Alignment: Calculus • James Stewart • Seventh Edition

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Table of Contents

  • 1 Functions and Limits
    • 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 The Tangent and Velocity Problems
    • 1.5 The Limit of a Function
    • 1.6 Calculating Limits Using the Limit Laws
    • 1.7 The Precise Definition of a Limit
    • 1.8 Continuity
  • 2 Derivatives
    • 2.1 Derivatives and Rates of Change
    • 2.2 The Derivative as a Function
    • 2.3 Differentiation Formulas
    • 2.4 Derivatives of Trigonometric Functions
    • 2.5 The Chain Rule
    • 2.6 Implicit Differentiation
    • 2.7 Rates of Change in the Natural and Social Sciences
    • 2.8 Related Rates
    • 2.9 Linear Approximations and Differentials
  • 3 Applications of Differentiation
    • 3.1 Maximum and Minimum Values
    • 3.2 The Mean Value Theorem
    • 3.3 How Derivatives Affect the Shape of a Graph
    • 3.4 Limits at Infinity; Horizontal Asymptotes
    • 3.5 Summary of Curve Sketching
    • 3.6 Graphing with Calculus and Calculators
    • 3.7 Optimization Problems
    • 3.8 Newton’s Method
    • 3.9 Antiderivatives
  • 4 Integrals
    • 4.1 Areas and Distances
    • 4.2 The Definite Integral
    • 4.3 The Fundamental Theorem of Calculus
    • 4.4 Indefinite Integrals and the Net Change Theorem
    • 4.5 The Substitution Rule
  • 5 Applications of Integration
    • 5.1 Areas between Curves
    • 5.2 Volumes
    • 5.3 Volumes by Cylindrical Shells
    • 5.4 Work
    • 5.5 Average Value of a Function
  • 6 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
    • 6.1 Inverse Functions
    • 6.2 Exponential Functions and Their Derivatives
    • 6.3 Logarithmic Functions
    • 6.4 Derivatives of Logarithmic Functions
    • 6.5 Exponential Growth and Decay
    • 6.6 Inverse Trigonometric Functions
    • 6.7 Hyperbolic Functions
    • 6.8 Indeterminate Forms and L’Hospital’s Rule
  • 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 Integration Using Tables and Computer Algebra Systems
    • 7.7 Approximate Integration
    • 7.8 Improper Integrals
  • 8 Further Applications of Integration
    • 8.1 Arc Length
    • 8.2 Area of a Surface of Revolution
    • 8.3 Applications to Physics and Engineering
    • 8.4 Applications to Economics and Biology
    • 8.5 Probability
  • 9 Differential Equations
    • 9.1 Modeling with Differential Equations
    • 9.2 Direction Fields and Euler’s Method
    • 9.3 Separable Equations
    • 9.4 Models for Population Growth
    • 9.5 Linear Equations
    • 9.6 Predator-Prey Systems
  • 10 Parametric Equations and Polar Coordinates
    • 10.1 Curves Defined by Parametric Equations
    • 10.2 Calculus with Parametric Curves
    • 10.3 Polar Coordinates
    • 10.4 Areas and Lengths in Polar Coordinates
    • 10.5 Conic Sections
    • 10.6 Conic Sections in Polar Coordinates
  • 11 Infinite Sequences and Series
    • 11.1 Sequences
    • 11.2 Series
    • 11.3 The Integral Test and Estimates of Sums
    • 11.4 The Comparison Tests
    • 11.5 Alternating Series
    • 11.6 Absolute Convergence and the Ratio and Root Tests
    • 11.7 Strategy for Testing Series
    • 11.8 Power Series
    • 11.9 Representations of Functions as Power Series
    • 11.10 Taylor and Maclaurin Series
    • 11.11 Applications of Taylor Polynomials
  • 12 Vectors and the Geometry of Space
    • 12.1 Three-Dimensional Coordinate Systems
    • 12.2 Vectors
    • 12.3 The Dot Product
    • 12.4 The Cross Product
    • 12.5 Equations of Lines and Planes
    • 12.6 Cylinders and Quadric Surfaces
  • 13 Vector Functions
    • 13.1 Vector Functions and Space Curves
    • 13.2 Derivatives and Integrals of Vector Functions
    • 13.3 Arc Length and Curvature
    • 13.4 Motion in Space: Velocity and Acceleration
  • 14 Partial Derivatives
    • 14.1 Functions of Several Variables
    • 14.2 Limits and Continuity
    • 14.3 Partial Derivatives
    • 14.4 Tangent Planes and Linear Approximations
    • 14.5 The Chain Rule
    • 14.6 Directional Derivatives and the Gradient Vector
    • 14.7 Maximum and Minimum Values
    • 14.8 Lagrange Multipliers
  • 15 Multiple Integrals
    • 15.1 Double Integrals over Rectangles
    • 15.2 Iterated Integrals
    • 15.3 Double Integrals over General Regions
    • 15.4 Double Integrals in Polar Coordinates
    • 15.5 Applications of Double Integrals
    • 15.6 Surface Area
    • 15.7 Triple Integrals
    • 15.8 Triple Integrals in Cylindrical Coordinates
    • 15.9 Triple Integrals in Spherical Coordinates
    • 15.10 Change of Variables in Multiple Integrals
  • 16 Vector Calculus
    • 16.1 Vector Fields
    • 16.2 Line Integrals
    • 16.3 The Fundamental Theorem for Line Integrals
    • 16.4 Green’s Theorem
    • 16.5 Curl and Divergence
    • 16.6 Parametric Surfaces and Their Areas
    • 16.7 Surface Integrals
    • 16.8 Stokes’ Theorem
    • 16.9 The Divergence Theorem
    • 16.10 Summary
  • 17 Second-Order Differential Equations
    • 17.1 Second-Order Linear Equations
    • 17.2 Nonhomogeneous Linear Equations
    • 17.3 Applications of Second-Order Differential Equations
    • 17.4 Series Solutions

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