Calculus: Concepts and Contexts 5th edition

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• Chapter DT: Diagnostic Tests
  • DT.A: Algebra
  • DT.B: Analytic Geometry
  • DT.C: Functions
  • DT.D: Trigonometry
  
  
• 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 1: Functions and Models
  • 1.1: Four Ways to Represent a Function
  • 1.2: Mathematical Models: A Catalog of Essential Functions
  • 1.3: New Functions from Old Functions
  • 1.4: Exponential Functions
  • 1.5: Inverse Functions and Logarithms
  • 1.6: Parametric Curves
  • 1: Concepts and Vocabulary
  • 1: True-False Quiz
  • 1: Review Exercises
  • 1: Principles of Problem Solving
  • 1: Extra Problems
  • 1: Just-in-Time Questions
  
  
• Chapter 2: Limits and Derivatives
  • 2.1: The Tangent and Velocity Problems
  • 2.2: The Limit of a Function
  • 2.3: Calculating Limits Using the Limit Laws
  • 2.4: Continuity
  • 2.5: Limits Involving Infinity
  • 2.6: Derivatives and Rates of Change
  • 2.7: The Derivative as a Function
  • 2: Concepts and Vocabulary
  • 2: True-False Quiz
  • 2: Review Exercises
  • 2: Principles of Problem Solving
  • 2: Extra Problems
  • 2: Just-in-Time Questions
  
  
• Chapter 3: Differentiation Rules
  • 3.1: Derivatives of Polynomials and Exponential Functions
  • 3.2: The Product and Quotient Rules
  • 3.3: Derivatives of Trigonometric Functions
  • 3.4: The Chain Rule
  • 3.5: Implicit Differentiation
  • 3.6: Inverse Trigonometric Functions and Their Derivatives
  • 3.7: Derivatives of Logarithmic Functions
  • 3.8: Rates of Change in the Natural and Social Sciences
  • 3.9: Linear Approximations and Differentials
  • 3: Concepts and Vocabulary
  • 3: True-False Quiz
  • 3: Review Exercises
  • 3: Principles of Problem Solving
  • 3: Extra Problems
  • 3: Just-in-Time Questions
  
  
• Chapter 4: Applications of Differentiation
  • 4.1: Related Rates
  • 4.2: Maximum and Minimum Values
  • 4.3: Derivatives and the Shapes of Curves
  • 4.4: Graphing with Calculus and Calculators
  • 4.5: Indeterminate Forms and l'Hospital's Rule
  • 4.6: Optimization Problems
  • 4.7: Newton's Method
  • 4.8: Antiderivatives
  • 4: Concepts and Vocabulary
  • 4: True-False Quiz
  • 4: Review Exercises
  • 4: Principles of Problem Solving
  • 4: Extra Problems
  • 4: Just-in-Time Questions
  
  
• 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
  • 5.6: Integration by Parts
  • 5.7: Additional Techniques of Integration
  • 5.8: Integration Using Tables and Computer Algebra Systems
  • 5.9: Approximate Integration
  • 5.10: Improper Integrals
  • 5: Concepts and Vocabulary
  • 5: True-False Quiz
  • 5: Review Exercises
  • 5: Principles of Problem Solving
  • 5: Extra Problems
  • 5: Just-in-Time Questions
  
  
• Chapter 6: Applications of Integration
  • 6.1: More about Areas
  • 6.2: Volumes
  • 6.3: Volumes by Cylindrical Shells
  • 6.4: Arc Length
  • 6.5: Average Value of a Function
  • 6.6: Applications to Physics and Engineering
  • 6.7: Applications to Economics and Biology
  • 6.8: Probability
  • 6: Concepts and Vocabulary
  • 6: True-False Quiz
  • 6: Review Exercises
  • 6: Principles of Problem Solving
  • 6: Extra Problems
  • 6: Just-in-Time Questions
  
