Calculus, Multivariable : Late Transcendental Functions

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  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 2007-01-05
  • Publisher: McGraw-Hill Science/Engineering/Math

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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 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

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
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
Related Rates
Rates of Change in Economics and the Sciences
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
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
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
Table of Contents provided by Publisher. All Rights Reserved.

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