Applied Mathematics Body and Soul, Volume 2: Integrals and Geometry in Rn

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.

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes (Springer Monographs in Mathematics)

Average customer rating:

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes (Springer Monographs in Mathematics)
Igor Chudinovich , and Christian Constanda
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Look Inside Science Books | Trip | Specialty Stores | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Engineering | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 1852338881

Book Description

The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces. The analysis, performed in spaces of distributions, is applicable to a wide variety of data with less smoothness than that required in the corresponding classical problems, and is very useful for constructing error estimates in numerical computations. This illustrative model was chosen because of its practical importance and some unusual mathematical features, but the solution technique can easily be adapted to many other hyperbolic systems of partial differential equations arising in continuum mechanics.

Optimal Stopping and Free-Boundary Problems (Lectures in Mathematics. ETH Zürich)

Average customer rating:

Optimal Stopping and Free-Boundary Problems (Lectures in Mathematics. ETH Zürich)
Goran Peskir , and Albert Shiryaev
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

Accessories:

ASIN: 3764324198

Book Description

The book aims at disclosing a fascinating connection between optimal stopping problems in probability and free-boundary problems in analysis using minimal tools and focusing on key examples.

The general theory of optimal stopping is exposed at the level of basic principles in both discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from classic ones (such as change of time, change of space, change of measure) to more recent ones (such as local time-space calculus and nonlinear integral equations).

A detailed chapter on stochastic processes is included making the material more accessible to a wider cross-disciplinary audience. The book may be viewed as an ideal compendium for an interested reader who wishes to master stochastic calculus via fundamental examples.

Areas of application where examples are worked out in full detail include financial mathematics, financial engineering, mathematical statistics, and stochastic analysis.

The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators (Grundlehren der mathematischen Wissenschaften)

Average customer rating:

The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators (Grundlehren der mathematischen Wissenschaften)
L. Hörmander
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 3540138293

Book Description

From the reviews: These two volumes (III & IV) complete L. Hoermander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators. Bull. AMS 16,1 (1987). This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation. ZBfM 612 (1987)

Linear Integral Equations (Applied Mathematical Sciences)

Average customer rating:

The right place to look.

Linear Integral Equations (Applied Mathematical Sciences)
Rainer Kress
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

General | Medicine | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Medicine | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0387987002

Book Description

This book resulted from the author's fascination with the mathematical beauty of integral equations. It is an attempt to combine theory, applications, and numerical methods, and cover each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers, the author has made the work as self-contained as possible, by requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book. Problems are included at the end of each chapter. For the second edition, in addition to corrections and adjustments throughout the text, as well as an updated reference section, new topics have been added.

Customer Reviews:

The right place to look........2000-05-23

Integral equations has become (I don't know why) a somewhat misterious subject. I've heard physicists say "I have enough with differential equations. Why to study more complicated types of equations?", or "I have enough trouble with differential equations; please don't tell me there's something else", and even "Why to study integral equations? What are they good for?".

The subject of integral equations is a natural part of analysis which serves to connect several related topics (complex analysis, harmonic analysis, potential theory, differential equations,...) and to use all the power thus gained to solve important boundary value problems of mathematics and physics.

Everyone interested in mathematical physics should get a thorough training in integral equations, and this book is the right place to start. Using a modern and comprehensive language, the author exposes the most important highlights of the theory, up to the numerical aspect, and puts the reader in the track to current research.

The contents of the book are: Normed spaces, bounded and compact operators, the Riesz theory, dual systems and Fredholm theory, regularizations in dual systems, potential theory, singular integral equations, Sobolev spaces, the heat equation, operator approximations, degenerate kernel approximation, quadrature methods, projection methods, iterative solution and stability, equations of the first kind, Tikhonov regularization, regularization by discretization, inverse scattering theory.

Includes motivation for each topic, excercises for each chapter, and extensive references. Suitable for graduate students and advanced undergraduates with a strong background in real and complex analysis.

Book Description

This book contains a systematic and self-contained treatment of Feynman-Kac path measures, their genealogical and interacting particle interpretations, and their applications to a variety of problems arising in statistical physics, biology, and advanced engineering sciences. Topics include spectral analysis of Feynman-Kac-Schrödinger operators, Dirichlet problems with boundary conditions, finance, molecular analysis, rare events and directed polymers simulation, genetic algorithms, Metropolis-Hastings type models, as well as filtering problems and hidden Markov chains.

This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviations principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods and worked out illustrations of the key aspect of the theory.

With practical and easy to use references as well as deeper and modern mathematics studies, the book will be of use to engineers and researchers in pure and applied mathematics, statistics, physics, biology, and operation research who have a background in probability and Markov chain theory.

From the reviews:

"I also recommend this book as informal reading for anyone intersted in the subject, preferably with a strong background in Markov processes; in particular, for someone also familiar with one of the many fields to which the book applies Feynman-Kac models. The book is entertaining and informative." Journal of the American Statistical Association, December 2005

Average customer rating:

Integral Equations
B. L. Moiseiwitsch
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

ASIN: 0486441628

Book Description

Geared toward upper-level undergraduate students, this text begins with a straightforward account, accompanied by simple examples of a variety of integral equations and the methods of their solution. The treatment becomes gradually more abstract, with discussions of Hilbert space and linear operators, the resolvent, Fredholm theory, and more. 1977 edition.

Heun's Differential Equations (Oxford Science Publications)

Average customer rating:

Heun's Differential Equations (Oxford Science Publications)

Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Book Description

Heun's equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger's equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada), P. Maroni (France), and Gerhard Wolf (Germany).

Linear analysis;: Measure and integral, Banach and Hilbert space, linear integral equations

Average customer rating:

Linear analysis;: Measure and integral, Banach and Hilbert space, linear integral equations
Adriaan C Zaanen
Manufacturer: North Holland Pub. Co
ProductGroup: Book
Binding: Unknown Binding

Problems in Operator Theory (Graduate Studies in Mathematics, V. 51)

Average customer rating:

Problems in Operator Theory (Graduate Studies in Mathematics, V. 51)
Y. A. Abramovich , and Charalambos D. Aliprantis
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Study & Teaching | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

An Invitation to Operator Theory (Graduate Studies in Mathematics, V. 50)

ASIN: 0821821474

Book Description

This is one of the few books available in the literature that contains problems devoted entirely to the theory of operators on Banach spaces and Banach lattices. The book contains complete solutions to the more than 600 exercises in the companion volume, An Invitation to Operator Theory, Volume 50 in the AMS series Graduate Studies in Mathematics, also by Abramovich and Aliprantis.

The exercises and solutions contained in this volume serve many purposes. First, they provide an opportunity to the readers to test their understanding of the theory. Second, they are used to demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Third, the exercises include many well-known results whose proofs are not readily available elsewhere. Finally, the book contains a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible.

The book can be very useful as a supplementary text to graduate courses in operator theory, real analysis, function theory, integration theory, measure theory, and functional analysis. It will also make a nice reference tool for researchers in physics, engineering, economics, and finance.

Books:

Books Index

Books Home

Recommended Books