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eBook Differential Geometry and Its Applications download

by John Oprea

eBook Differential Geometry and Its Applications download ISBN: 0133407381
Author: John Oprea
Publisher: Prentice Hall College Div; 1 edition (October 28, 1996)
Language: English
Pages: 387
ePub: 1347 kb
Fb2: 1449 kb
Rating: 4.9
Other formats: docx txt lrf lit
Category: Math Sciences
Subcategory: Mathematics

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.

This book studies the differential geometry of surfaces with the goal of helping students make the transition from . Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences.

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.

Differential geometry provides the perfect transition course to higher math- ematics and its applications. Suppose a robot arm with three fingers at its end is to move and grasp an object. It is a subject which allows students to see mathematics for what it is - not the compartmentalized courses of a stan- dard university curriculum, but a unified whole mixing together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and various notions from the sciences. How should a path be programmed for the "hand" so that the fingers end up in the proper "grasping" position?

Differential Geometry and Its Applications by John Opera .

Differential Geometry and Its Applications by John Opera, Elements of Differential Geometry by Millman and Parker, notes on Differential Geometry by Hicks, Elementary Differential Geometry by Barrett O'Neil . Apart from the above two books, as mentioned in another answer, you could refer The Large Scale Structure of Space-Time by Hawking and Ellis.

Designed not just for the math major but for all readers of science, this book provides an introduction to the basics of the calculus of variations and optimal control theory as well as differential geometry. It then applies these essential ideas to understand various phenomena, such as soap film formation and particle motion on surfaces.

Автор: John Oprea Название: Differential Geometry and its Applications Издательство: Cambridge Academ .

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.

Start by marking Differential Geometry and Its Applications as Want to Read .

Start by marking Differential Geometry and Its Applications as Want to Read: Want to Read savin. ant to Read. NEW - New Maple projects for calculation and visualization - Provides students with another practical side to pure math. NEW - New examples for Gauss-Bonnet.

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.

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.

Appropriate for undergraduate courses in Differential Geometry.Designed not just for the math major but for all students of science, this text provides an introduction to the basics of the calculus of variations and optimal control theory as well as differential geometry. It then applies these essential ideas to understand various phenomena, such as soap film formation and particle motion on surfaces.
Comments: (7)
Runemane
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.
Thomeena
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.
Unde
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.
Jonariara
Clear and concise examples. The hints for the exercises are very helpful.
Malara
Great bridge to upper division. Written to be very accessible.
Yndanol
Has several examples with programming examples.
Sardleem
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.