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• Chapter A: Algebra Review
  • A.1: The Cartesian Coordinate Plane (52)
  • A.2: Linear and Quadratic Functions (36)
  • A.3: Polynomial Functions (31)
  • A.4: Rational Functions (46)
  • A.5: Further Topics in Functions (53)
  • A.6: Exponential and Logarithmic Functions (46)
  • A.7: Hooked on Conics (17)
  • A.8: Systems of Equations and Matrices (24)
  • A.9: Sequences and the Binomial Theorem (24)
  
  
• Chapter T: Trigonometry Review
  • T.1: Foundations of Trigonometry (95)
  • T.2: Applications of Trigonometry (5)
  
  
• Chapter 0: Preliminaries
  • 0.1: The Real Numbers and the Cartesian Plane (1)
  • 0.2: Lines and Functions (9)
  • 0.3: Graphing Calculators and Computer Algebra Systems (1)
  • 0.4: Trigonometric Functions (4)
  • 0.5: Transformations of Functions (13)
  
  
• Chapter 1: Limits and Continuity
  • 1.1: A Brief Preview of Calculus: Tangent Lines and the Length of a Curve (1)
  • 1.2: The Concept of Limit (3)
  • 1.3: Computation of Limits (11)
  • 1.4: Continuity and Its Consequences (9)
  • 1.5: Limits Involving Infinity; Asymptotes (22)
  • 1.6: Formal Definition of the Limit (3)
  • 1.7: Limits and Loss-of-Significance Errors
  
  
• Chapter 2: Differentiation
  • 2.1: Tangent Lines and Velocity (3)
  • 2.2: The Derivative
  • 2.3: Computation of Derivatives: The Power Rule (13)
  • 2.4: The Product and Quotient Rule (9)
  • 2.5: The Chain Rule (5)
  • 2.6: Derivatives of Trigonometric Functions (6)
  • 2.7: Implicit Differentiation (7)
  • 2.8: The Mean Value Theorem (11)
  
  
• Chapter 3: Applications of Differentiation
  • 3.1: Linear Approximations and Newton's Method (19)
  • 3.2: Maximum and Minimum Values (9)
  • 3.3: Increasing and Decreasing Functions (5)
  • 3.4: Concavity and the Second Derivative Test (9)
  • 3.5: Overview of Curve Sketching (16)
  • 3.6: Optimization (18)
  • 3.7: Related Rates (13)
  • 3.8: Rates of Change in Economics and the Sciences (1)
  
  
• Chapter 4: Integration
  • 4.1: Antiderivatives (18)
  • 4.2: Sums and Sigma Notation (1)
  • 4.3: Area (5)
  • 4.4: The Definite Integral (15)
  • 4.5: The Fundamental Theorem of Calculus (34)
  • 4.6: Integration by Substitution (18)
  • 4.7: Numerical Integration (12)
  
  
• Chapter 5: Applications of the Definite Integral
  • 5.1: Area Between Curves (13)
  • 5.2: Volume: Slicing, Disks and Washers (20)
  • 5.3: Volumes by Cylindrical Shells (15)
  • 5.4: Arc Length and Surface Area (20)
  • 5.5: Projectile Motion (5)
  • 5.6: Applications of Integration to Physics and Engineering (15)
  
  
• Chapter 6: Exponentials, Logarithms and Other Transcendental Functions
  • 6.1: The Natural Logarithm (40)
  • 6.2: Inverse Functions (7)
  • 6.3: The Exponential Function (24)
  • 6.4: The Inverse Trigonometric Functions (1)
  • 6.5: The Calculus of the Inverse Trigonometric Functions (4)
  • 6.6: The Hyperbolic Functions (12)
  
  
• Chapter 7: Integration Techniques
  • 7.1: Review of Formulas and Techniques (2)
  • 7.2: Integration by Parts (25)
  • 7.3: Trigonometric Techniques of Integration (43)
  • 7.4: Integration of Rational Functions Using Partial Fractions (23)
  • 7.5: Integration Tables and Computer Algebra Systems (12)
  • 7.6: Indeterminate Forms and L'Hopital's Rule (22)
  • 7.7: Improper Integrals (2)
  • 7.8: Probability (8)
  
  
• Chapter 8: First-Order Differential Equations
  • 8.1: Modeling with Differential Equations (4)
  • 8.2: Separable Differential Equations (5)
  • 8.3: Direction Fields and Euler's Method (1)
  • 8.4: Systems of First-Order Differential Equations
  
  
• Chapter 9: Infinite Series
  • 9.1: Sequences of Real Numbers (26)
  • 9.2: Infinite Series (16)
  • 9.3: The Integral Test and Comparison Tests (34)
  • 9.4: Alternating Series (5)
  • 9.5: Absolute Convergence and the Ratio Test (49)
  • 9.6: Power Series (27)
  • 9.7: Taylor Series (14)
  • 9.8: Applications of Taylor Series (5)
  • 9.9: Fourier Series
  
  
• Chapter 10: Parametric Equations and Polar Coordinates
  • 10.1: Plane Curves and Parametric Equations (15)
  • 10.2: Calculus and Parametric Equations (16)
  • 10.3: Arc Length and Surface Area (9)
  • 10.4: Polar Coordinates (21)
  • 10.5: Calculus and Polar Coordinates (20)
  • 10.6: Conic Sections (13)
  • 10.7: Conic Sections in Polar Coordinates (4)