Differential Geometry and Its Applications

Author: John Oprea

Publisher: MAA

ISBN: 9780883857489

Category: Mathematics

Page: 469

View: 5865

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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. Students will not only “see” geodesics on surfaces, but they will also see 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. 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.
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Differential Geometry, Global Analysis, and Topology

Proceedings of a Special Session of the Canadian Mathematical Society Summer Meeting Held June 1-3, 1990

Author: Canadian Mathematical Society. Summer Meeting,Andrew J. Nicas

Publisher: American Mathematical Soc.

ISBN: 9780821860175

Category: Mathematics

Page: 185

View: 3644

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This book contains the proceedings of a special session on differential geometry, global analysis, and topology, held during the Summer Meeting of the Canadian Mathematical Society in June 1990 at Dalhousie University in Halifax. The session featured many fascinating talks on topics of current interest. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay among geometry, global analysis, and topology. Some of the topics include applications to low dimensional manifolds, control theory, integrable systems, Lie algebras of operators, and algebraic geometry. Readers will appreciate the insight the book provides into some recent trends in these areas.
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Differential Geometry and Mathematical Physics

Author: John K. Beem,Krishan L. Duggal,American Mathematical Society,Canadian Mathematical Society

Publisher: American Mathematical Soc.

ISBN: 0821851721

Category: Mathematics

Page: 224

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This book contains the proceedings of the Special Session, Geometric Methods in Mathematical Physics, held at the joint AMS-CMS meeting in Vancouver in August 1993. The papers collected here contain a number of new results in differential geometry and its applications to physics. The major themes include black holes, singularities, censorship, the Einstein field equations, geodesics, index theory, submanifolds, CR-structures, and space-time symmetries. In addition, there are papers on Yang-Mills fields, geometric techniques in control theory, and equilibria. Containing new results by established researchers in the field, this book provides a look at developments in this exciting area of research.
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Differential Geometry and Its Applications

Proceedings of the 10th International Conference, DGA 2007, Olomouc, Czech Republic, 27-31 August 2007

Author: Old?ich Kowalski,Olga Krupkova

Publisher: World Scientific

ISBN: 9812790608

Category: Mathematics

Page: 717

View: 1061

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This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture ?Leonhard Euler ? 300 years on? by R Wilson. Notable contributors include J F Cari¤ena, M Castrill¢n L¢pez, J Erichhorn, J-H Eschenburg, I Kol ?, A P Kopylov, J Korba?, O Kowalski, B Kruglikov, D Krupka, O Krupkov , R L‚andre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Mu¤oz Masqu‚, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slov k, J Szilasi, L Tam ssy, P Walczak, and others.
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The Heart of Calculus

Explorations and Applications

Author: Philip M. Anselone,John W. Lee

Publisher: The Mathematical Association of America

ISBN: 0883857871

Category: Mathematics

Page: 245

View: 7558

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This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs. The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives. The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth. A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.
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Differential Geometry of Curves and Surfaces

Author: Thomas F. Banchoff,Stephen T. Lovett

Publisher: CRC Press

ISBN: 1482247372

Category: Mathematics

Page: 430

View: 2226

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Differential Geometry of Curves and Surfaces, Second Edition takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students' geometric intuition through interactive computer graphics applets suppor
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Partial Differential Equations and Their Applications

Author: Canadian Mathematical Society. Seminar

Publisher: American Mathematical Soc.

ISBN: 0821806874

Category: Mathematics

Page: 315

View: 6540

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This volume presents lectures given at the 1995 Annual Seminar of the Canadian Mathematical Society on Partial Differential Equations and Their Applications held at the University of Toronto in June 1995. The conference consisted of a combination of minicourses, invited presentations, and contributed talks. In this volume readers will find contributions on a variety of topics related to PDE, such as spectral asymptotics, harmonic analysis, differential operators in hyperbolic manifolds, applications to geometry, mathematical physics, hydrodynamics, and the interaction between theory and numerical methods in PDE.
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