Average customer rating:
- Fantastic - for the scientist
- a book worth keeping
- Phenomenal
- You should buy this, despite its flaws
- The perfect first book in differential geometry
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The Geometry of Physics: An Introduction, Second Edition
Theodore Frankel
Manufacturer: Cambridge University Press
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Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics)
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Geometrical Methods of Mathematical Physics
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General Relativity
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Lie Groups, Lie Algebras, and Some of Their Applications
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Advanced Calculus: A Differential Forms Approach
ASIN: 0521833302 |
Book Description
Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact Lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. First Edition Hb (1997): 0-521-38334-X First Edition Pb (1999): 0-521-38753-1
Customer Reviews:
Fantastic - for the scientist.......2007-07-18
A very good book: buy it. But only if you are a scientist or student of physics/mathematics. This is not popular-science-common-public level.
a book worth keeping.......2007-05-01
This book can be quite confusing if you start without any background on the idea of manifold or knows nothing about general relativity. However, it does have strong points:
1. The notation is very up-to-date, and is entirely coordinate-independant approach.
2. The author explains in great details of formulation of modern differential geometry, and the details are comparatively lacking in other reference books.
3. The author never hesitate to use graphs and diagrams to illustrate points, and stroke nice balance in between mathematics rigor and physical insight.
Although it appears quite verbose at some point, it is mainly because differential geometry is such a heavy subject. Another book nice to have as companion reading is Goldburg's "Tensor analysis on Manifold", a terse, well-written text book.
Phenomenal .......2006-11-13
I just finished reading this book and I found it phenomenal. The physical ideas are made very clear in a natural mathematical framework.
You should buy this, despite its flaws.......2006-03-03
The other reviews on this page give this book anywhere from 1 to 5 stars, and they are all correct in their own way. The book is inspired, deep and full of physics applications and insights. On the other hand, it skims over mathematical rigor to a large degree and focuses more on defining things, getting a feel for them and moving on to application.
My advice: buy the book for its strengths, and read other books in parallel if you need more rigor. But still, buy it.
Also, things can be confusing on the first two or three reads, but keep at it and you will be glad you did.
The perfect first book in differential geometry.......2005-01-28
Differential geometry can be a very intimidating subject due to its heavy formalism. There are complete books (such as Kobayashi& Nomizu) very good as reference books, and there very few books that show the reader the picture behind the formulas.
This is one such book. It tells you the intuition behind each construction and from this point of view it has many things in common with Arnold's famous book on Math. Methods in Classical Mechanics. But where as Arnold does not pay too much attention to formalism, this book achieves this task as well. It shows the reader how to do those impossible computations as well.
This is definitely the first place to look at if you want to really learn differential geometry. If it seems difficult it is only because the subject is so.
Average customer rating:
- Numerical Geometry of Images
- Some additional info.
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Numerical Geometry of Images: Theory, Algorithms, and Applications
Ron Kimmel
Manufacturer: Springer
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Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
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Handbook of Mathematical Models in Computer Vision
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Geometric Level Set Methods in Imaging, Vision, and Graphics
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Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (Cambridge ... on Applied and Computational Mathematics)
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Modelling and Control of Robot Manipulators (Advanced Textbooks in Control and Signal Processing)
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An Introduction to Copulas (Springer Series in Statistics)
ASIN: 0387955623 |
Book Description
Numerical Geometry of Images examines computational methods and algorithms in image processing. It explores applications like shape from shading, color-image enhancement and segmentation, edge integration, offset curve computation, symmetry axis computation, path planning, minimal geodesic computation, and invariant signature calculation. In addition, it describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Graduate students, professionals, and researchers with interests in computational geometry, image processing, computer graphics, and algorithms will find this new text / reference an indispensable source of insight of instruction.
Customer Reviews:
Numerical Geometry of Images.......2004-09-26
A very well-written, interesting and useful book covering a wide range of topics in image processing and computer vision and beyond. A good balance between theory and implementation issues that make the things work. A 100% recommendation to students and specialists in the field.
