Multivariable Mathematics (3rd Edition)

3.5 avg rating
( 8 ratings by GoodReads )
 
9780131816459: Multivariable Mathematics (3rd Edition)

This book explores the standard problem-solving techniques of multivariable mathematics -- integrating vector algebra ideas with multivariable calculus and differential equations. Provides many routine, computational exercises illuminating both theory and practice. Offers flexibility in coverage -- topics can be covered in a variety of orders, and subsections (which are presented in order of decreasing importance) can be omitted if desired. Provides proofs and includes the definitions and statements of theorems" to show how the subject matter can be organized around a few central ideas. Includes new sections on: flow lines and flows; centroids and moments; arc-length and curvature; improper integrals; quadratic surfaces; infinite series--with application to differential equations; and numerical methods. Presents refined method for solving linear systems using exponential matrices.

"synopsis" may belong to another edition of this title.

From the Publisher:

This text explores the standard problem-solving techniques of multivariable mathematics -- integrating vector algebra ideas with multivariable calculus and differential equations.

Excerpt. © Reprinted by permission. All rights reserved.:

This book covers material that is often studied after a first course in one-variable calculus, namely the algebra and geometry of vectors and matrices, multivariable and vector calculus, and differential equations, including systems. The branches of these three areas are strongly intertwined and we've designed our treatment to display the connections effectively. Our aim has been to teach basic problem solving, both pure and applied, in a framework that is mathematically coherent, while allowing for selective emphasis on traditional rigor.

While the sequence of topics follows rather traditional lines of mathematical classification, the actual route taken may vary widely from course to course. An underlying theme is the encouragement of geometric thinking in two and three dimensions, extended to arbitrary dimension when it's useful to do so. Thus, most of Chapters 1 and 2 on vectors and matrices is prerequisite for the rest of the book, but otherwise there is considerable flexibility for course scheduling. Chapter 3 on linear algebra, with an introduction to general vector spaces and linear transformations, is included for those who want to cover this material at some point, but none of it is prerequisite for later chapters. In particular the material on differentiability in Chapter 5 is organized so that the motivation for the definition depends on gradient vectors rather than linear transformations.

For this edition the exposition has been completely rewritten in many places and, in addition to Chapter 3, a number of topics that are optional additions to a basic course have been added, as follows:

Additional emphasis on scientific applications in Section 113 of Chapter 2.
Subsection on vector integrals in Chapter 4, Section 1.
Subsections on quadric surfaces in Chapter 4.
Subsection on flow lines in Chapter 6, Section 1.
Subsection on use of the chain rule in coordinate changes.
Expanded treatment of the second-derivative criterion for extrema.
Section 5 on centroids and moments in Chapter 7.
Section 6 on application of improper integrals in Chapter 7.
Section 4, Chapter 8 relating flow lines, divergence, and curl.
Subsection on finding potentials in Chapter 9, Section 2.
Additional subsection on flows in Chapter 12, Section 1.
More efficient computation of exponential matrices in Chapter 13, Section 2.
Chapter on infinite series, with applications to differential equations.
Sections in Chapter 4 on computer plotting of curves and surfaces.
Subsection on the steepest ascent method.
Subsection on the midpoint and Simpson rules for multiple integrals.
Subsection on Newton's method for vector functions.
Java applets for the graphical and numerical work.

The figures are a salient feature of the text, including those in the answer section and the one on the cover, which represents a trajectory of a Lotka-Volterra system modified for three species and discussed in Exercise 34 in Chapter 12, Section 4.

The impetus for this edition came from George Lobell, whose knowledge of the field and continued support has helped us a great deal. Allan Gunter read the entire text, making insightful suggestions and working all the exercises; his collaboration was invaluable. Jeanne Audino's experienced and good humored oversight of the production has made working out final details a pleasure rather than a chore. Corrections can be sent to rewn@dartmouth.edu or hft@math.princeton.edu.

Richard E. Williamson
Hale F. Trotter

"About this title" may belong to another edition of this title.

Buy New View Book
List Price: US$ 100.00
US$ 50.89

Convert Currency

Shipping: FREE
From India to U.S.A.

Destination, Rates & Speeds

Add to Basket

Top Search Results from the AbeBooks Marketplace

1.

