ISBN: 0486450147
An accessible exposition of gravitation theory and celestial
mechanics, this classic volume was written by a distinguished
Soviet astronomer. It explains with exceptional clarity the
methods used by physicists in studying celestial phenomena. A
historical introduction explains the Ptolemaic view of planetary
motion and its displacement by the studies of Copernicus, Kepler,
and Newton. Succeeding chapters examine the making of celestial
observations and measurements; perturbed motion; satellite
technology, including a detailed look at the first artificial
satellite, Sputnik I; planetary rotation; the calculation of
units of time; and the motions of the stars. 1959 ed. Translation
by G. Yankovsky. 58 figures.
Table of Contents for An Elementary Survey of Celestial Mechanics
Introduction
1. Ancient Conceptions Concerning the Motions of the Sun, Moon,
Planets and Stars
2. The Geometry of Planetary Motions for Copernicus to Kepler
3. The Discovery of the Law of Gravitation
4. The Attraction of Material Bodies of Different Shapes
5. Experimental Detection of Attractions between Material Bodies
on Earth
6. Newton's Law--The Theoretical Basis of Celestial Motion
7. Celestial Motion and the Two-Body Problem
8. The Concept of Perturbed Motion. Celestial Mechanics and
Practical Astronomy
9. Ways of Describing Perturbed Motion. The Variational Orbit
10. The Problem of Motion in the Solar System
11. Successive Approximations in the Theory of Motion of Heavenly
Bodies
12. The Discovery of Neptune
13. Periodic and Secular Perturbations
14. Numerical Methods in Celestial Mechanics
15. Satellite Theory
16. Artificial Earth Satellites and Their Motion
17. The Motions of Asteroids
18. Planetary Motion
19. Problems of Qualitative Celestial Mechanics
10. Stellar Motions and the Law of Gravitation
12. What Is Gravitation?
Appendix
ISBN: 0486450384
This book offers advanced undergraduates and graduate students in
physics, engineering, and other natural sciences a solid
foundation in several fields of mathematics. Clear and well-written,
it assumes a previous knowledge of the theory of functions of
real and complex variables, and it is ideal for classroom use,
self-study, or as a supplementary text. Topics include vector
spaces and matrices; orthogonal functions; the roots of
polynomial equations; asymptotic expansions; ordinary
differential equations; conformal mapping; and extremum problems.
Exercises appear at the end of each chapter, along with solutions
at the back of the book. 1962 ed.
Table of Contents for Mathematics for the Physical Sciences
1. Vector Spaces and Matrices
2. Orthogonal Functions
3. The Roots of Polynomial Equations
4. Asymptotic Expansions
5. Ordinary Differential Equations
6. Conformal Mapping
7. Extremum Problems
Solutions of the Exercises
Books Referred to in the Text
Original Works Cited in the Text
Index
ISBN: 0486449998
Designed to acquaint students of particle physics already
familiar with SU(2) and SU(3) with techniques applicable to all
simple Lie algebras, this text is especially suited to the study
of grand unification theories. Author Robert N. Cahn, who is
affiliated with the Lawrence Berkeley National Laboratory in
Berkeley, California, has provided a new preface for this edition.
Subjects include the killing form, the structure of simple Lie
algebras and their representations, simple roots and the Cartan
matrix, the classical Lie algebras, and the exceptional Lie
algebras. Additional topics include Casimir operators and
Freudenthal's formula, the Weyl group, Weyl's dimension formula,
reducing product representations, subalgebras, and branching
rules. 1984 ed.
Table of Contents for Semi-Simple Lie Algebras and Their
Representations
1. SU(2)
2. SU(3)
3. The Killing Form
4. The Structure of Simple Lie Algebras
5. A Little about Representations
6. More on the Structure of Simple Lie Algebras
7. Simple Roots and the Cartan Matrix
8. The Classical Lie Algebras
9. The Exceptional Lie Algebras
10. More on Representations
11. Casimir Operators and Freudenthal’s Formula
12. The Weyl Group
13. Weyl’s Dimension Formula
14. Reducing Product Representations
15. Subalgebras
16. Branching Rules
Bibliography
Index
ISBN: 0486450163
Geared toward undergraduate mathematics majors, engineering
students, and future high school mathematics teachers, this text
offers an understanding of the principles involved in numerical
analysis. Its main theme is interpolation of the standpoint of
finite differences, least squares theory, and harmonic analysis.