Some additional info........2004-04-18
The book is an extended version of my lecture notes. Including
introduction to variational methods, differential geometry,
level sets and fast marching numerical methods, and geometric active
contours for segmentation with Matlab pseudo code, 3D face recognition,
texture mapping and more applications.
Thanks to the many who bought the book.
Book Description
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Customer Reviews:
Terrific geometry book for physicists.......2006-05-07
Advanced mathematics, such as differential geometry and topology, plays an important role in many areas of physics. This excellent book covers one of these topics, differential geometry. This is a topic essential for understanding general relativity and gauge theory. There are several good books aimed at physicists that cover differential geometry. While some of these have a broader scope than this book, nevertheless this book is my favorite one for differential geometry.
The topics covered include those necessary for reading advanced treatments of general relativity (such as Wald or Misner/Thorne/Wheeler). These include manifolds, fiber bundles, tangent/cotangent bundles, forms, Lie derivatives, Killing vectors and Lie groups.
Following this basic material a chapter covering some applications to physics, one example is electromagnetism. Up to this point the consideration of manifolds had been fairly general. In the final chapter the implications of adding a connection, and then a metric, are considered.
Why do I think this book is so good? It's not the breadth of material covered, this book is very focused on a limited range of material. It's the quality of the presentation for what it does cover. The development follows a logical order, the writing is exceptionally clear and the diagrams are very useful since Schutz explains them so well.
Integrability conditions discussed.......2004-01-21
Written in a attractive and even seductive way, relying more on Lie algebraic language than is typical, this book is probably as stimulating an intro. to modern geometry as you can find, within certain limits. The section on noncoordinate bases might have been more clearly written, however. Frobenius's theorm is discussed, something that Fomenko et al should have covered, and the section on connections can be worked throuigh independently of the heavy machinery of exterior differential forms, which is attractive for physics students.
Not as good as "a first course in general relativity".......2001-10-23
I had read first the "first course in general relativity"and was exited,so i fygured out that this book from the same author would reach the same standards,but it didnt.If Ihadnt read the first book from Schutz this book would be incomprenheceble.The greatest problem i think is the lack of exercices.Without them you cant really go anywhere.Another problem ,i believe,is the short space given to analyzeeach topic.Eventhough i understand tensor calculus very well I just cant get anywhere with the differential forms.
Eventhough its not the worst book out there its not the best either.My advise,buy a better book.
A Very Accessible Book ! Buy It !.......2000-11-06
This is a very enjoyable and clearly written book. From a physics point of view the approach is rather abstract, so although differential geometry is developed from 'scratch', it is probably better to have studied a more elementary text on the theory of 2-surfaces in 3-space first (eg Faber's book Differential Geometry and Relativity Theory ). The first chapter sets the mathematical background expected of the reader. The rudiments of analysis, topology, calculus of many variables and basic linear algebra is reviewed.The ensuing chapters cover differential geometry from a 'modern' viewpoint but the style is quite relaxed and the links to 'co-ordinate approach' are well explained. The exercises concentrate on the abstract approach. Throughout the book the underlying structure of manifolds is concentrated upon. No extra 'structure' eg connections and 'distance' concepts are added until the final chapter on Riemannian spaces. For example the metric tensor throughout the body of the book is merely used as a map between a tangent space and its dual space. It is only used as a 'distance' operator in the final chapter.For the purposes of independent study this is a sound book, there are hints and partial solutions for many of the exercises, which is always a welcome feature for those studying entirely on their own.
A Great Introduction to Diff. Geometry.......2000-08-08
This book presents the basic concepts of differential geometry in a clear, concise manner using modern notation. Schutz's writing style is very readable and there is a considerable breadth of coverage. In areas where one might wish for greater depth, Schutz provides excellent references. My only regret is that the physical applications chapters weren't longer. An excellent starter book and a good quick reference if you continue in differential geometry, GR or field theory.
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Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves
Denis Serre
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Systems of Conservation Laws 2: Geometric Structures, Oscillations, and Initial-Boundary Value Problems
ASIN: 0521582334 |
Book Description
Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self contained, with large numbers of exercises and full discussion of all the ideas. This makes it an ideal text for graduate courses in the area of partial differential equations.
