Calculus, Multivariable : Late Transcendental Functions

by SMITH

• ISBN13: 9780073314204
• ISBN10: 007331420X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2007-01-05
• Publisher: McGraw-Hill Science/Engineering/Math

Summary

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 most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, reality-based applications that appeal to students' interests and demonstrate the elegance of math in the world around us. New features include: Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises New exploratory exercises in every section that challenge students to make connections to previous introduced material. New commentaries ("Beyond Formulas") that encourage students to think mathematically beyond the procedures they learn. New counterpoints to the historical notes, "Today in Mathematics," 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. Exceptional Media Resources: Within MathZone, instructors and students have access to a series of unique Conceptual Videos that help students understand key Calculus concepts proven to be most difficult to comprehend, 248 Interactive Applets that help students master concepts and procedures and functions, 1600 algorithms , and 113 e-Professors.

Table of Contents

Preliminaries

The Real Numbers and the Cartesian Plane

Lines and Functions

Graphing Calculators and Computer Algebra Systems

Trigonometric Functions

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 Asysmptotes

The Formal Definition of the Limit

Limits and Loss-of-Significance Errors Computer Representation or Real Numbers

Differentiation

Tangent Lines and Velocity

The Derivative Alternative Derivative Notations 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

Implicit Differentiation

The Mean Value Theorem

Applications of Differentiation

Linear Approximations and Newton's Method

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 under a Curve

The Definite Integral Average Value of a Function

The Fundamental Theorem of Calculus

Integration by Substitution

Numerical Integration Error bounds for Numerical Integration

Applications of the Definite Integral

Area Between Curves

Volume: Slicing, Disks, and Washers

Volumes by Cylindrical Shells

Arc Length and Srface Area

Projectile Motion

Applications of Integration to Physics and Engineering

Exponentials, Logarithms and other Transcendental Functions

The Natural Logarithm

Inverse Functions

Exponentials

The Inverse Trigonometric Functions

The Calculus of the Inverse Trigonometric Functions

The Hyperbolic Function

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

Indeterminate Forms and L'Hopital's Rule Improper Integrals A Comparison Test

Probability

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 Equations

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 Test

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 the Geometry of Space

Vectors in the Plane

Vectors in Space

The Dot Product Compo

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