"Symmetry in Mechanics is directed to students at the undergraduate
level and beyond, and offers a lovely presentation of the
subject...The first chapter presents a standard derivation of the
equations for two-body planetary motion. Kepler's laws are then
obtained and the rule of conservation laws is emphasized. .....
Singer uses this example from classical physics throughout the book
as a vehicle for explaining the concepts of differential geometry
and for illustrating their use. ... These ideas and techniques will
allow the reader to understand advanced texts and research
literature in which considerably more difficult problems are
treated and solved by identical or related methods. The book
contains 122 student exercises, many of which are solved in an
appendix. The solutions, especially, are valuable for showing how a
mathematician approaches and solves specific problems. Using this
presentation, the book removes some of the language barriers that
divide the worlds of mathematics and physics..." ---- Physics Today
Recent years have seen the appearance of several books bridging
the gap between mathematics and physics; most are aimed at the
graduate level and above. Symmetry in Mechanics: A Gentle, Modern
Introduction is aimed at anyone who has observed that symmetry
yields simplification and wants to know why. The monograph was
written with two goals in mind: to chip away at the language
barrier between physicists and mathematicians and to link the
abstract constructions of symplectic mechanics to concrete,
explicitly calculated examples. The context is the two-body
problem, i.e., the derivation of Kepler's Laws of planetary motion
from Newton's laws of gravitation. After astraightforward and
elementary presentation of this derivation in the language of
vector calculus, subsequent chapters slowly and carefully introduce
symplectic manifolds, Hamiltonian flows, Lie group actions, Lie
algebras, momentum maps and symplectic reduction, with many
examples, illustrations and exercises. The work ends with the
derivation it started with, but in the more sophisticated language
of symplectic and differential geometry. For the student,
mathematician or physicist, this gentle introduction to mechanics
via symplectic reduction will be a rewarding experience. The
freestanding chapter on differential geometry will be a useful
supplement to any first course on manifolds. The book contains a
number of exercises with solutions, and is an excellent resource
for self-study or classroom use at the undergraduate level.
Requires only competency in multivariable calculus, linear algebra
and introductory physics.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
