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by John Oprea

  • ISBN: 0883857480
  • Category: Math & Science
  • Author: John Oprea
  • Subcategory: Mathematics
  • Other formats: lit txt mbr mobi
  • Language: English
  • Publisher: The Mathematical Association of America; 2 edition (December 31, 2007)
  • Pages: 487 pages
  • FB2 size: 1647 kb
  • EPUB size: 1203 kb
  • Rating: 4.8
  • Votes: 908
Download Differential Geometry and its Applications (Mathematical Association of America Textbooks) fb2

This book studies the differential geometry of surfaces and aims to help students make the transition from the . 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 .

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. 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.

Differential geometry has a long, wonderful history. The Mathematical Association of America

Differential geometry has a long, wonderful history. The Mathematical Association of America.

Differential geometry has a long, wonderful history

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.

This book studies the differential geometry of surfaces with the goal of. .

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 geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Oprea is a member of the Mathematical Association of America and the America Mathematical Society. In 1996, Oprea was awarded the MAA's Lester R. Ford award for his Monthly article, Geometry and the Foucault Pendulum.

Creative Mathematics (Classroom Resource Materials) (Mathematical Association of America Textbooks). Differential Geometry and its Applications (Classroom Resource Materials) (Mathematical Association of America Textbooks). Категория: Математика, Прикладная математика. 5 Mb. Knot Theory (Mathematical Association of America Textbooks). 5. 9 Mb.

Publisher: Mathematical Association of America. Publication Date: 2007. John Oprea begins Differential Geometry and Its Applications with the notion that differential geometry is the natural next course in the undergraduate mathematics sequence after linear algebra. He argues that once students have studied some multivariable calculus and linear algebra, a differential geometry course provides an attractive transition to more advanced abstract or applied courses. His thoughtful presentation in this book makes an excellent case for this.

The most downloaded articles from Differential Geometry and its Applications in the last 90 days. Poisson geometry - Open archive. Real hypersurfaces with constant ϕ-sectional curvature in complex projective space. Jong Taek Cho Makoto Kimura. You can hear the local orientability of an orbifold. Sean Richardson Elizabeth Stanhope.

John Oprea Cleveland State University. The Mathematical Association of America

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Автор: John Oprea Название: Differential Geometry and its .

Differential geometry has a long, wonderful history and has found relevance in many areas. This book studies the differential geometry of surfaces with the goal of helping 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. Differential geometry is not just for mathematics majors, but also for students in engineering and the sciences. Into the mix of these ideas comes 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. 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.
Reviews about Differential Geometry and its Applications (Mathematical Association of America Textbooks) (7):
Kaim
The other reviewers are correct; that this is an excellent introductory text that fits into the undergraduate curriculum following the normal calculus sequence for scientists and engineers.
Sadly, however, its power has been greatly weakened by changes that have been made in MAPLE, an applications program that is used in the book to illustrate geometrical points. Syntactical changes made as MAPLE has evolved from version 10 to version 18 and beyond, have made it impossible to run Oprea' demonstrations. Without these demonstrations, a very interesting and useful book has been rendered less effective.

One can hope that eventual updates and a version three is in the planning process. Perhaps the author can find some interest at MAPLE about speeding up an update of this book.
Modimeena
By far my favorite undergraduate differential geometry textbook. Oprea does a great job of introducing calculus of nth dimensional surfaces, and even gives a sneak peak on the wonderful world of abstract surfaces. His chapter on minimal surfaces could be a book on its own.
Wohald
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.
Hulbine
Clear and concise examples. The hints for the exercises are very helpful.
Unh
Great bridge to upper division. Written to be very accessible.
Kage
Has several examples with programming examples.
Zieryn
Well-conceived and decently written, but horribly produced. The binding immediately gave out and the formatting was relatively poor. I would give this book a higher rating if it were more durable and easier to reference.
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.

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