Book Description
This established and authoritative text focuses on the design and analysis of nonlinear control systems. The author considers the latest research results and techniques in this updated and extended edition. Examples are given from mechanical, electrical and aerospace engineering. The approach consists of a rigorous mathematical formulation of control problems and respective methods of solution. The two appendices outline the most important concepts of differential geometry and present some specific findings not often found in other standard works. The book is, therefore, suitable both as a graduate and undergraduate text and as a source for reference.
Customer Reviews:
Isidori's Magnum Opus.......2003-01-04
This is simply the best book written on nonlinear control theory. The contents form the basis for feedback linearization techniques, nonlinear observers, sliding mode control, understanding relative degree, nonminimum phase systems, exact linearization, and a host of other topics. A careful reading of this book will provide vast rewards. A fantastic book.
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- comprehensive but biased view of tensor analysis...
- The definitive book on tensors in analytical mechanics
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Tensor Calculus and Analytical Dynamics (Engineering Mathematics)
John G. Papastavridis
Manufacturer: CRC
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ASIN: 0849385148 |
Book Description
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: o tensor calculus in nonholonomic variables o Pfaffian nonholonomic constraints o related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.
Customer Reviews:
comprehensive but biased view of tensor analysis..........2006-01-26
Papastavridis is an author with a unique attitude towards mathematics. He avoids the coordinate free formulation of tensors on manifolds. In his view, the exterior differential calculus is an esoteric abstraction which is hard to grasp by many and thus has the danger of turning down able people from embarking on doing research in analytical mechanics. This is basically a recapitulation of his views which have been explicitly stated within the book in a broader context.
With that said, don`t expect to find anything pertaining to modern differential geometric view of mechanics. However, this book presents one of the most extensive survey of tensor analysis with indices. The bibliography is indeed comprehensive, and a welcome feature in such a monograph.
Personally, I benefitted alot from this book both in terms of physical aspects of mechanics and in terms of classical tensor analysis. However, I still believe in the power of mathematical abstractions in grasping of the holistic image of a physical and/or mathematical entity. In this respect, the language of differential forms is rather important and allows further useful topological generalizations like cohomology. It is true that the current engineering/science curricula does not leave much space for the modern view, but this is ultimately where it will be heading to. Despite his dislike of exterior calculus, Papastavridis inevitably builds a strong basis for delving into tensor analysis on manifolds. For the latter Bishop and Goldberg is still the best choice with an unbeatable price.
The definitive book on tensors in analytical mechanics.......2000-08-28
This book is not a text book. It is, in some sense, the final word on tensor formalism in finite degree of freedom (analytical) mechanics. It is one of the most scholarly books I have come across. The list of references is very exhaustive and the author is well read in the literature on the subject, not just in english, but also in russian, french, and german. The style is clear and concise, the notation is carefully chosen and summarized in a useful section where conventions, notation, and basic formulae are listed.
Average customer rating:
- Calculus + Linear Algebra in One Series
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Applied Mathematics Body and Soul, Volume 1: Derivatives and Geometry in R3
K. Eriksson ,
D. Estep , and
C. Johnson
Manufacturer: Springer
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ASIN: 354000890X |
Book Description
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.
Volume I (Derivatives and Geometry in R3) presents basics of Calculus starting with the construction of the natural, rational, real and complex numbers, and proceeding to analytic geometry in two and three space dimensions, Lipschitz continuous functions and derivatives, together with a variety of applications.
Volume II (Integrals and Geomtery in Rn) develops the Riemann integral as the solution to the problem of determining a function given its derivative, and proceeds to generalizations in the form of initial value problems for general systems of ordinary differential equations, including a variety of applications. Linear algebra including numerics is also presented.
Volume III (Calculus in Several Dimensions) presents Calculus in several variables including partial derivatives, multi-dimensional integrals, partial differential equations and finite element methods, together with a variety of applications modeled as systems of partial differential equations.
The authors are leading researchers in Computational Mathematics who have written various successful books.
Further information on Applied Mathematics: Body and Soul can be found at http://www.phi.chalmers.se/bodysoul/.
