**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

**Download Vector Calculus 6th Edition by Jerrold E. Marsde and Anthony Tromba in PDF Format For Free.**