Calculus 1st edition

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• Chapter 1: Functions and Graphs
  • 1.1: Review of Functions
  • 1.2: Basic Classes of Functions
  • 1.3: Trigonometric Functions
  • 1.4: Inverse Functions
  • 1.5: Exponential and Logarithmic Functions
  • 1: Review Exercises
  
  
• Chapter 2: Limits
  • 2.1: A Preview of Calculus
  • 2.2: The Limit of a Function
  • 2.3: The Limit Laws
  • 2.4: Continuity
  • 2.5: The Precise Definition of a Limit
  • 2: Review Exercises
  
  
• Chapter 3: Derivatives
  • 3.1: Defining the Derivative
  • 3.2: The Derivative as a Function
  • 3.3: Differentiation Rules
  • 3.4: Derivatives as Rates of Change
  • 3.5: Derivatives of Trigonometric Functions
  • 3.6: The Chain Rule
  • 3.7: Derivatives of Inverse Functions
  • 3.8: Implicit Differentiation
  • 3.9: Derivatives of Exponential and Logarithmic Functions
  • 3: Review Exercises
  
  
• Chapter 4: Applications of Derivatives
  • 4.1: Related Rates
  • 4.2: Linear Approximations and Differentials
  • 4.3: Maxima and Minima
  • 4.4: The Mean Value Theorem
  • 4.5: Derivatives and the Shape of a Graph
  • 4.6: Limits at Infinity and Asymptotes
  • 4.7: Applied Optimization Problems
  • 4.8: L'Hôpital's Rule
  • 4.9: Newton's Method
  • 4.10: Antiderivatives
  • 4: Review Exercises
  
  
• Chapter 5: Integration
  • 5.1: Approximating Areas
  • 5.2: The Definite Integral
  • 5.3: The Fundamental Theorem of Calculus
  • 5.4: Integration Formulas and the Net Change Theorem
  • 5.5: Substitution
  • 5.6: Integrals Involving Exponential and Logarithmic Functions
  • 5.7: Integrals Resulting in Inverse Trigonometric Functions
  • 5: Review Exercises
  
  
• Chapter 6: Applications of Integrations
  • 6.1: Areas between Curves
  • 6.2: Determining Volumes by Slicing
  • 6.3: Volumes of Revolution: Cylindrical Shells
  • 6.4: Arc Length of a Curve and Surface Area
  • 6.5: Physical Applications
  • 6.6: Moments and Centers of Mass
  • 6.7: Integrals, Exponential Functions, and Logarithms
  • 6.8: Exponential Growth and Decay
  • 6.9: Calculus of the Hyperbolic Functions
  • 6: Review Exercises
  
  
• Chapter 7: Techniques of Integration
  • 7.1: Integration by Parts
  • 7.2: Trigonometric Integrals
  • 7.3: Trigonometric Substitution
  • 7.4: Partial Fractions
  • 7.5: Other Strategies for Integration
  • 7.6: Numerical Integration
  • 7.7: Improper Integrals
  • 7: Review Exercises
  
  
• Chapter 8: Introduction to Differential Equations
  • 8.1: Basics of Differential Equations
  • 8.2: Direction Fields and Numerical Methods
  • 8.3: Separable Equations
  • 8.4: The Logistic Equation
  • 8.5: First-order Linear Equations
  • 8: Review Exercises
  
  
• Chapter 9: Sequences and Series
  • 9.1: Sequences
  • 9.2: Infinite Series
  • 9.3: The Divergence and Integral Tests
  • 9.4: Comparison Tests
  • 9.5: Alternating Series
  • 9.6: Ratio and Root Tests
  • 9: Review Exercises
  
  
• Chapter 10: Power Series
  • 10.1: Power Series and Functions
  • 10.2: Properties of Power Series
  • 10.3: Taylor and Maclaurin Series
  • 10.4: Working with Taylor Series
  • 10: Review Exercises
  
  
• Chapter 11: Parametric Equations and Polar Coordinates
  • 11.1: Parametric Equations
  • 11.2: Calculus of Parametric Curves
  • 11.3: Polar Coordinates
  • 11.4: Area and Arc Length in Polar Coordinates
  • 11.5: Conic Sections
  • 11: Review Exercises
  
  
• Chapter 12: Vectors in Space
  • 12.1: Vectors in the Plane
  • 12.2: Vectors in Three Dimensions
  • 12.3: The Dot Product
  • 12.4: The Cross Product
  • 12.5: Equations of Lines and Planes in Space
  • 12.6: Quadric Surfaces
  • 12.7: Cylindrical and Spherical Coordinates
  • 12: Review Exercises
  
  
• Chapter 13: Vector-Valued Functions
  • 13.1: Vector-Valued Functions and Space Curves
  • 13.2: Calculus of Vector-Valued Functions
  • 13.3: Arc Length and Curvature
  • 13.4: Motion in Space
  • 13: Review Exercises
  
  
• Chapter 14: Differentiation of Functions of Several Variables
  • 14.1: Functions of Several Variables
  • 14.2: Limits and Continuity
  • 14.3: Partial Derivatives
  • 14.4: Tangent Planes and Linear Approximations
  • 14.5: The Chain Rule
  • 14.6: Directional Derivatives and the Gradient
  • 14.7: Maxima/Minima Problems
  • 14.8: Lagrange Multipliers
  • 14: Review Exercises
  
  
• Chapter 15: Multiple Integration
  • 15.1: Double Integrals over Rectangular Regions
  • 15.2: Double Integrals over General Regions
  • 15.3: Double Integrals in Polar Coordinates
  • 15.4: Triple Integrals
  • 15.5: Triple Integrals in Cylindrical and Spherical Coordinates
  • 15.6: Calculating Centers of Mass and Moments of Inertia
  • 15.7: Change of Variables in Multiple Integrals
  • 15: Review Exercises
  
  
• Chapter 16: Vector Calculus
  • 16.1: Vector Fields
  • 16.2: Line Integrals
  • 16.3: Conservative Vector Fields
  • 16.4: Green's Theorem
  • 16.5: Divergence and Curl
  • 16.6: Surface Integrals
  • 16.7: Stokes' Theorem
  • 16.8: The Divergence Theorem
  • 16: Review Exercises
  
  
• Chapter 17: Second-Order Differential Equations
  • 17.1: Second-Order Linear Equations
  • 17.2: Nonhomogeneous Linear Equations
  • 17.3: Applications
  • 17.4: Series Solutions of Differential Equations
  • 17: Review Exercises