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Calculus: Early Transcendental Functions

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Efnisyfirlit

  • Cover
  • Title
  • Copyright
  • Dedication
  • About the Authors
  • Brief Table of Contents
  • Table of Contents
  • Seeing the Beauty and Power of Mathematics
  • Applications Index
  • Chapter 0: Preliminaries
    • 0.1 Polynomials and Rational Functions
      • The Real Number System and Inequalities
      • Equations of Lines
      • Functions
    • 0.2 Graphing Calculators and Computer Algebra Systems
    • 0.3 Inverse Functions
    • 0.4 Trigonometric and Inverse Trigonometric Functions
      • The Inverse Trigonometric Functions
    • 0.5 Exponential and Logarithmic Functions
      • Hyperbolic Functions
      • Fitting a Curve to Data
    • 0.6 Transformations of Functions
  • Chapter 1: Limits and Continuity
    • 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
    • 1.2 The Concept of Limit
    • 1.3 Computation of Limits
    • 1.4 Continuity and its Consequences
      • The Method of Bisections
    • 1.5 Limits Involving Infinity; Asymptotes
      • Limits at Infinity
    • 1.6 Formal Definition of the Limit
      • Exploring the Definition of Limit Graphically
      • Limits Involving Infinity
    • 1.7 Limits and Loss-of-Significance Errors
      • Computer Representation of Real Numbers
  • Chapter 2: Differentiation
    • 2.1 Tangent Lines and Velocity
      • The General Case
      • Velocity
    • 2.2 The Derivative
      • Alternative Derivative Notations
      • Numerical Differentiation
    • 2.3 Computation of Derivatives: The Power Rule
      • The Power Rule
      • General Derivative Rules
      • Higher Order Derivatives
      • Acceleration
    • 2.4 The Product and Quotient Rules
      • Product Rule
      • Quotient Rule
      • Applications
    • 2.5 The Chain Rule
      • Concept Mapping
    • 2.6 Derivatives of Trigonometric Functions
      • Applications
    • 2.7 Derivatives of Exponential and Logarithmic Functions
      • Derivatives of the Exponential Functions
      • Derivative of the Natural Logarithm
      • Logarithmic Differentiation
    • 2.8 Implicit Differentiation and Inverse Trigonometric Functions
      • Derivatives of the Inverse Trigonometric Functions
    • 2.9 The Hyperbolic Functions
      • The Inverse Hyperbolic Functions
    • 2.10 The Mean Value Theorem
  • Chapter 3: Applications of Differentiation
    • 3.1 Linear Approximations and Newton’s Method
      • Linear Approximations
      • Newton’s Method
    • 3.2 Indeterminate Forms and L’Hôpital’s Rule
      • Other Indeterminate Forms
    • 3.3 Maximum and Minimum Values
    • 3.4 Increasing and Decreasing Functions
      • What You See May Not Be What You Get
    • 3.5 Concavity and the Second Derivative Test
      • Concept Mapping
    • 3.6 Overview of Curve Sketching
    • 3.7 Optimization
    • 3.8 Related Rates
    • 3.9 Rates of Change in Economics and the Sciences
  • Chapter 4: Integration
    • 4.1 Antiderivatives
    • 4.2 Sums and Sigma Notation
      • Principle of Mathematical Induction
    • 4.3 Area
    • 4.4 The Definite Integral
      • Average Value of a Function
    • 4.5 The Fundamental Theorem of Calculus
    • 4.6 Integration by Substitution
      • Substitution in Definite Integrals
    • 4.7 Numerical Integration
      • Simpson’s Rule
      • Error Bounds for Numerical Integration
    • 4.8 The Natural Logarithm as an Integral
      • The Exponential Function as the Inverse of the Natural Logarithm
  • Chapter 5: Applications of the Definite Integral
    • 5.1 Area Between Curves
    • 5.2 Volume: Slicing, Disks and Washers
      • Volumes by Slicing
      • The Method of Disks
      • The Method of Washers
    • 5.3 Volumes by Cylindrical Shells
    • 5.4 Arc Length and Surface Area
      • Arc Length
      • Surface Area
    • 5.5 Projectile Motion
    • 5.6 Applications of Integration to Physics and Engineering
    • 5.7 Probability
  • Chapter 6: Integration Techniques
    • 6.1 Review of Formulas and Techniques
      • Concept Mapping
    • 6.2 Integration by Parts
    • 6.3 Trigonometric Techniques of Integration
      • Integrals Involving Powers of Trigonometric Functions
      • Trigonometric Substitution
    • 6.4 Integration of Rational Functions Using Partial Fractions
      • Brief Summary of Integration Techniques
    • 6.5 Integration Tables and Computer Algebra Systems
      • Using Tables of Integrals
      • Integration Using a Computer Algebra System
    • 6.6 Improper Integrals
      • Improper Integrals with a Discontinuous Integrand
      • Improper Integrals with an Infinite Limit of Integration