Additional considerations include the numerical solutions of
ordinary differential equations and approximation through Fourier
series. More than 70 worked-out illustrative examples are
featured; and over 280 multipart exercises range from drill
problems to those requiring some degree of ingenuity on the part
of the student. Answers are provided to problems with numerical
solutions. 1967 ed. 16 figures. 33 tables.
Table of Contents for Introductory Numerical Analysis
1. Finite Difference
2. Interpolation
3. Numerical Differentiation and Integration
4. Summation of Series
5. Matrices and Systems of Linear Equations
6. The Method of Least Squares
7. Fourier Series and Harmonic Analysis
8. Numerical Solutions of Ordinary Differential Equations
Appendix--Determinants
Answers
Index
ISBN: 0486450090
In the mathematical subfield of numerical analysis, interpolation
is a procedure that assists in "reading between the lines"
in a set of tables by constructing new data points from existing
points. This rigorous presentation employs only formulas for
which it is possible to calculate error limits. Subjects include
displacement symbols and differences, divided differences,
formulas of interpolation, factorial coefficients, numerical
differentiation, and construction of tables. Additional topics
include inverse interpolation, elementary methods of summation,
repeated summation, mechanical quadrature, numerical integration
of differential equations, the calculus of symbols, interpolation
with several variables, and mechanical cubature. 1950 ed.
Table of Contents for Interpolation: Second Edition
1. Introduction
2. Displacement-Symbols and Differences
3. Divided Differences
4. Interpolation-Formulas
5. Some Applications
6. Factorial Coefficients
7. Numerical Differentiation
8. Construction of Tables
9. Inverse Interpolation
10. Elementary Methods of Summation
11. Repeated Summation
12. Laplace's and Gauss’s Summation-Formulas
13. Bernoulli's Polynomials
14. Euler's Summation-Formula
15. Lubbock's and Woolhouse's Formulas
16. Mechanical Quadrature
17. Numerical Integration of Differential Equations
18. The Calculus of Symbols
19. Interpolation with Several Variables
20. Mechanical Cubature
Appendix
ISBN: 0486450791
Simple and concise, this survey of the fundamental principles of
the method of least squares includes everything essential to the
solution of ordinary problems. Frequent references throughout the
text assist students in further extending their studies. Starting
with an overview of general principles, the text proceeds to
examine the adjustment of observations and the precision of
observations. Additional topics include the computation of the
precision measures and a consideration of miscellaneous theorems.
The treatment concludes with a survey of Gauss's method of
substitution. 1915 edition.
Table of Contents for General Principles of the Method of Least
Squares
1. General Principles
2. The Adjustment of Observations
3. The Precision of Observations
4. Computation of the Precision Measures
5. Miscellaneous Theorems
6. Gauss's Method of Substitution
Appendix
Logical Foundations for Mathematics and Computer Science,
Lecture Notes in Logic 23
Summary
Logicism, as put forward by Bertrand Russell, was predicated on a
belief that all of mathematics can be deduced from a very small
number of fundamental logical principles. In Logicism Renewed,
the author revisits this concept in light of advances in
mathematical logic and the need for languages that can be
understood by both humans and computers that require
distinguishing between the intension and extension of predicates.
Using Intensional Type Theory (ITT) the author provides a unified
foundation for mathematics and computer science, yielding a much
simpler foundation for recursion theory and the semantics of
computer programs than that currently provided by category theory.
Details
Pages: 250
Year: 2005
ISBN: 1-56881-276-0
Format: Paperback
ISBN: 1-56881-275-2
Format: Hardcover
Summary
Generating functions, one of the most important tools in
enumerative combinatorics, are a bridge between discrete
mathematics and continuous analysis. Generating functions have
numerous applications in mathematics, especially in
Combinatorics
Probability Theory
Statistics
Theory of Markov Chains
Number Theory
One of the most important and relevant recent applications of
combinatorics lies in the development of Internet search engines
whose incredible capabilities dazzle even the mathematically
trained user.
Details
ISBN: 1-56881-279-5
Year: 2005
Format: Hardcover
Pages: 192