Differential Geometry And Its Applications (classroom Resource Materials) (mathematical Association Of America Textbooks)

E-Book Overview

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. It mixes together 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. The mix of ideas offer students 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 observe 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. 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.

E-Book Information

  • Year: 2,007

  • Edition: 2

  • Pages: 496

  • Pages In File: 496

  • Language: English

  • Topic: 121

  • Issue: 2011 12 30

  • Identifier: 0883857480,9780883857489

  • Ddc: 516.3/6

  • Lcc: QA641 .O67 2007

  • Org File Size: 60,808,917

  • Extension: pdf

  • Tags: Математика Топология Дифференциальная геометрия и топология Дифференциальная геометрия

  • Toc: 1......Page 1 0001......Page 2 0002......Page 3 0003......Page 4 0004......Page 5 0005......Page 6 0006......Page 7 0007......Page 8 0008......Page 9 0009......Page 10 0010......Page 11 0011......Page 12 0012......Page 13 0013......Page 14 0014......Page 15 0015......Page 16 0016......Page 17 0017......Page 18 0018......Page 19 0019......Page 20 0020......Page 21 0021......Page 22 0022......Page 23 0023......Page 24 0024......Page 25 0025......Page 26 0026......Page 27 0027......Page 28 0028......Page 29 0029......Page 30 0030......Page 31 0031......Page 32 0032......Page 33 0033......Page 34 0034......Page 35 0035......Page 36 0036......Page 37 0037......Page 38 0038......Page 39 0039......Page 40 0040......Page 41 0041......Page 42 0042......Page 43 0043......Page 44 0044......Page 45 0045......Page 46 0046......Page 47 0047......Page 48 0048......Page 49 0049......Page 50 0050..

You might also like

Mathematical Models In Biology: Solution Manual
Authors: Elizabeth S. Allman , John A. Rhodes    247    0


Computationalism: New Directions
Authors: Matthias Scheutz    270    0




Mathematical Writing
Authors: Donald E. Knuth    228    0


Proceedings Of International Congress Of Mathematicians
Authors: S.D. Chatterji    188    0



Frobenius Splitting Methods In Geometry And Representation Theory
Authors: Michel Brion , Shrawan Kumar (auth.)    236    0


Set Theory And Its Philosophy: A Critical Introduction
Authors: Michael Potter    210    0


Combinatorial Commutative Algebra
Authors: Ezra Miller , Bernd Sturmfels    220    0