# Alignment: Calculus • James Stewart • Single Variable Calculus: Early Transcendentals • Eighth Edition

### Table of Contents

• 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
• 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 The Precise Definition of a Limit
• 2.5 Continuity
• 2.6 Limits at Infinity; Horizontal Asymptotes
• 2.7 Derivatives and Rates of Change
• 2.8 The Derivative as a Function
• 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 Derivatives of Logarithmic Functions
• 3.7 Rates of Change in the Natural and Social Sciences
• 3.8 Exponential Growth and Decay
• 3.9 Related Rates
• 3.10 Linear Approximations and Differentials
• 3.11 Hyperbolic Functions
• 4 Applications of Differentiation
• 4.1 Maximum and Minimum Values
• 4.2 The Mean Value Theorem
• 4.3 How Derivatives Affect the Shape of a Graph
• 4.4 Indeterminate Forms and l’Hospital’s Rule
• 4.5 Summary of Curve Sketching
• 4.6 Graphing with Calculus and Calculators
• 4.7 Optimization Problems
• 4.8 Newton’s Method
• 4.9 Antiderivatives
• 5 Integrals
• 5.1 Areas and Distances
• 5.2 The Definite Integral
• 5.3 The Fundamental Theorem of Calculus
• 5.4 Indefinite Integrals and the Net Change Theorem
• 5.5 The Substitution Rule
• 6 Applications of Integration
• 6.1 Areas between Curves
• 6.2 Volumes
• 6.3 Volumes by Cylindrical Shells
• 6.4 Work
• 6.5 Average Value of a Function
• 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
• Appendixes
• A Numbers, Inequalities, and Absolute Values
• B Coordinate Geometry and Lines
• C Graphs of Second-Degree Equations
• D Trigonometry
• E Sigma Notation
• F Proofs of Theorems
• G The Logarithm Defined as an Integral
• H Complex Numbers
• I Answers to Odd-Numbered Exercises

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