# Alignment: Calculus • James Stewart • Seventh Edition

• 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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