Book:Roland E. Larson/Calculus/Ninth Edition

Subject Matter

 * Calculus

9th edition of

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