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Calculus with MathZone : Early Transcendental Functions,9780073229737
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Calculus with MathZone : Early Transcendental Functions



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McGraw-Hill Science/Engineering/Math
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This is the 3rd edition with a publication date of 1/23/2006.

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Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors' approach, which combines the best elements of reform with the most reliable aspects of mainstream calculus teaching, resulting in a motivating, challenging book.Smith/Minton also provide exceptional, reality-based applications that appeal to students' interests and demonstrate the elegance of math in the world around us.New features include:- A new organization placing all transcendental functions early in the book and consolidating the introduction to L'H˘pital's Rule in a single section.- More concisely written explanations in every chapter.- Many new exercises (for a total of 7,000 throughout the book) that require additional rigor not found in the 2nd Edition.- New exploratory exercises in every section that challenge students to synthesize key concepts to solve intriguing projects.- New commentaries ("Beyond Formulas") that encourage students to think mathematically beyond the procedures they learn.- New counterpoints to the historical notes, "Today in Mathematics," that stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present.- An enhanced discussion of differential equations and additional applications of vector calculus.

Table of Contents

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 First Look at Calculus
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
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
Related Rates
Rates of Change in Economics and the Sciences
Sums and Sigma Notation Principle of Mathematical Induction
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 Economics and the Sciences
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 General Strategies for Integration Techniques
Integration Tables and Computer Algebra Systems
Improper Integrals A Comparison Test
First Order Differential Equations
Growth and Decay Problems Compound Interest Modeling with Differential Equations
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
Table of Contents provided by Publisher. All Rights Reserved.

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