Calculus I with Precalculus 3rd edition

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• Chapter P: Prerequisites
  • P.1: Solving Equations
  • P.2: Solving Inequalities
  • P.3: Graphical Representation of Data
  • P.4: Graphs of Equations
  • P.5: Linear Equations in Two Variables
  • P: Review Exercises
  
  
• Chapter 1: Functions and Their Graphs
  • 1.1: Functions
  • 1.2: Analyzing Graphs of Functions
  • 1.3: Transformations of Functions
  • 1.4: Combinations of Functions
  • 1.5: Inverse Functions
  • 1.6: Mathematical Modeling and Variation
  • 1: Review Exercises
  
  
• Chapter 2: Polynomial and Rational Functions
  • 2.1: Quadratic Functions and Models
  • 2.2: Polynomial Functions of Higher Degree
  • 2.3: Polynomial and Synthetic Division
  • 2.4: Complex Numbers
  • 2.5: The Fundamental Theorem of Algebra
  • 2.6: Rational Functions
  • 2: Review Exercises
  
  
• Chapter 3: Limits and Their Properties
  • 3.1: A Preview of Calculus
  • 3.2: Finding Limits Graphically and Numerically
  • 3.3: Evaluating Limits Analytically
  • 3.4: Continuity and One-Sided Limits
  • 3.5: Infinite Limits
  • 3: Review Exercises
  
  
• Chapter 4: Differentiation
  • 4.1: The Derivative and the Tangent Line Problem
  • 4.2: Basic Differentiation Rules and Rates of Change
  • 4.3: Product and Quotient Rules and Higher-Order Derivatives
  • 4.4: The Chain Rule
  • 4.5: Implicit Differentiation
  • 4.6: Related Rates
  • 4: Review Exercises
  
  
• Chapter 5: Applications of Differentiation
  • 5.1: Extrema on an Interval
  • 5.2: Rolle's Theorem and the Mean Value Theorem
  • 5.3: Increasing and Decreasing Functions and the First Derivative Test
  • 5.4: Concavity and the Second Derivative Test
  • 5.5: Limits at Infinity
  • 5.6: A Summary of Curve Sketching
  • 5.7: Optimization Problems
  • 5.8: Differentials
  • 5: Review Exercises
  
  
• Chapter 6: Integration
  • 6.1: Antiderivatives and Indefinite Integration
  • 6.2: Area
  • 6.3: Riemann Sums and Definite Integrals
  • 6.4: The Fundamental Theorem of Calculus
  • 6.5: Integration by Substitution
  • 6.6: Numerical Integration
  • 6: Review Exercises
  
  
• Chapter 7: Exponential and Logarithmic Functions
  • 7.1: Exponential Functions and Their Graphs
  • 7.2: Logarithmic Functions and Their Graphs
  • 7.3: Using Properties of Logarithms
  • 7.4: Exponential and Logarithmic Equations
  • 7.5: Exponential and Logarithmic Models
  • 7: Review Exercises
  
  
• Chapter 8: Exponential and Logarithmic Functions and Calculus
  • 8.1: Exponential Functions: Differentiation and Integration
  • 8.2: Logarithmic Functions and Differentiation
  • 8.3: Logarithmic Functions and Integration
  • 8.4: Differential Equations: Growth and Decay
  • 8: Review Exercises
  
  
• Chapter 9: Trigonometric Functions
  • 9.1: Radian and Degree Measure
  • 9.2: Trigonometric Functions: The Unit Circle
  • 9.3: Right Triangle Trigonometry
  • 9.4: Trigonometric Functions of Any Angle
  • 9.5: Graphs of Sine and Cosine Functions
  • 9.6: Graphs of Other Trigonometric Functions
  • 9.7: Inverse Trigonometric Functions
  • 9.8: Applications and Models
  • 9: Review Exercises
  
  
• Chapter 10: Analytic Trigonometry
  • 10.1: Using Fundamental Trigonometric Identities
  • 10.2: Verifying Trigonometric Identities
  • 10.3: Solving Trigonometric Equations
  • 10.4: Sum and Difference Formulas
  • 10.5: Multiple-Angle and Product-to-Sum Formulas
  • 10: Review Exercises
  
  
• Chapter 11: Trigonometric Functions and Calculus
  • 11.1: Limits of Trigonometric Functions
  • 11.2: Trigonometric Functions: Differentiation
  • 11.3: Trigonometric Functions: Integration
  • 11.4: Inverse Trigonometric Functions: Differentiation
  • 11.5: Inverse Trigonometric Functions: Integration
  • 11.6: Hyperbolic Functions
  • 11: Review Exercises
  
  
• Chapter 12: Topics in Analytic Geometry
  • 12.1: Introduction to Conics: Parabolas
  • 12.2: Ellipses and Implicit Differentiation
  • 12.3: Hyperbolas and Implicit Differentiation
  • 12.4: Parametric Equations and Calculus
  • 12.5: Polar Coordinates and Calculus
  • 12.6: Graphs of Polar Coordinates
  • 12.7: Polar Equations of Conics
  • 12: Review Exercises
  
  
• Chapter 13: Additional Topics in Trigonometry
  • 13.1: Law of Sines
  • 13.2: Law of Cosines
  • 13.3: Vectors in the Plane
  • 13.4: Vectors and Dot Products
  • 13.5: Trigonometric Form of a Complex Number
  • 13: Review Exercises
  
  
• Chapter 14: Systems of Equations and Matrices
  • 14.1: Systems of Linear Equations in Two Variables
  • 14.2: Multivariable Linear Systems
  • 14.3: Systems Inequalities
  • 14.4: Matrices and Systems of Equations
  • 14.5: Operations with Matrices
  • 14.6: The Inverse of a Square Matrix
  • 14.7: The Determinant of a Square Matrix
  • 14: Review Exercises