# Book:Roland E. Larson/Calculus/Eighth Edition

## Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: *Calculus (with Analytical Geometry) (8th Edition)*

Published $2005$, **Brooks Cole**

- ISBN 0-618-50298-X.

### Subject Matter

8th edition of 1978: Roland E. Larson and Robert P. Hostetler: *Calculus*

### 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