Customer Reviews:
Calculus + Linear Algebra in One Series.......2005-01-05
I wish Amazon would put a text list of the "Table of Contents" for books.
Sorry about the length: Amazon does not allow postings for each volume in a series!
Volume 1: Derivatives and Geometry in R^3
1. What is Mathematics?
2. The Mathematics Library
3. Introduction to Modeling
4. A Very Short Calculus Course
5. Natural Numbers and Integers
6. Mathematical Induction
7. Rational Numbers
8. Pythagoras and Euclid
9. What is a Function?
10. Polynomial Functions
11. Combinations of Functions
12. Lipschitz Continuity
13. Sequences and Limits
14. The Square Root of Two
15. Real Numbers
16. The Bisection Algorithm for f(x) = 0
17. Do Mathematicians Quarrel?
18. The Function y = x^r
19. Fixed Points and Contraction Mappings
20. Analytic Geometry in R^2
21. Analytic Geometry in R^3
22. Complex Numbers
23. The Derivative
24. Differentiation Rules
25. Newton's Method
26. Galileo, Newton, Hooke, Malthus and Fourier
Volume 2: Integrals and Geometry in R^n
27: The Integral
28: Properties of the Integral
29. The Logarithm log(x)
30. Numerical Quadrature
31. The Exponential Function exp(x) = e^x
32. Trigonometric Functions
33. The Functions exp(z), log(z), sin(z) and cos(z) for z e C
34. Techniques of Integration
35. Solving Differential Equations Using the Exponential
36. Improper Integrals
37. Series
38. Scalar Autonomous Initial Value Problems
39. Separable Scalar Initial Value Problems
40. The General Initial Value Problem
41. Calculus Tool Bag I
42. Analytic Geometry in R^n
43. The Spectral Theorem
44. Solving Linear Algebraic Systems
45. Linear Algebra Tool Bag
46. The Matrix Exponential exp(xA)
47. Lagrange and the Principle of Least Action
48. N-Body Systems
49. The Crash Model
50. Electrical Circuits
51. String Theory
52. Piecewise Linear Approximation
53. FEM for Two-Point Boundary Value Problems
Volume 3: Calculus in Several Dimensions
54. Vector-Valued Functions of Several Real Variables
55. Level Curves/Surfaces and the Gradient
56. Linearization and Stability of Initial Value Problems
57. Adaptive Solvers for IVPs
58. Lorenz and the Essence of Chaos
59. The Solar System
60. Optimization
61. The Divergence, Rotation and Laplacian
62. Meteorology and Coriolis Forces
63. Curve Integrals
64. Double Integrals
65. Surface Integrals
66. Multiple Integrals
67. Gauss' Theorem and Green's Formula in R^2
68. Gauss' Theorem and Green's Formula in R^3
69. Stoke's Theorem
70. Potential Fields
71. Center of Mass and Archimedes' Principle
72. Newton's Nightmare
73. Laplacian Models
74. Chemical Reactions
75. Calculus Tool Bag II
76. Piecewise Linear Polynomials in R^2 and R^3
77. FEM for Boundary Value Problems in R^2 and R^3
78. Inverse Problems
79. Optimal Control
80. Differential Equations Tool Bag
81. Applications Tool Bag
82. Analytic Functions
83. Fourier Series
84. Fourier Transforms
85. Analytic Functions Tool Bag
86. Fourier Analysis Tool Bag
87. Incompressible Navier-Stokes: Quick and Easy
This book/series has some problems; however, the attempt to wed Mathematical Analysis, Numerical Computation, and Application AND to also talk about Calculus and Linear Algebra at the same time -- makes these three books worth a look.
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Finite Element Methods for Maxwell's Equations (Numerical Analysis and Scientific Computation Series)
Peter Monk
Manufacturer: Oxford University Press, USA
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The Finite Element Method in Electromagnetics
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Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences)
ASIN: 0198508883 |
Book Description
Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.
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Handbook of Computational Geometry
Manufacturer: North Holland
ProductGroup: Book
Binding: Hardcover
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ASIN: 0444825371 |
Book Description
Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.
Book Description
Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances.
In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study.
While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas.
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