Calculus – Ron Larson, Robert Hostetler – 9th Edition

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or the ninth edition of CALCULUS, the authors analyzed the copious data they receive from their website, http: //www.CalcChat.com. The site offers to odd-numbered exercises in the text. The site currently has over 1 million hits per month. The authors analyzed these hits to see which exercise solutions were accessing most often. They revised and refined the exercise sets based on this analysis. The result is the only calculus book on that uses real data about its exercises to address needs.

The Larson Calculus program has a long history of innovation in the calculus market. It has been widely praised by a generation of and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and products for successful teaching and learning.

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  • Chapter 0: Preparation for Calculus
    0.1: Graphs and Models
    0.2: Linear Models and Rates of Change
    0.3: Functions and Their Graphs
    0.4: 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 Derivatives2
    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
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