Book:Roland E. Larson/Calculus/Eighth Edition

Subject Matter

 * Calculus

8th edition of

Contents

 * A Word from the Authors
 * Integrated Learning Systems for Calculus
 * Features


 * Chapter P: Preparation for Calculus
 * P.1 Graphs and Models
 * P.2 Linear Models and Rates of Change
 * P.3 Functions and Their Graphs
 * P.4 Fitting Models to Data
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 1: Limits and Their Properties
 * 1.1 A Preview of Calculus
 * 1.2 Finding Limits Graphically and Numerically
 * 1.3 Evaluating Limits Analytically
 * 1.4 Continuity and One-Sided Limits
 * 1.5 Infinite Limits
 * Section Project: Graphs and Limits of Trigonometric Functions
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 2: Differentiation
 * 2.1 The Derivative and the Tangent Line Problem
 * 2.2 Basic Differentiation Rules and Rates of Change
 * 2.3 Product and Quotient Rules and Higher-Order Derivatives
 * 2.4 The Chain Rule
 * 2.5 Implicit Differentiation
 * Section Project: Optical Illusions
 * 2.6 Related Rates
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 3: Application of Differentiation
 * 3.1 Extrema on an Interval
 * 3.2 Rolle's Theorem and the Mean Value Theorem
 * 3.3 Increasing and Decreasing Functions and the First Derivative Test
 * Section Project: Rainbows
 * 3.4 Concavity and the Second Derivative Test
 * 3.5 Limits at Infinity
 * 3.6 A Summary of Curve Sketching
 * 3.7 Optimization Problems
 * Section Project: Connecticut River
 * 3.8 Newton's Method
 * 3.9 Differentials
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 4: Integration
 * 4.1 Antiderivatives and Indefinite Integration
 * 4.2 Area
 * 4.3 Riemann Sums and Definite Integrals
 * 4.4 The Fundamental Theorem of Calculus
 * Section Project: Demonstrating the Fundamental Theorem
 * 4.5 Integration by Substitution
 * 4.6 Numerical Integration
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
 * 5.1 The Natural Logarithmic Function: Differentiation
 * 5.2 The Natural Logarithmic Function: Integration
 * 5.3 Inverse Functions
 * 5.4 Exponential Functions: Differentiation and Integration
 * 5.5 Bases Other Than $e$ and Applications
 * Section Project: Using Graphing Utilities to Estimate Slope
 * 5.6 Inverse Trigonometric Functions: Differentiation
 * 5.7 Inverse Trigonometric Functions: Integration
 * 5.8 Hyperbolic Functions
 * Section Project: St. Louis Arch
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 6: Differential Equations
 * 6.1 Slope Fields and Euler's Method
 * 6.2 Differential Equations: Growth and Decay
 * 6.3 Separation of Variables and the Logistic Equation
 * 6.4 First-Order Linear Differential Equations
 * Section Project: Weight Loss
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 7: Applications of Integration
 * 7.1 Area of a Region Between Two Curves
 * 7.2 Volume: The Disk Method
 * 7.3 Volume: The Shell Method
 * Section Project: Saturn
 * 7.4 Arc Length and Surfaces of Revolution
 * 7.5 Work
 * Section Project: Tidal Energy
 * 7.6 Moments, Centers of Mass, and Centroids
 * 7.7 Fluid Pressure and Fluid Force
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 8: Integration Techniques, L'Hôpital's Rule, and Improper Integrals
 * 8.1 Basic Integration Rules
 * 8.2 Integration by Parts
 * 8.3 Trigonometric Integrals
 * Section Project: Power Lines
 * 8.4 Trigonometric Substitution
 * 8.5 Partial Fractions
 * 8.6 Integration by Tables and Other Integration Techniques
 * 8.7 Indeterminate Forms and L'Hôpital's Rule
 * 8.8 Improper Integrals
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 9: Infinite Series
 * 9.1 Sequences
 * 9.2 Series and Convergence
 * Section Project: Cantor's Disappearing Table
 * 9.3 The Integral Test and $p$-Series
 * Section Project: The Harmonic Series
 * 9.4 Comparisons of Series
 * Section Project: Solera Method
 * 9.5 Alternating Series
 * 9.6 The Ratio and Root Tests
 * 9.7 Taylor Polynomials and Approximations
 * 9.8 Power Series
 * 9.9 Representation of Functions by Power Series
 * 9.10 Taylor and Maclaurin Series
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 10: Conics, Parametric Equations, and Polar Coordinates
 * 10.1 Conics and Calculus
 * 10.2 Plane Curves and Parametric Equations
 * Section Project: Cycloids
 * 10.3 Parametric Equations and Calculus
 * 10.4 Polar Coordinates and Polar Graphs
 * Section Project: Anamorphic Art
 * 10.5 Areaa and Arc Length in Polar Coordinates
 * 10.6 Polar Equations of Conics and Kepler's Laws
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 11: Vectors and the Geometry of Space
 * 11.1 Vectors in the Plane
 * 11.2 Space Coordinates and Vectors in Space
 * 11.3 The Dot Product of Two Vectors
 * 11.4 The Cross Product of Two Vectors in Space
 * 11.5 Lines and Planes in Space
 * Section Project: Distances in Space
 * 11.6 Surfaces in Space
 * 11.7 Cylindrical and Spherical Coordinates
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 12: Vector-Valued Functions
 * 12.1 Vector-Valued Functions
 * Section Project: Witch of Agnesi
 * 12.2 Differentiation and Integration of Vector-Valued Functions
 * 12.3 Velocity and Acceleration
 * 12.4 Tangent Vectors and Normal Vectors
 * 12.5 Arc Length and Curvature
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 13: Functions of Several Variables
 * 13.1 Introduction to Functions of Several Variables
 * 13.2 Limits and Continuity
 * 13.3 Partial Derivatives
 * Section Project: Moiré Fringes
 * 13.4 Differentials
 * 13.5 Chain Rules for Functions of Several Variables
 * 13.6 Directional Derivatives and Gradients
 * 13.7 Tangent Planes and Normal Lines
 * Section Project: Wildflowers
 * 13.8 Extrema of Functions of Two Variables
 * 13.9 Applications of Extrema of Functions of Two Variables
 * Section Project: Building a Pipeline
 * 13.10 Lagrange Multipliers
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 14: Multiple Integration
 * 14.1 Iterated Integrals and Area in the Plane
 * 14.2 Double Integrals and Volume
 * 14.3 Change of Variables: Polar Coordinates
 * 14.4 Center of Mass and Moments of Inertia
 * Section Project: Center of Pressure on a Sail
 * 14.5 Surface Area
 * Section Project: Capillary Action
 * 14.6 Triple Integrals and Applications
 * 14.7 Triple Integrals in Cylindrical and Spherical Coordinates
 * Section Project: Wrinkled and Bumpy Spheres
 * 14.8 Change of Variables: Jacobians
 * Review Exercises
 * P.S. Problem Solving


 * Chapter 15: Vector Analysis
 * 15.1 Vector Fields
 * 15.2 Line Integrals
 * 15.3 Conservative Vector Fields and Independence of Path
 * 15.4 Green's Theorem
 * Section Project: Hyperbolic and Trigonometric Functions
 * 15.5 Parametric Surfaces
 * 15.6 Surface Integrals
 * Section Project: Hyperboloid of One Sheet
 * 15.7 Divergence Theorem
 * 15.8 Stokes's Theorem
 * Review Exercises
 * Section Project: The Planimeter
 * P.S. Problem Solving