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Multivariable Calculus with Engineering and Science Applications (Preliminary Version), 1/e

Philip Anselone, (Emeritus) Oregon State University
John Lee, Oregon State University

Published December, 1995 by Prentice Hall Engineering/Science/Mathematics

Copyright 1996, 577 pp.
Paper
ISBN 0-13-045279-3


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Summary

Innovative in approach, this text is designed for students aiming at careers in science, engineering, or mathematics. Unlike other calculus texts — which present rigorous proofs first and then explain and apply them — or present intuitive ideas, but not much more — this text approaches each new topic from an intuitive perspective first, and then adds the appropriate precision and rigor. It emphasizes that calculus is best understood via geometry and interdisciplinary applications. Its rich selection of significant applications, careful arrangement of topics, and exceptionally readable explanations of difficult material ensure student motivation and comprehension regardless of objective.

Features


offers an intuitive overview of calculus (Ch. 1) without technical details — and weaves essential background material into the story of calculus when it is needed.
combines an informal conversational style with an intuition-before-rigor approach.

  • When presenting a new topic, begins with a special case or an elementary example that illustrates salient geometric or numerical features of the general situations.
  • then adds precision and appropriate rigor.
  • The more difficult passages are deferred to ends of sections and some are started as optional.
provides a considerable variety of interesting science and engineering applications throughout.
  • Applications drawn from the physical sciences usually involve motion, force, work, or energy, and treat seriously both the physical and mathematical points of view — so students understand and appreciate both the physical concepts and the related mathematics.
  • Applications modeled by differential equations appear early and often.
includes problem sets and chapter projects that offer a richer source of applied problems than is common.
  • chapter-end “do-it-yourself” projects on topics in science, engineering, and probability use the methods of the chapter (or earlier chapters) and appropriate graphic utilities, a CAS, or other appropriate software to delve more deeply into an interesting application.
  • presents projects in a “problem format” and encourages students to write up each project in the form of a full report.
uses a technology friendly, but not technologically dependent, approach.
  • restricts discussion of technology primarily to general issues regarding the appropriate and effective use of technology in calculus.
  • occasionally includes short examples of Matlab code.
  • locates discussion of technology at the end of appropriate sections — highlighting the interplay between the use of technology and the calculus just covered.
presents a simpler method of graphing based on critical points and end points.


Table of Contents
(NOTE: Each chapter contains Highlights and Review Problems).
    1. Sequences and Series.

      Sequences. Monotone Sequences and Successive Approximations. Infinite Series. Series with Nonnegative Terms and Comparison Tests. Absolute and Conditional Convergence; Alternating Series. The Ratio and Root Tests. Chapter Project: Dynamical Systems.

    2. Power Series.

      Taylor Polynomials. Taylor Series and Power Series. Differentiation and Integration of Power Series. Power Series and Differential Equations; The Binomial Series. Chapter Project: Random Walks.

    3. Vectors.

      Rectangular Coordinates in 3-Space. Vectors. The Dot Product. The Cross Product. Lines and Planes. Chapter Project: Friction.

    4. Vector Calculus.

      Parametric Curves. Vector Functions and Curve Length. Velocity, Speed, and Acceleration. Curvature; Tangential and Normal Components of Acceleration. Motion in Polar Coordinates. Chapter Project: Pursuit Problems.

    5. Differential Calculus for Functions of Two and Three Variables.

      Functions and Graphs. Limits and Continuity. Partial Derivatives. Tangent Planes, Linear Approximations, and Differentials. Chain Rules and Directional Derivatives. Gradients. Chapter Project: Curves of Steepest Descent and Ascent.

    6. Max-Min Problems for Functions of Two and Three Variables.

      Maximum and Minimum Values. Higher Order Partial Derivatives and the Second Partials Test. Constrained Max-Min Problems and Lagrange Multipliers. Chapter Project: Optimal Location.

    7. Integral Calculus for Functions of Two and Three Variables.

      Double Integrals in Rectangular Coordinates. Triple Integrals in Rectangular Coordinates. Double and Triple Integrals in Polar and Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Further Applications of Double and Triple Integrals. Chapter Project: Numerical Integration.

    8. Elements of Vector Analysis.

      Scalar and Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem and Applications. Surface Area and Surface Integrals. The Divergence Theorem (Gauss' Theorem) and Applications. Stokes' Theorem and Applications. Chapter Project: Heat Conduction.

    Appendices.

      Radius of Convergence of a Power Series. Differentiation and Integration of Power Series. Answers to Selected Odd-Numbered Problems.

    Index.

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