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.
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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
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
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.
- 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.
includes problem sets and chapter projects that
offer a richer source of applied problems than is common.
- 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.
uses a technology friendly, but not technologically dependent,
- 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
- presents projects in a problem format
and encourages students to write up each project in the form of a
presents a simpler method of graphing based on critical
points and end points.
- restricts discussion of technology primarily to general
issues regarding the appropriate and effective use of technology in
- 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.
(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.
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
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.
Radius of Convergence of a Power Series. Differentiation and
Integration of Power Series. Answers to Selected Odd-Numbered Problems.