9780073309446

Calculus: Early Transcendental Functions

by ;
  • ISBN13:

    9780073309446

  • ISBN10:

    0073309443

  • Edition: 3rd
  • Format: Package
  • Copyright: 3/28/2007
  • Publisher: McGraw-Hill Science/Engineering/Math
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Table of Contents

Preliminaries
Polynomials and Rational Functions
Graphing Calculators and Computer Algebra Systems
Inverse Functions
Trigonometric and Inverse Trigonometric Functions
Exponential and Logarithmic Functions Hyperbolic Functions Fitting a Curve to Data
Transformations of Functions
Limits and Continuity
A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
The Concept of Limit
Computation of Limits
Continuity and its Consequences The Method of Bisections
Limits Involving Infinity Asymptotes
Formal Definition of the Limit Exploring the Definition of Limit Graphically
Limits and Loss-of-Significance Errors Computer Representation of Real Numbers
Differentiation
Tangent Lines and Velocity
The Derivative Numerical Differentiation
Computation of Derivatives: The Power Rule Higher Order Derivatives Acceleration
The Product and Quotient Rules
The Chain Rule
Derivatives of the Trigonometric Functions
Derivatives of the Exponential and Logarithmic Functions
Implicit Differentiation and Inverse Trigonometric Functions
The Mean Value Theorem
Applications of Differentiation
Linear Approximations and Newton’s Method
Indeterminate Forms and L’Hopital’s Rule
Maximum and Minimum Values
Increasing and Decreasing Functions
Concavity and the Second Derivative Test
Overview of Curve Sketching
Optimization
Related Rates
Rates of Change in Economics and the Sciences
Integration
Antiderivatives
Sums and Sigma Notation Principle of Mathematical Induction
Area
The Definite Integral Average Value of a Function
The Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration Error Bounds for Numerical Integration
The Natural Logarithm as an Integral The Exponential Function as the Inverse of the Natural Logarithm
Applications of the Definite Integral
Area Between Curves
Volume: Slicing, Disks, and Washers
Volumes by Cylindrical Shells
Arc Length and Surface Area
Projectile Motion
Applications of Integration to Physics and Engineering
Probability
Integration Techniques
Review of Formulas and Techniques
Integration by Parts
Trigonometric Techniques of Integration Integrals Involving Powers of Trigonometric Functions Trigonometric Substitution
Integration of Rational Functions Using Partial Fractions Brief Summary of Integration Techniques
Integration Tables and Computer Algebra Systems
Improper Integrals A Comparison Test
First-Order Differential Equations
Modeling with Differential Equations Growth and Decay Problems Compound Interest
Separable Differential Equations Logistic Growth
Direction Fields and Euler's Method
Systems of First-Order Differential Equations Predator-Prey Systems
Infinite Series
Sequences of Real Numbers
Infinite Series
The Integral Test and Comparison Tests
Alternating Series Estimating the Sum of an Alternating Series
Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Tests
Power Series
Taylor Series Representations of Functions as Series Proof of Taylor’s Theorem
Applications of Taylor Series The Binomial Series
Fourier Series
Parametric Equations and Polar Coordinates
Plane Curves and Parametric Equations
Calculus and Parametric Equations
Arc Length and Surface Area in Parametric Equations
Polar Coordinates
Calculus and Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
Vectors and th
Table of Contents provided by Publisher. All Rights Reserved.

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