Differential Geometry: A Geometric Introduction

Overview

The only book that introduces differential geometry through a combination of an intuitive geometric foundation, a rigorous connection with the standard formalisms, computer exercises with Maple, and a problems-based approach. Starting with basic geometric ideas, Differential Geometry uses basic intuitive geometry as a starting point to make the material more accessible and the formalism more meaningful. The book presents topics through problems to provide readers with a deeper understanding. And, it introduces ...
See more details below
Available through our Marketplace sellers.
Other sellers (Paperback)
  • All (7) from $16.07   
  • New (3) from $70.00   
  • Used (4) from $16.07   
Close
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any BN.com coupons and promotions
$70.00
Seller since 2006

Feedback rating:

(342)

Condition:

New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.

New
Upper Saddle River, NJ 1997 Hard cover New. HARDCOVER. BRAND NEW; gift quality. 250 p. Audience: General/trade.

Ships from: Northbrook, IL

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
$137.70
Seller since 2014

Feedback rating:

(323)

Condition: New
Brand New Item.

Ships from: Chatham, NJ

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
$162.12
Seller since 2008

Feedback rating:

(196)

Condition: New

Ships from: Chicago, IL

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
Page 1 of 1
Showing All
Close
Sort by
Sending request ...

Overview

The only book that introduces differential geometry through a combination of an intuitive geometric foundation, a rigorous connection with the standard formalisms, computer exercises with Maple, and a problems-based approach. Starting with basic geometric ideas, Differential Geometry uses basic intuitive geometry as a starting point to make the material more accessible and the formalism more meaningful. The book presents topics through problems to provide readers with a deeper understanding. And, it introduces hyperbolic geometry in the first chapter rather than in a closing chapter as in other books. An important reference and resource book for any reader who needs to understand the foundations of differential geometry.
Read More Show Less

Product Details

  • ISBN-13: 9780135699638
  • Publisher: Simon & Schuster Adult Publishing Group
  • Publication date: 7/24/1997
  • Edition number: 1
  • Pages: 250
  • Product dimensions: 6.26 (w) x 9.34 (h) x 0.70 (d)

Table of Contents

Preface.
How to Use This Book.
1. Surfaces and Straightness.
When Do You Call a Straight Line? How Do You Construct a Straight Line? Local (and Infinitesimal) Straightness. Intrinsic Straight Lines on Cylinders. Geodesics on Cones. Is "Shortest" Always "Straight"? Locally Isometric Surfaces. Local Coordinates for Cylinders and Cones. Geodesics in Local Coordinates. What Is Straight on a Sphere? Intrinsic Curvature on a Sphere. Local Coordinates on a Sphere. Strakes, Augers, and Helicoids. Surfaces of Revolution. Hyperbolic Plane. Surface as Graph of a Function z=f(x,y)

2. Extrinsic Curves.
Introduction. Give Examples of F.O.V.'s. Archimedian Property. Vectors and Affine Linear Space. Smoothness and Tangent Directions. Curvature of a Curve in Space. Curvature of the Graph of a Function. Osculating Circle. Strakes. When a Curve Does Not Lie in a Plane.

3. Extrinsic Descriptions of Intrinsic Curvature.
Smooth Surfaces and Tangent Planes. Extrinsic Curvature - Geodesics on Sphere. Intrinsic Curvature - Curves on Sphere. Intrinsic (Geodesic) Curvature. Geodesics on Surfaces—the Ribbon Test. Ruled Surfaces and the Converse of the Ribbon Test.

4. Tangent Space, Metric, Directional Derivative.
The Tangent Space. Mean Value Theorem: Curves, Surfaces. Natural Parametrizations of Curves. Riemannian Metric. Riemannian Metric in Local Coordinates on a Sphere. Riemannian Metric in Local Coordinates on a Strake. Vectors inExtrinsic Local Coordinates. Measuring Using the Riemannian Metric. Directional Derivatives. Directional Derivative in Local Coordinates. Differentiating a Metric. Expressing Normal Curvature. Geodesic Local Coordinates. Differential Operator. Metric in Geodesic Coordinates.

5. Area, Parallel Transport, Intrinsic Curvature.
The Area of a Triangle on a Sphere. Introducing Parallel Transport. The Holonomy of a Small Geodesic Triangle. Dissection of Polygons into Triangles. Gauss-Bonnet for Polygons on a Sphere. Parallel Fields and Intrinsic Curvature. Holonomy on Surfaces. Holonomy Explains Foucault's Pendulum. Intrinsic Curvature of a Surface.

6. Gaussian Curvature Extrinsically Defined.
Pep Talk to the Reader. Gaussian Curvature, Extrinsic Definition. Second Fundamental Form. The Gauss Map. Gauss-Bonnet and Intrinsic Curvature. Matrix of the Second Fundamental. Mean Curvature and Minimal Surfaces. Celebration of Our Hard Work.

7. Applications of Gaussian Curvature.
Gaussian Curvature in Local Coordinates. Curvature on Sphere, Strake, Catenoid. Circles, Polar Coordinates, and Curvature. Exponential Map and Shortest Is Straight. Ruled Surfaces and Ribbons. Surfaces with Constant Curvature. Curvature of the Hyperbolic Plane.

8. Intrinsic Local Descriptions and Manifolds.
Covariant Derivative and Connections. Manifolds—Intrinsic and Extrinsic. Christoffel Symbols, Intrinsic Descriptions. Intrinsic Curvature and Geodesics. Lie Brackets, Coordinate Vector Fields. Riemann Curvature Tensors. Calculation of Curvature Tensors in Local Coordinates. Intrinsic Calculations in Examples.

Appendix A. Linear Algebra—a Geometric Point of View.
Where Do We Start? Geometric Affine Spaces. Vector Spaces. Inner Product—Lengths and Angles. Linear Transformations and Operators. Areas, Cross Products, and Triple Products. Volumes, Orientation, and Determinants. Eigenvalues and Eigenvectors. Introduction to Tensors.

Appendix B. Analysis from a Geometric Point of View.
Smooth Functions. Invariance of Domain. Inverse Function Theorem. Implicit Function Theorem.

Appendix C. Computer Scripts.
Standard Functions. Strake. Surfaces of Revolution. Surfaces as Graph of a Function. Tangent Vectors to Curves. Curvature and Tangent Vectors. Osculating Planes. Osculating Circles. Frenet Frame. Tangent Planes to Surfaces. Curves on a Surface. Extrinisic Curvature Vectors. The Three Curvature Vectors. Ruled Surfaces. Non-dissectable Polyhedron. Sign of (Gaussian) Curvature. Mulitple Principle Directions. Gauss Map. Helicoid to Catenoid.

Bibliography.
Notation Index.
Subject Index.
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)