Williamson, Richard E.; Trotter, Hale F.
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Quantity Available: 5
Seller
firstbookstore
(New Delhi, India)
Rating
[?]

Book Description Book Condition: Brand New. Brand New Original US Edition, Perfect Condition. Printed in English. Excellent Quality, Service and customer satisfaction guaranteed!. Bookseller Inventory # AIND-26317

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 50.89
Convert Currency

Add to Basket

Shipping: FREE
From India to U.S.A.
Destination, Rates & Speeds

2.

Williamson, Richard E.; Trotter, Hale F.
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Quantity Available: 2
Seller
Bookshub
(Karol Bagh, India)
Rating
[?]

Book Description Book Condition: New. New. US edition. Perfect condition. Ship by express service to USA, Canada, Australia, France, Italy, UK, Germany and Netherland. Customer satisfaction our priority. Bookseller Inventory # ABE-190516-7143

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 51.44
Convert Currency

Add to Basket

Shipping: FREE
From India to U.S.A.
Destination, Rates & Speeds

3.

Williamson, Richard E.; Trotter, Hale F.
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Quantity Available: 2
Seller
EBOOKSTORE2010
(New Delhi, ND, India)
Rating
[?]

Book Description Book Condition: Brand New. New. US edition. Customer Satisfaction guaranteed!!. Bookseller Inventory # SHAK7143

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 51.49
Convert Currency

Add to Basket

Shipping: FREE
From India to U.S.A.
Destination, Rates & Speeds

4.

Williamson, Richard E.; Trotter, Hale F.
Published by Prentice Hall College Div (1995)
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Hardcover Quantity Available: 1
Seller
Irish Booksellers
(Rumford, ME, U.S.A.)
Rating
[?]

Book Description Prentice Hall College Div, 1995. Hardcover. Book Condition: New. book. Bookseller Inventory # 0131816454

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 52.01
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

5.

Williamson, Richard E.; Trotter, Hale F.
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Quantity Available: 5
Seller
Romtrade Corp.
(STERLING HEIGHTS, MI, U.S.A.)
Rating
[?]

Book Description Book Condition: New. Brand New Original US Edition.We Ship to PO BOX Address also. EXPEDITED shipping option also available for faster delivery. Bookseller Inventory # AUSBNEW-26317

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 54.25
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

6.

Williamson, Richard E.; Trotter, Hale F.
Published by Prentice Hall College Div (1995)
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Hardcover Quantity Available: 1
Seller
Ergodebooks
(RICHMOND, TX, U.S.A.)
Rating
[?]

Book Description Prentice Hall College Div, 1995. Hardcover. Book Condition: New. 3 Sub. Bookseller Inventory # DADAX0131816454

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 51.53
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

7.

Williamson, Richard E.; Trotter, Hale F.
Published by Prentice Hall College Div
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Hardcover Quantity Available: 1
Seller
Cloud 9 Books
(West Palm Beach, FL, U.S.A.)
Rating
[?]

Book Description Prentice Hall College Div. Hardcover. Book Condition: New. 0131816454 New Condition. Bookseller Inventory # NEW6.0048739

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 67.58
Convert Currency

Add to Basket

Shipping: US$ 4.99
Within U.S.A.
Destination, Rates & Speeds

8.

Williamson, Richard E.; Trotter, Hale F.
Published by Prentice-Hall
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Quantity Available: 1
Seller
Majestic Books
(London, ,, United Kingdom)
Rating
[?]

Book Description Prentice-Hall. Book Condition: New. Bookseller Inventory # 6343411

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 71.86
Convert Currency

Add to Basket

Shipping: US$ 6.81
From United Kingdom to U.S.A.
Destination, Rates & Speeds

9.

Williamson, Richard E.; Trotter, Hale F.
Published by Prentice Hall College Div (1995)
ISBN 10: 0131816454 ISBN 13: 9780131816459
New Hardcover Quantity Available: 3
Seller
Murray Media
(North Miami Beach, FL, U.S.A.)
Rating
[?]

Book Description Prentice Hall College Div, 1995. Hardcover. Book Condition: New. Bookseller Inventory # P110131816454

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 91.33
Convert Currency

Add to Basket

Shipping: US$ 2.99
Within U.S.A.
Destination, Rates & Speeds