# Calculus: Early Transcendental Functions

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## Efnisyfirlit

• Cover
• Title
• Dedication
• 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
• 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.
Fá vöru senda með tölvupósti
7.990 kr.