DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS OPREA PDF

Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options. Differential Geometry and Its Applications 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. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction.

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Differential Geometry and Its Applications. John Oprea. Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of 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 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.

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. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints. 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.

Constant Mean Curvature Surfaces. Geodesies Metrics and Isometries. Holonomy and the GaussBonnet Theorem. The Calculus of Variations and Geometry. A Glimpse at Higher Dimensions. A List of Examples. Examples in Chapter 3. Examples in Chapter 7. B Hints and Solutions to Selected Problems.

Suggested Projects for Differential Geometry. About the Author. Cornea, G. Lupton and D.

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Differential Geometry and Its Applications

John F. Oprea , Cleveland State University Follow. Differential geometry has a wide range of applications, going far beyond strictly mathematical pursuits to include architecture, engineering, and just about every scientific discipline. John Oprea's second edition of Differential Geometry and Its Applications illuminates a wide range of ideas that can be beneficial to students majoring not only in mathematics but also in other fields. Differential Geometry and Its Applications was written to help students adapt to "a type of mathematics that is a unified whole," one that mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and various notions from the sciences. The textbook touches on many different mathematical concepts, including aspects of linear algebra, the Gauss-Bonnet Theorem, and geodesics. It also encourages students to visualize and experiment with the ideas they are studying through their use of the computer program Maple.

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