Calculus / Edition 5

Calculus / Edition 5

by William G. McCallum, Deborah Hughes-Hallett, Andrew M. Gleason, David O. Lomen
     
 

ISBN-10: 0470131586

ISBN-13: 9780470131589

Pub. Date: 10/24/2008

Publisher: Wiley

CALCULUS 5e brings together the best of both new and traditionalcurricula in an effort to meet the needs of even more instructorsteaching calculus. The author team's extensive experience teachingfrom both traditional and innovative books and their expertise indeveloping innovative problems put them in an unique position tomake this new curriculum meaningful to

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Overview

CALCULUS 5e brings together the best of both new and traditionalcurricula in an effort to meet the needs of even more instructorsteaching calculus. The author team's extensive experience teachingfrom both traditional and innovative books and their expertise indeveloping innovative problems put them in an unique position tomake this new curriculum meaningful to students going intomathematics and those going into the sciences and engineering. Theauthors believe this edition will work well for those departmentswho are looking for a calculus book that offers a middle ground fortheir calculus instructors.

CALCULUS 5e exhibits the same strengths from earlier editionsincluding the Rule of Four, an emphasis on modeling, expositionthat students can read and understand and a flexible approach totechnology. The conceptual and modeling problems, praised for theircreativity and variety, continue to motivate and challengestudents.

Product Details

ISBN-13:
9780470131589
Publisher:
Wiley
Publication date:
10/24/2008
Edition description:
Older Edition
Pages:
480
Product dimensions:
8.50(w) x 10.40(h) x 0.90(d)

Related Subjects

Table of Contents

12 FUNCTIONS OF SEVERAL VARIABLES.

12.1 Functions of Two Variables.

12.2 Graphs of Functions of Two Variables.

12.3 Contour Diagrams.

12.4 Linear Functions.

12.5 Functions Of Three Variables.

12.6 Limits and Continuity.

Projects: A Heater in a Room, Light in a Wave-Guide.

13 A FUNDAMENTAL TOOL: VECTORS.

13.1 Displacement Vectors.

13.2 Vectors in General.

13.3 The Dot Product.

13.4 The Cross Product.

Projects: Cross Product of Vectors in the Plane, The Dot Productin Genetics, a Warren Truss.

14 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES.

14.1 The Partial Derivative.

14.2 Computing Partial Derivatives Algebraically.

14.3 Local Linearity and the Differential.

14.4 Gradients and Directional Derivatives in the Plane.

14.5 Gradients and Directional Derivatives in Space.

14.6 The Chain Rule.

14.7 Second-Order Partial Derivatives.

14.8 Differentiability.

Projects: Heat Equation, Matching Birthdays.

15 OPTIMIZATION: LOCAL AND GLOBAL EXTREMA.

15.1 Local Extrema.

15.2 Optimization.

15.3 Constrained Optimization: Lagrange Multipliers.

Projects: Optimization in Manufacturing, Fitting a Line to DataUsing Least Squares, Hockey and Entropy.

16 INTEGRATING FUNCTIONS OF SEVERAL VARIABLES.

16.1 The Definite Integral of a Function of Two Variables.

16.2 Iterated Integrals.

16.3 Triple Integrals.

16.4 Double Integrals in Polar Coordinates.

16.5 Integrals in Cylindrical and Spherical Coordinates.

16.6 Applications of Integration to Probability.

16.7 Change of Variables in a Multiple Integral.

Projects: A Connection Between e and π,Average Distance Walked to an Airport Gate.

17 PARAMETERIZATION AND VECTOR FIELDS.

17.1 Parameterized Curves.

17.2 Motion, Velocity, and Acceleration.

17.3 Vector Fields.

17.4 The Flow of a Vector Field.

17.5 Parameterized Surfaces.

Projects: Shooting a Basketball, Kepler’s Second Law, FluxDiagrams.

18 LINE INTEGRALS.

18.1 The Idea of a Line Integral.

18.2 Computing Line Integrals Over Parameterized Curves.

18.3 Gradient Fields and Path-Independent Fields.

18.4 Path-Dependent Vector Fields and Green’s Theorem.

Projects: Conservation of Energy, Planimeters, Ampere'sLaw.

19 FLUX INTEGRALS.

19.1 The Idea of a Flux Integral.

19.2 Flux Integrals For Graphs, Cylinders, and Spheres.

19.3 Flux Integrals Over Parameterized Surfaces.

Projects: Gauss’ Law Applied to a Charged Wire and aCharged Sheet, Flux Across a Cylinder Due to a Point Charge:Obtaining Gauss’ Law from Coulomb’s Law.

20 CALCULUS OF VECTOR FIELDS.

20.1 The Divergence of a Vector Field.

20.2 The Divergence Theorem.

20.3 The Curl of a Vector Field.

20.4 Stokes’ Theorem.

20.5 The Three Fundamental Theorems.

Projects: Divergence of Spherically Symmetric Vector Fields,Divergence of Cylindrically Symmetric Vector Fields.

APPENDIX.

A Roots, Accuracy, and Bounds.

B Complex Numbers.

C Newton’s Method.

D Vectors in the Plane.

E Determinants.

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