Vector Calculus 6th Edition by Jerrold E. Marsde and Anthony Tromba

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Vector Calculus 6th Edition by Jerrold E. Marsde and Anthony Tromba

PDF Free Download|Vector Calculus 6th Edition by Jerrold E. Marsde and Anthony Tromba.

Preface to Vector Calculus 6th Edition

This text is intended for a one-semester course in the
calculus of functions of several variables and vector analysis, which is
normally taught at the sophomore level.

In addition to making changes and
improvements throughout the text, we have also attempted to convey a sense of
excitement, relevance, and importance of the subject matter.

Prerequisites

Sometimes courses in vector calculus are preceded by the first
course in linear algebra, but this is not an essential prerequisite.

We require
only the bare rudiments of matrix algebra, and the necessary concepts are
developed in the text. If this course is preceded by a course in linear
algebra, the instructor will have no difficulty enhancing the material.
However, we do assume a knowledge of the fundamentals of one-variable
calculus—the process of differentiation and integration and their geometric and
physical meaning as well as a knowledge of the standard functions, such as the
trigonometric and exponential functions.

The Role of Theory

The text includes much of the basic theory as well as many
concrete examples and problems. Some of the technical proofs for theorems in
Chapters 2 and 5 are given in optional sections that are readily available on
the Book Companion Web Site at www.whfreeman.com/marsdenvc6e (see the description on the next page).

Section 2.2, on limits and continuity, is
designed to be treated lightly and is deliberately brief. More sophisticated
theoretical topics, such as compactness and delicate proofs in integration
theory, have been omitted because they usually belong to a more advanced
course in real analysis.

Concrete and Student-Oriented

Computational skills and intuitive understanding are important
at this level, and we have tried to meet this need by making the book concrete
and student-oriented.

For example, although we formulate the definition of the
derivative correctly, it is done by using matrices of partial derivatives
rather than abstract linear transformations.

We also include a number of
physical illustrations such as fluid mechanics, gravitation, and
electromagnetic theory, and from economics as well, although knowledge of these
subjects are not assumed.

Order of Topics

A special feature of the text is the early introduction of
vector fields, divergence, and curl in Chapter 4, before integration.

Vector
analysis often suffers in a course of this type, and the present arrangement is
designed to offset this tendency.

To go even further, one might consider
teaching Chapter 3 (Taylor’s theorems, maxima, and minima, Lagrange multipliers)
after Chapter 8 (the integral theorems of vector analysis).

New to Vector Calculus 6th Edition

This sixth edition was completely redesigned but retains
and improves on the balance between theory, applications, optional material,
and historical notes that were present in earlier editions.

We are excited about
this new edition of Vector Calculus, especially the inclusion of many new
exercises and examples.

The exercises have been graded from less difficult to
more difficult, allowing instructors to have more flexibility in assigning
practice problems.

The modern redesign emphasizes the pedagogical features,
making the text more concise, student-friendly, and accessible.

The quality of
the artwork has been significantly improved, especially for the crucial
three-dimensional figures, to better reflect key concepts to students.

We have
also trimmed some of the historical material, making it more relevant to mathematics under discussion.

Finally, we have moved some of the more difficult
discussions in the fifth edition—such as those on Conservation Laws, the
derivation of Euler’s Equation of a Perfect Fluid, and a discussion of the Heat
Equation—to the Book Companion Web Site. We hope that the reader will be
equally pleased.

Vector Calculus Contents

  • The Geometry of Euclidean Space
  • Differentiation
  • Higher-Order Derivatives: Maxima and Minima
  • Vector-Valued Functions
  • Double and Triple Integrals
  • The Change of Variables Formula and Applications of Integration
  • Integrals Over Paths and Surfaces

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