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• Cover Page
• Title Page
• Dedication
• Copyright
• Preface
• Acknowledgments
• Chapter 1: Foundation for Calculus: Functions and Limits
• 1.1 Functions and change
• 1.2 Exponential functions
• 1.3 New functions from old
• 1.4 Logarithmic functions
• 1.5 Trigonometric functions
• 1.6 Powers, Polynomials, and Rational functions
• 1.7 Introduction to limits and continuity
• 1.8 Extending the idea of a limit
• 1.9 Further limit calculations using Algebra
• 1.10 Optional preview of the formal definition of a limit
• Chapter 2: Key Concept: The Derivative
• 2.1 How do we measure speed?
• 2.2 The Derivative at a point
• 2.3 The Derivative function
• 2.4 Interpretations of the derivative
• 2.5 The second derivative
• 2.6 Differentiability
• Chapter 3: Short-Cuts to Differentiation
• 3.1 Powers and Polynomials
• 3.2 The Exponential Function
• 3.3 The Product and Quotient Rules
• 3.4 The Chain Rule
• 3.5 The Trigonometric functions
• 3.6 The chain rule and inverse functions
• 3.7 Implicit functions
• 3.8 Hyperbolic functions
• 3.9 Linear approximation and the derivative
• 3.10 Theorems about differentiable functions
• Chapter 4 Using the Derivative
• 4.1 Using first and second derivatives
• 4.2 Optimization
• 4.3 Optimization and Modeling
• 4.4 Families of functions and Modeling
• 4.5 Applications to marginality
• 4.6 Rates and related rates
• 4.7 L’Hopital’s rule, growth, and dominance
• 4.8 Parametric Equations
• Chapter 5: Key Concept: The Definite Integral
• 5.1 How do we measure distance traveled?
• 5.2 The definite integral
• 5.3 The fundamental theorem and interpretations
• 5.4 Theorems about definite integrals
• Chapter 6: Constructing Antiderivatives
• 6.1 Antiderivatives graphically and numerically
• 6.2 Constructing antiderivatives analytically
• 6.3 Differential equations and motion
• 6.4 Second fundamental theorem of calculus
• Chapter 7: Integration
• 7.1 Integration by substitution
• 7.2 Integration by parts
• 7.3 Tables of integrals
• 7.4 Algebraic identities and trigonometric substitutions
• 7.5 Numerical methods for definite integrals
• 7.6 Improper integrals
• 7.7 Comparison of improper integrals
• Chapter 8: Using the Definite Integral
• 8.1 Areas and volumes
• 8.2 Applications to geometry
• 8.3 Area and ARC length in polar coordinates
• 8.4 Density and center of mass
• 8.5 Applications to physics
• 8.6 Applications to economics
• 8.7 Distribution Functions
• 8.8 Probability, mean, and median
• Chapter 9: Sequences and Series
• 9.1 Sequences
• 9.2 Geometric series
• 9.3 Convergence of series
• 9.4 Tests for convergence
• 9.5 Power series and interval of convergence
• Chapter 10: Approximating Functions using Series
• 10.1 Taylor polynomials
• 10.2 Taylor series
• 10.3 Finding and using taylor series
• 10.4 The error in taylor polynomial approximations
• 10.5 Fourier Series
• Chapter 11: Differential Equations
• 11.1 What is a differential equation?
• 11.2 Slope fields
• 11.3 Euler’s method
• 11.4 Separation of variables
• 11.5 Growth and decay
• 11.6 Applications and modeling
• 11.7 The Logistic model
• 11.8 Systems of differential equations
• 11.9 Analyzing the phase plane
• 11.10 Second-order differential equations: Oscillations
• 11.11 Linear second-order differential equations
• Chapter 12: Functions of Several Variables
• 12.1 Functions of two variables
• 12.2 Graphs and surfaces
• 12.3 Contour diagrams
• 12.4 Linear functions
• 12.5 Functions of three variables
• 12.6 Limits and continuity
• Chapter 13: A Fundamental Tool: Vectors
• 13.1 Displacement vectors
• 13.2 Vectors in general
• 13.3 The Dot product
• 13.4 The Cross product
• Chapter 14: Differentiating Functions of Several Variables
• 14.1 The Partial derivative
• 14.2 Computing partial derivatives algebraically
• 14.3 Local linearity and the differential
• 14.4 Gradients and directional derivatives in the plane
• 14.5 Gradients and directional derivatives in space
• 14.6 The Chain Rule
• 14.7 Second-order partial derivatives
• 14.8 Differentiability
• Chapter 15: Optimization: Local and Global Extrema
• 15.1 Critical Points: Local extrema and saddle points
• 15.2 Optimization
• 15.3 Constrained optimization: Lagrange multipliers
• Chapter 16: Integrating Functions of Several Variables
• 16.1 The Definite integral of a function of two variables
• 16.2 Iterated integrals
• 16.3 Triple integrals
• 16.4 Double integrals in polar coordinates
• 16.5 Integrals in cylindrical and spherical coordinates
• 16.6 Applications of integration to probability
• Chapter 17: Parameterization and Vector Fields
• 17.1 Parameterized curves
• 17.2 Motion, velocity, and acceleration
• 17.3 Vector fields
• 17.4 The Flow of a vector field
• Chapter 18: Line Integrals
• 18.1 The Idea of a line integral
• 18.2 Computing line integrals over parameterized curves
• 18.3 Gradient fields and path-independent fields
• 18.4 Path-dependent vector fields and green’s theorem
• Chapter 19: Flux Integrals and Divergence
• 19.1 The Idea of a flux integral
• 19.2 Flux integrals for graphs, cylinders, and spheres
• 19.3 The Divergence of a vector field
• 19.4 The Divergence theorem
• Chapter 20: The Curl and Stokes’ Theorem
• 20.1 The Curl of a vector field
• 20.2 Stokes’ theorem
• 20.3 The Three fundamental theorems
• Chapter 21: Parameters, Coordinates, and Integrals
• 21.1 Coordinates and parameterized surfaces
• 21.2 Change of coordinates in a multiple integral
• 21.3 Flux integrals over parameterized surfaces
• Appendices
• A Roots, Accuracy, and Bounds
• B Complex Numbers
• C Newton’s Method
• D Vectors in the Plane
• Ready Reference
• Index
• EULA