      • A Comparison Test
  • Chapter 7: First-Order Differential Equations
    • 7.1 Modeling with Differential Equations
      • Growth and Decay Problems
      • Compound Interest
    • 7.2 Separable Differential Equations
      • Logistic Growth
    • 7.3 First-Order Linear Differential Equations
      • General Solution of Linear Differential Equations of the First Order
    • 7.4 Direction Fields and Euler’s Method
    • 7.5 Systems of First-Order Differential Equations
      • Predator–Prey Systems
  • Chapter 8: Infinite Series
    • 8.1 Sequences of Real Numbers
    • 8.2 Infinite Series
    • 8.3 The Integral Test and Comparison Tests
      • Comparison Tests
    • 8.4 Alternating Series
      • Estimating the Sum of an Alternating Series
    • 8.5 Absolute Convergence and the Ratio Test
      • The Ratio Test
      • The Root Test
      • Summary of Convergence Tests
      • Concept Mapping
    • 8.6 Power Series
    • 8.7 Taylor Series
      • Representation of Functions as Power Series
      • Proof of Taylor’s Theorem
    • 8.8 Applications of Taylor Series
      • The Binomial Series
    • 8.9 Fourier Series
      • Functions of Period Other Than 2p
      • Fourier Series and Music Synthesizers
  • Chapter 9: Parametric Equations and Polar Coordinates
    • 9.1 Plane Curves and Parametric Equations
    • 9.2 Calculus and Parametric Equations
    • 9.3 Arc Length and Surface Area in Parametric Equations
    • 9.4 Polar Coordinates
    • 9.5 Calculus and Polar Coordinates
    • 9.6 Conic Sections
      • Parabolas
      • Ellipses
      • Hyperbolas
    • 9.7 Conic Sections in Polar Coordinates
  • Chapter 10: Vectors and the Geometry of Space
    • 10.1 Vectors in the Plane
    • 10.2 Vectors in Space
      • Vectors in R3
    • 10.3 The Dot Product
      • Components and Projections
    • 10.4 The Cross Product
    • 10.5 Lines and Planes in Space
      • Planes in R3
    • 10.6 Surfaces in Space
      • Cylindrical Surfaces
      • Quadric Surfaces
      • An Application
  • Chapter 11: Vector-Valued Functions
    • 11.1 Vector-Valued Functions
      • Arc Length in R3
    • 11.2 The Calculus of Vector-Valued Functions
    • 11.3 Motion in Space
      • Equations of Motion
    • 11.4 Curvature
    • 11.5 Tangent and Normal Vectors
      • Tangential and Normal Components of Acceleration
      • Kepler’s Laws
    • 11.6 Parametric Surfaces
  • Chapter 12: Functions of Several Variables and Partial Differentiation
    • 12.1 Functions of Several Variables
    • 12.2 Limits and Continuity
    • 12.3 Partial Derivatives
    • 12.4 Tangent Planes and Linear Approximations
      • Increments and Differentials
    • 12.5 The Chain Rule
      • Implicit Differentiation
    • 12.6 The Gradient and Directional Derivatives
    • 12.7 Extrema of Functions of Several Variables
      • Proof of the Second Derivatives Test
    • 12.8 Constrained Optimization and Lagrange Multipliers
  • Chapter 13: Multiple Integrals
    • 13.1 Double Integrals
      • Double Integrals over a Rectangle
      • Double Integrals over General Regions
    • 13.2 Area, Volume and Center of Mass
      • Moments and Center of Mass
    • 13.3 Double Integrals in Polar Coordinates
    • 13.4 Surface Area
    • 13.5 Triple Integrals
      • Mass and Center of Mass
    • 13.6 Cylindrical Coordinates
    • 13.7 Spherical Coordinates
      • Triple Integrals in Spherical Coordinates
    • 13.8 Change of Variables in Multiple Integrals
  • Chapter 14: Vector Calculus
    • 14.1 Vector Fields
    • 14.2 Line Integrals
    • 14.3 Independence of Path and Conservative Vector Fields
    • 14.4 Green’s Theorem
    • 14.5 Curl and Divergence
    • 14.6 Surface Integrals
      • Parametric Representation of Surfaces
    • 14.7 The Divergence Theorem
    • 14.8 Stokes’ Theorem
    • 14.9 Applications of Vector Calculus
  • Chapter 15: Second-Order Differential Equations
    • 15.1 Second-Order Equations with Constant Coefficients
    • 15.2 Nonhomogeneous Equations: Undetermined Coefficients
    • 15.3 Applications of Second-Order Equations
    • 15.4 Power Series Solutions of Differential Equations
    • 15.5 Laplace Transforms
    • 15.6 Solving Differential Equations Using Laplace Transforms
  • Appendix A: Proofs of Selected Theorems
  • Credits
  • Subject Index
  • Derivative Formulas
  • Table of Integrals

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Vörumerki: McGrawHill
Vörunúmer: 9780077166656
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Calculus: Early Transcendental Functions

Vörumerki: McGrawHill
Vörunúmer: 9780077166656
Rafræn bók. Uppl. sendar á netfangið þitt eftir kaup
7.990 kr.
Get the product now
7.990 kr.