Essential Calculus: Early Transcendentals 2nd edition

Access is contingent on use of this textbook in the instructor's classroom.

• 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 0: Diagnostic Tests
  • 0.A: Diagnostic Test: Algebra
  • 0.B: Diagnostic Test: Analytic Geometry
  • 0.C: Diagnostic Test: Functions
  • 0.D: Diagnostic Test: Trigonometry
  
  
• Chapter 1: Functions and Limits
  • 1.1: Functions and Their Representations
  • 1.2: A Catalog of Essential Functions
  • 1.3: The Limit of a Function
  • 1.4: Calculating Limits
  • 1.5: Continuity
  • 1.6: Limits Involving Infinity
  • 1: Concept Check
  • 1: True-False Quiz
  • 1: Review Exercises
  
  
• Chapter 2: Derivatives
  • 2.1: Derivatives and Rates of Change
  • 2.2: The Derivative as a Function
  • 2.3: Basic Differentiation Formulas
  • 2.4: The Product and Quotient Rules
  • 2.5: The Chain Rule
  • 2.6: Implicit Differentiation
  • 2.7: Related Rates
  • 2.8: Linear Approximations and Differentials
  • 2: Concept Check
  • 2: True-False Quiz
  • 2: Review Exercises
  
  
• Chapter 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
  • 3.1: Exponential Functions
  • 3.2: Inverse Functions and Logarithms
  • 3.3: Derivatives of Logarithmic and Exponential Functions
  • 3.4: Exponential Growth and Decay
  • 3.5: Inverse Trigonometric Functions
  • 3.6: Hyperbolic Functions
  • 3.7: Indeterminate Forms and l'Hospital's Rule
  • 3: Concept Check
  • 3: True-False Quiz
  • 3: Review Exercises
  
  
• Chapter 4: Applications of Differentiation
  • 4.1: Maximum and Minimum Values
  • 4.2: The Mean Value Theorem
  • 4.3: Derivatives and the Shapes of Graphs
  • 4.4: Curve Sketching
  • 4.5: Optimization Problems
  • 4.6: Newton's Method
  • 4.7: Antiderivatives
  • 4: Concept Check
  • 4: True-False Quiz
  • 4: Review Exercises
  
  
• Chapter 5: Integrals
  • 5.1: Areas and Distances
  • 5.2: The Definite Integral
  • 5.3: Evaluating Definite Integrals
  • 5.4: The Fundamental Theorem of Calculus
  • 5.5: The Substitution Rule
  • 5: Concept Check
  • 5: True-False Quiz
  • 5: Review Exercises
  
  
• Chapter 6: Techniques of Integration
  • 6.1: Integration by Parts
  • 6.2: Trigonometric Integrals and Substitutions
  • 6.3: Partial Fractions
  • 6.4: Integration with Tables and Computer Algebra Systems
  • 6.5: Approximate Integration
  • 6.6: Improper Integrals
  • 6: Concept Check
  • 6: True-False Quiz
  • 6: Review Exercises
  
  
• Chapter 7: Applications of Integration
  • 7.1: Areas Between Curves
  • 7.2: Volumes
  • 7.3: Volumes by Cylindrical Shells
  • 7.4: Arc Length
  • 7.5: Area of a Surface of Revolution
  • 7.6: Applications to Physics and Engineering
  • 7.7: Differential Equations
  • 7: Concept Check
  • 7: True-False Quiz
  • 7: Review Exercises
  
  
• Chapter 8: Series
  • 8.1: Sequences
  • 8.2: Series
  • 8.3: The Integral and Comparison Tests
  • 8.4: Other Convergence Tests
  • 8.5: Power Series
  • 8.6: Representing Functions as Power Series
  • 8.7: Taylor and Maclaurin Series
  • 8.8: Applications of Taylor Polynomials
  • 8: Concept Check
  • 8: True-False Quiz
  • 8: Review Exercises
  
  
• Chapter 9: Parametric Equations and Polar Coordinates
  • 9.1: Parametric Curves
  • 9.2: Calculus with Parametric Curves
  • 9.3: Polar Coordinates
  • 9.4: Areas and Lengths in Polar Coordinates
  • 9.5: Conic Sections in Polar Coordinates
  • 9: Concept Check
  • 9: True-False Quiz
  • 9: Review Exercises
  
  
• Chapter 10: Vectors and the Geometry of Space
  • 10.1: Three-Dimensional Coordinate Systems
  • 10.2: Vectors
  • 10.3: The Dot Product
  • 10.4: The Cross Product
  • 10.5: Equations of Lines and Planes
  • 10.6: Cylinders and Quadric Surfaces
  • 10.7: Vector Functions and Space Curves
  • 10.8: Arc Length and Curvature
  • 10.9: Motion in Space: Velocity and Acceleration
  • 10: Concept Check
  • 10: True-False Quiz
  • 10: Review Exercises
  
  
• Chapter 11: Partial Derivatives
  • 11.1: Functions of Several Variables
  • 11.2: Limits and Continuity
  • 11.3: Partial Derivatives
  • 11.4: Tangent Planes and Linear Approximations
  • 11.5: The Chain Rule
  • 11.6: Directional Derivatives and the Gradient Vector
  • 11.7: Maximum and Minimum Values
  • 11.8: Lagrange Multipliers
  • 11: Concept Check
  • 11: True-False Quiz
  • 11: Review Exercises
  
  
• Chapter 12: Multiple Integrals
  • 12.1: Double Integrals over Rectangles
  • 12.2: Double Integrals over General Regions
  • 12.3: Double Integrals in Polar Coordinates
  • 12.4: Applications of Double Integrals
  • 12.5: Triple Integrals
  • 12.6: Triple Integrals in Cylindrical Coordinates
  • 12.7: Triple Integrals in Spherical Coordinates
  • 12.8: Change of Variables in Multiple Integrals
  • 12: Concept Check
  • 12: True-False Quiz
  • 12: Review Exercises
  
  
• Chapter 13: Vector Calculus
  • 13.1: Vector Fields
  • 13.2: Line Integrals
  • 13.3: The Fundamental Theorem for Line Integrals
  • 13.4: Green's Theorem
  • 13.5: Curl and Divergence
  • 13.6: Parametric Surfaces and Their Areas
  • 13.7: Surface Integrals
  • 13.8: Stokes' Theorem
  • 13.9: The Divergence Theorem
  • 13: Concept Check
  • 13: True-False Quiz
  • 13: Review Exercises
  
  
• Chapter A: Appendixes
  • A.A: Trigonometry
  • A.B: Sigma Notation
  • A.C: The Logarithm Defined as an Integral
  • A.D: Proofs
  • A.E: Answers to Odd-Numbered Exercises