Function
  • 2.3: Derivatives of Polynomials, the Natural Exponential Function, and the Natural Logarithmic Function
  • 2.4: The Product and Quotient Rules
  • 2.5: Derivatives of Trigonometric Functions
  • 2: Chapter AP^® Review
  • 2: Cumulative Review
  • 2: Extra Problems
  
  
• Chapter 3: Differentiation: Composite, Implicit, and Inverse Functions
  • 3.1: The Chain Rule
  • 3.2: Implicit Differentiation and Derivatives of Inverse Functions
  • 3.3: Derivatives of Logarithmic Functions
  • 3: Chapter AP^® Review
  • 3: Cumulative Review
  • 3: Extra Problems
  
  
• Chapter 4: Contextual Applications of Differentiation
  • 4.1: Applications of the Derivative
  • 4.2: Related Rates
  • 4.3: Local Linearity
  • 4.4: Indeterminate Forms and l'Hôpital's Rule
  • 4: Chapter AP^® Review
  • 4: Cumulative Review
  • 4: Extra Problems
  
  
• Chapter 5: Analytical Applications of Differentiation
  • 5.1: Maximum and Minimum Vales
  • 5.2: The Mean Value Theorem
  • 5.3: How Derivatives Affect the Shape of a Graph
  • 5.4: Summary of Curve Sketching
  • 5.5: Optimization Problems
  • 5: Chapter AP^® Review
  • 5: Cumulative Review
  • 5: Extra Problems
  
  
• Chapter 6: Integration and Accumulation of Change
  • 6.1: Antiderivatives
  • 6.2: Riemann Sums
  • 6.3: The Definite Integral
  • 6.4: The Fundamental Theorem of Calculus
  • 6.5: Indefinite Integrals and Net Change
  • 6.6: The Method of Substitution
  • 6.7: Integration by Parts
  • 6.8: Integration of Rational Functions by Partial Fractions
  • 6.9: Strategy for Integration
  • 6: Chapter AP^® Review
  • 6: Cumulative Review
  • 6: Extra Problems
  
  
• Chapter 7: Differential Equations
  • 7.1: Slope Fields and Euler's Method
  • 7.2: Separable Equations
  • 7.3: Models for Population Growth
  • 7: Chapter AP^® Review
  • 7: Cumulative Review
  • 7: Extra Problems
  
  
• Chapter 8: Applications of Integration
  • 8.1: Areas Between Curves
  • 8.2: Average Value of a Function
  • 8.3: The Definite Integral as an Accumulation Function
  • 8.4: Rectilinear Motion Revisited
  • 8.5: Volumes
  • 8.6: Arc Length
  • 8: Chapter AP^® Review
  • 8: Cumulative Review
  • 8: Extra Problems
  • 8: AP^® AB Practice Exam
  
  
• Chapter 9: Parametric Equations and Polar Coordinates
  • 9.1: Curves Defined by Parametric Equations
  • 9.2: Calculus with Parametric Curves
  • 9.3: Polar Coordinates and Derivatives
  • 9.4: Areas and Lengths in Polar Coordinates
  • 9: Chapter AP^® Review
  • 9: Cumulative Review
  • 9: Extra Problems
  
  
• Chapter 10: Infinite Sequences and Series
  • 10.1: Sequences
  • 10.2: Series
  • 10.3: The Integral Test and Estimates of Sums
  • 10.4: The Comparison Tests
  • 10.5: Alternating Series
  • 10.6: Absolute Convergence and the Ratio and Root Tests
  • 10.7: Strategy for Testing Series
  • 10.8: Power Series
  • 10.9: Representations of Functions as Power Series
  • 10.10: Taylor and Maclaurin Series
  • 10: Chapter AP^® Review
  • 10: Cumulative Review
  • 10: Extra Problems
  • 10: AP^® BC Practice Exam
  
  
• Chapter 0: Functions and Models
  • 0.1: The Rule of Four
  • 0.2: Mathematical Models: A Catalog of Essential Functions
  • 0.3: Trigonometric Functions
  • 0.4: New Functions from Old Functions
  • 0.5: Exponential Functions
  • 0.6: Inverse Functions and Logarithms
  • 0.7: Technology in AP^® Calculus
  • 0: Chapter AP^® Review
  • 0: Cumulative Review
  • 0: Extra Problems
  
  
• Chapter A: Appendices
  • A.A: Numbers, Inequalities, and Absolute Values
  • A.B: Coordinate Geometry and Lines
  • A.C: Graphs of Second-Degree Equations
  • A.D: Volumes by Cylindrical Shells
  • A.E: Answers to Odd-Numbered Exercises
  
  
• 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