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

## Roland E. Larson and Robert P. Hostetler: *Calculus (9th Edition)*

Published $2009$, **Brooks Cole**

- ISBN 0-547-16702-4.

### Subject Matter

9th edition of 1978: Roland E. Larson and Robert P. Hostetler: *Calculus*

### Contents

- 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

- Chapter 1: Limits and Their Properties
- 1.1: A Preview of Calculus
- 1.2: Finding Limits Graphicalls and Numerically
- 1.3: Evaluating Limits Analytically
- 1.4: Continuity and One-Sided Limits
- 1.5: Infinite Limits

- 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
- 2.6: Related Rates

- Chapter 3: Applications 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
- 3.4: Concavity and the Second Derivative Test
- 3.5: Limits at Infinity
- 3.6: A summary of Curve Sketching
- 3.7: Optimization Problems
- 3.8: Newton's Method
- 3.9: Differentials

- 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
- 4.5: Integration by Substitution
- 4.6: Numerical Integration

- 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: Exponential Functions: Differentiation and Integration
- 5.6: Inverse Trigonometric Functions: Differentiation
- 5.7: Inverse Trigonometric Functions: Integration
- 5.8: Hyperbolic Functions

- 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

- 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
- 7.4: Arc Length and Surfaces of Revolution
- 7.5: Work
- 7.6: Moments, Centers of Mass, and Centroids
- 7.7: Fluid Pressure and Fluid Force

- Chapter 8: Integration Techniques, L'Hopital's Rule, and Improper Integrals
- 8.1: Basic Integration Rules
- 8.2: Integration by Parts
- 8.3: Trigonometric Integrals
- 8.4: Trigonometric Substitution
- 8.5: Partial Fractions
- 8.6: Integration by Tables and Other Integration Techniques
- 8.7: Indeterminate Forms and L'Hopital's Rule
- 8.8: Improper Integrals

- Chapter 9: Infinite Series
- 9.1: Sequences
- 9.2: Series and Convergence
- 9.3: The Integral Test and p-Series
- 9.4: Comparisons of Series
- 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

- Chapter 10: Conics, Parametric Equations, and Polar Coordinates
- 10.1: Conics and Calculus
- 10.2: Plane Curves and Parametric Equations
- 10.3: Parametric Equations and Calculus
- 10.4: Polar Coordinates and Polar Graphs
- 10.5: Area and Arc Length in Polar Coordinates
- 10.6: Polar Equations of Conics and Kepler's Laws

- 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
- 11.6: Surfaces in Space
- 11.7: Cylindrical and Spherical Coordinates

- Chapter 12: Vector-Valued Functions
- 12.1: Vector-Valued Functions
- 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

- Chapter 13: Functions of Several Variables
- 13.1: Introduction to Functions of Several Variables
- 13.2: Limits and Continuity
- 13.3: Partial Derivatives
- 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
- 13.8: Extrema of Functions of Two Variables
- 13.9: Applications of Extrema of Functions of Two Variables
- 13.10: Lagrange Multipliers

- 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
- 14.5: Surface Area
- 14.6: Triple Integrals and Applications
- 14.7: Triple Integrals in Cylindrical and Spherical Coordinates
- 14.8: Change of Variables: Jacobians

- 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
- 15.5: Parametric Surfaces
- 15.6: Surface Integrals
- 15.7: Divergence Theorem
- 15.8: Stokes's Theorem

- Chapter 16: Additional Topics in Differential Equations
- 16.1: Exact First-Order Equations
- 16.2: Second-Order Homogeneous Linear Equations
- 16.3: Second-Order Nonhomogeneous Linear Equations
- 16.4: Series Solutions of Differential Equations

- Chapter QP: Quick Prep Topics
- QP.1 Definition and Representations of Functions
- QP.2 Working with Representations of Functions
- QP.3 Function Notation
- QP.4 Domain and Range of a Function
- QP.5 Solving Linear Equations
- QP.6 Linear Functions
- QP.7 Parabolas
- QP.8 Factoring Quadratic Equations and Finding x-intercepts of a Quadratic Function
- QP.9 Polynomials
- QP.10 More about Factoring Polynomials
- QP.11 Finding Roots
- QP.12 Dividing Polynomials
- QP.13 Rational Functions
- QP.14 Root Functions
- QP.15 Rationalizing the Numerator or Denominator
- QP.16 Exponential Functions
- QP.17 Logarithmic Functions
- QP.18 Trigonometric Functions and the Unit Circle
- QP.19 Graphs of Trigonometric Functions
- QP.20 Trigonometric Identities
- QP.21 Special Functions
- QP.22 Algebraic Combinations of Functions
- QP.23 Composition of Functions
- QP.24 Transformations of Functions
- QP.25 Inverse Functions