Calculus for AP: A Complete Course 1st edition

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• Chapter 1: Functions and Models
  • 1.1: The Rule of Four
  • 1.2: Mathematical Models: A Catalog of Essential Functions
  • 1.3: Trigonometric Functions
  • 1.4: New Functions from Old Functions
  • 1.5: Exponential Functions
  • 1.6: Inverse Functions and Logarithms
  • 1.7: Technology in AP^® Calculus
  • 1: Review
  • 1: True-False
  • 1: Principles of Problem Solving
  
  
• Chapter 2: Limits
  • 2.1: The Tangent and Velocity Problems
  • 2.2: An Introduction to the Limit of a Function
  • 2.3: Calculating Limits Using the Limit Laws
  • 2.4: Limits at Infinity and Horizontal Asymptotes
  • 2.5: Continuity
  • 2.6: The Precise Definition of a Limit
  • 2: Review
  • 2: True-False
  • 2: Problems Plus
  
  
• Chapter 3: The Derivative
  • 3.1: Derivatives and Rates of Change
  • 3.2: The Derivative as a Function
  • 3.3: Derivatives of Polynomials and Exponential Functions
  • 3.4: The Product and Quotient Rules
  • 3.5: Derivatives of Trigonometric Functions
  • 3.6: The Chain Rule
  • 3.7: Implicit Differentiation and Derivatives of Inverse Functions
  • 3.8: Derivatives of Logarithmic Functions
  • 3.9: Applications of the Derivative
  • 3.10: Related Rates
  • 3.11: Local Linearity
  • 3: Review
  • 3: True-False
  • 3: Problems Plus
  
  
• Chapter 4: Applications of Differentiation
  • 4.1: Maximum and Minimum Values
  • 4.2: The Mean Value Theorem
  • 4.3: How Derivatives Affect the Shape of a Graph
  • 4.4: Indeterminate Forms and l'Hospital's Rule
  • 4.5: Summary of Curve Sketching
  • 4.6: Optimization Problems
  • 4: Review
  • 4: True-False
  • 4: Problems Plus
  
  
• Chapter 5: Integration
  • 5.1: Antiderivatives
  • 5.2: Riemann Sums
  • 5.3: The Definite Integral
  • 5.4: The Fundamental Theorem of Calculus
  • 5.5: Indefinite Integrals
  • 5.6: The Method of Substitution
  • 5: Review
  • 5: True-False
  • 5: Problems Plus
  
  
• Chapter 6: Applications of Integration
  • 6.1: Areas Between Curves
  • 6.2: Average Value of a Function
  • 6.3: The Definite Integral as an Accumulation Function
  • 6.4: Rectilinear Motion Revisited
  • 6.5: Volumes
  • 6.6: Arc Length
  • 6: Review
  • 6: True-False
  • 6: Problems Plus
  
  
• Chapter 7: Techniques of Integration
  • 7.1: Integration by Parts
  • 7.2: Trigonometric Integrals
  • 7.3: Trigonometric Substitution
  • 7.4: Integration of Rational Functions by Partial Fractions
  • 7.5: Strategy for Integration
  • 7.6: Improper Integrals
  • 7: Review
  • 7: True-False
  • 7: Problems Plus
  
  
• Chapter 8: Differential Equations
  • 8.1: Slope Fields and Euler's Method
  • 8.2: Separable Equations
  • 8.3: Models for Population Growth
  • 8: Review
  • 8: True-False
  • 8: Problems Plus
  
  
• Chapter 9: Infinite Sequences and Series
  • 9.1: Sequences
  • 9.2: Series
  • 9.3: The Integral Test and Estimates of Sums
  • 9.4: The Comparison Tests
  • 9.5: Alternating Series
  • 9.6: Absolute Convergence and the Ratio and Root Tests
  • 9.7: Strategy for Testing Series
  • 9.8: Power Series
  • 9.9: Representations of Functions as Power Series
  • 9.10: Taylor and Maclaurin Series
  • 9: Review
  • 9: True-False
  • 9: Problems Plus
  
  
• Chapter 10: Parametric Equations and Polar Coordinates
  • 10.1: Curves Defined by Parametric Equations
  • 10.2: Calculus with Parametric Curves
  • 10.3: Polar Coordinates and Derivatives
  • 10.4: Areas and Lengths in Polar Coordinates
  • 10: Review
  • 10: True-False
  • 10: Problems Plus
  
  
• 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
  • A.F: Trigonometry
  • A.G: Sigma Notation
  • A.H: Proofs of Theorems
  • A.I: The Logarithm Defined as an Integral
  • A.J: Complex Numbers
  
  
• 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 Their Properties
  • FT5.2: Differentiation
  • FT5.3: Applications of Derivatives
  • FT5.4: Integration
  • FT5.5: Differential Equations
  • FT5.6: Applications of Integration
  • FT5.7: Advanced Integration Techniques
  • FT5.8: Infinite Series
  • FT5.9: Parametric Equations, Vectors, and Polar Coordinates
  • FT5.ABT1: AB Practice Test 1
  • FT5.ABT2: AB Practice Test 2
  • FT5.BCT1: BC Practice Test 1
  • FT5.BCT2: BC Practice Test 2
  
  
• 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