  
• Chapter 7: Differential Equations
  • 7.1: Modeling with Differential Equations
  • 7.2: Slope Fields and Euler's Method
  • 7.3: Separable Equations
  • 7.4: Exponential Growth and Decay
  • 7.5: The Logistic Equation
  • 7.6: Predator-Prey Systems
  • 7: Concepts and Vocabulary
  • 7: True-False Quiz
  • 7: Review Exercises
  • 7: Principles of Problem Solving
  • 7: Extra Problems
  • 7: Just-in-Time Questions
  
  
• Chapter 8: Infinite Sequences and Series
  • 8.1: Sequences
  • 8.2: Series
  • 8.3: The Integral and Comparison Tests; Estimating Sums
  • 8.4: Other Convergence Tests
  • 8.5: Power Series
  • 8.6: Representations of Functions as Power Series
  • 8.7: Taylor and Maclaurin Series
  • 8.8: Applications of Taylor Polynomials
  • 8: Concepts and Vocabulary
  • 8: True-False Quiz
  • 8: Review Exercises
  • 8: Principles of Problem Solving
  • 8: Extra Problems
  • 8: Just-in-Time Questions
  
  
• Chapter 9: Vectors and the Geometry of Space
  • 9.1: Three-Dimensional Coordinate Systems
  • 9.2: Vectors
  • 9.3: The Dot Product
  • 9.4: The Cross Product
  • 9.5: Equations of Lines and Planes
  • 9.6: Functions and Surfaces
  • 9.7: Cylindrical and Spherical Coordinates
  • 9: Concepts and Vocabulary
  • 9: True-False Quiz
  • 9: Review Exercises
  • 9: Principles of Problem Solving
  • 9: Extra Problems
  • 9: Just-in-Time Questions
  
  
• Chapter 10: Vector Functions
  • 10.1: Vector Functions and Space Curves
  • 10.2: Derivatives and Integrals of Vector Functions
  • 10.3: Arc Length and Curvature
  • 10.4: Motion in Space: Velocity and Acceleration
  • 10.5: Parametric Surfaces
  • 10: Concepts and Vocabulary
  • 10: True-False Quiz
  • 10: Review Exercises
  • 10: Principles of Problem Solving
  • 10: Extra Problems
  • 10: Just-in-Time Questions
  
  
• 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: Concepts and Vocabulary
  • 11: True-False Quiz
  • 11: Review Exercises
  • 11: Principles of Problem Solving
  • 11: Extra Problems
  • 11: Just-in-Time Questions
  
  
• Chapter 12: Multiple Integrals
  • 12.1: Double Integrals over Rectangles
  • 12.2: Iterated Integrals
  • 12.3: Double Integrals over General Regions
  • 12.4: Double Integrals in Polar Coordinates
  • 12.5: Applications of Double Integrals
  • 12.6: Surface Area
  • 12.7: Triple Integrals
  • 12.8: Triple Integrals in Cylindrical and Spherical Coordinates
  • 12.9: Change of Variables in Multiple Integrals
  • 12: Concepts and Vocabulary
  • 12: True-False Quiz
  • 12: Review Exercises
  • 12: Principles of Problem Solving
  • 12: Extra Problems
  • 12: Just-in-Time Questions
  
  
• 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: Surface Integrals
  • 13.7: Stokes' Theorem
  • 13.8: The Divergence Theorem
  • 13.9: Summary
  • 13: Concepts and Vocabulary
  • 13: True-False Quiz
  • 13: Review Exercises
  • 13: Principles of Problem Solving
  • 13: Extra Problems
  • 13: Just-in-Time Questions
  
  
• Chapter A: Appendixes
  • A.A: Intervals, Inequalities, and Absolute Values
  • A.B: Coordinate Geometry
  • A.C: Trigonometry
  • A.D: Precise Definitions of Limits
  • A.E: A Few Proofs
  • A.F: Sigma Notation
  • A.G: Integration of Rational Functions by Partial Fractions
  • A.H: Polar Coordinates
  • A.I: Complex Numbers