This book covers classical differential geometry with modern applications to a variety of disciplines including math and science. Surfaces, curvatures, geometry of curves, holonomy and the Gauss-Bonnet Theorem, minimal surfaces and complex variables, geodesics, least area surfaces of revolution, surfaces of Delaunay, and more. For mathematicians, scientists and other professionals wish to learn how classic differential theory applies to practical situations in math, science and industry.

Differential Geometry and Its Applications

Science & Math

Oprea, John

Mathematics

PRENTICE/HALL

Algebraic Models in Geometry (Oxford Graduate Texts in Mathematics)

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kähler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods.

Félix, Yves

Tanré, Daniel

Oxford University Press

Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. 
The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. 
Through the Maple® applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. 
The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. 
® Waterloo Maple, Inc., Ontario, Canada.

The Mathematics of Soap Films: Explorations With Maple (Student Mathematical Library, Vol. 10) (Student Mathematical Library, V. 10)

Amer Mathematical Society

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.

Differential Geometry and its Applications (Mathematical Association of America Textbooks)

The Mathematical Association of America

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Books by Oprea, John

See the best price to sell, buy, or rent books by Oprea, John. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Differential Geometry and Its Applications

Algebraic Models in Geometry (Oxford Graduate Texts in Mathematics)

The Mathematics of Soap Films: Explorations With Maple (Student Mathematical Library, Vol. 10) (Student Mathematical Library, V. 10)

Differential Geometry and its Applications (Mathematical Association of America Textbooks)