Efnisyfirlit

• 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

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