Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors. It is also for students in engineering and the sciences. The mix of ideas offer students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only see geodesics on surfaces, but they will also observe the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
FREE Two-Day Shipping for Students. Learn more |
| ||||||||||||||||||
 Sell Back Your Copy for $16.83
Whether you buy it used on Amazon for $44.81 or somewhere else, you can sell it back through our Book Trade-In Program at the current price of $16.83.
Used Price$44.81
Trade-in Price$16.83
Price after
Trade-in$27.98 |
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Frequently Bought Together
Editorial Reviews
Review
This is a clearly written book which could serve well as a text for an undergraduate course in differential geometry for either one or two semesters....Overall, this is an impressive book that would be an excellent text for an undergraduate course in differential geometry. --Thomas E. Cecil, Mathematical Reviews
Book Description
This book studies the differential geometry of surfaces and aims to help students make the transition from the standard university curriculum to a type of mathematics that is a unified whole, by mixing geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences.
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
23 of 26 people found the following review helpful:
5.0 out of 5 stars
clearest undergrad differential geometry text around,
By
Amazon Verified Purchase(What's this?)
This review is from: Differential Geometry and Its Applications (2nd Edition) (Hardcover)
This is a very well-written text on modern differential geometry for undergraduates. The content of the book is similar to O'Neill's "Elementary Differential Geometry" (e.g. covariant derivatives, shape operators), but it's easier to read. There are many undergrad texts around -- O'Neill, do Carmo, Pressley -- but this one is the most lucidly written one hands-down.
Afer going through Oprea, one might like to tackle O'Neill's "Elementary Differential Geometry" and Vols 2-4 of Spivak's "Comprehensive Introduction to D.G." Like O'Neill, Oprea develops surface theory using the shape operator. But Oprea takes shortcuts and doesn't develop the theory in quite the same generality as O'Neill does. For example, Oprea doesn't introduce differential forms and the exterior calculus. As a consequence, Oprea restricts himself to the Serret-Frenet equations whereas O'Neill introduces Cartan's structural equations -- of which Serret-Frenet is simply a special case -- as the method of moving frames in full generality. The structural equations are then used (by O'Neill) in both curve and surface theory.
7 of 7 people found the following review helpful:
4.0 out of 5 stars
Nice introduction and applications of differential geometry,
By A Customer
This review is from: Differential Geometry and Its Applications (2nd Edition) (Hardcover)
I found this book to be a fine introduction to this subject. I was particularly pleased with the practical examples outlined in the book. Even though I am not extremely proficient with Maple, I found the exercises using this software provided important illustrations of applications.
13 of 30 people found the following review helpful:
2.0 out of 5 stars
Not a text for a rigorous mathematics course,
By A Customer
This review is from: Differential Geometry and Its Applications (Hardcover)
This book is not to be used as a rigorous introduction to differential geometry. There are some definitions and theorems that are casually described, and the motive behind particular definitions are vague. Those not interested in MAPLE might find constant instructions for MAPLE annoying. Not to be completely negative, there are some good excercizes in the text that I especially enjoyed.
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
First Sentence:
The world of Euclidean geometry is inhabited by lines and planes. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
shortest arclength, fixed endpoint problem, ruling patch, second geodesic equation, first geodesic equation, arclength integral, unit speed curve, arclength function, shape operator, tangent developable, arclength parametrization, minimal surface equation, geodesic equations, unit speed geodesic, constant precession, polar patch, constant mean curvature surfaces, first conjugate point, umbilic point, cylindrical helix, geodesic polar coordinates, parallel vector field, twisted cylinder, geodesic curvature, pursuit curve Key Phrases - Capitalized Phrases (CAPs): (learn more)
Weierstrass E-function, Newton's Law, Curvatures Exercise, New York New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The world of Euclidean geometry is inhabited by lines and planes. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
shortest arclength, fixed endpoint problem, ruling patch, second geodesic equation, first geodesic equation, arclength integral, unit speed curve, arclength function, shape operator, tangent developable, arclength parametrization, minimal surface equation, geodesic equations, unit speed geodesic, constant precession, polar patch, constant mean curvature surfaces, first conjugate point, umbilic point, cylindrical helix, geodesic polar coordinates, parallel vector field, twisted cylinder, geodesic curvature, pursuit curve Key Phrases - Capitalized Phrases (CAPs): (learn more)
Weierstrass E-function, Newton's Law, Curvatures Exercise, New York New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
So You'd Like to...
|
|
