Introduction To Graph Theory Dover Books On Mathematics

Total Download : 3597 | Total Read : 5679 | Total Likes: 3637

Author by : Richard J. Trudeau
Languange Used : English
Release Date : 1994-02-09
Publisher by : Dover Publications

Description :

A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg. Exercises are included at the end of each chapter. "The topics are so well motivated, the exposition so lucid and delightful, that the book's appeal should be virtually universal . . . Every library should have several copies" — Choice. 1976 edition.



Introduction To Analysis Dover Books On Mathematics

Total Download : 1434 | Total Read : 7630 | Total Likes: 9009

Author by : Maxwell Rosenlicht
Languange Used : English
Release Date : 1985-02-01
Publisher by : Dover Publications

Description :

This well-written text provides excellent instruction in basic real analysis, giving a solid foundation for direct entry into advanced work in such fields as complex analysis, differential equations, integration theory, and general topology. The nominal prerequisite is a year of calculus, but actually nothing is assumed other than the axioms of the real number system. Because of its clarity, simplicity of exposition, and stress on easier examples, this material is accessible to a wide range of students, of both mathematics and other fields.
Chapter headings include notions from set theory, the real number system, metric spaces, continuous functions, differentiation, Riemann integration, interchange of limit operations, the method of successive approximations, partial differentiation, and multiple integrals.
Following some introductory material on very basic set theory and the deduction of the most important properties of the real number system from its axioms, Professor Rosenlicht gets to the heart of the book: a rigorous and carefully presented discussion of metric spaces and continuous functions, including such topics as open and closed sets, limits and continuity, and convergent sequence of points and of functions. Subsequent chapters cover smoothly and efficiently the relevant aspects of elementary calculus together with several somewhat more advanced subjects, such as multivariable calculus and existence theorems. The exercises include both easy problems and more difficult ones, interesting examples and counter examples, and a number of more advanced results.
Introduction to Analysis lends itself to a one- or two-quarter or one-semester course at the undergraduate level. It grew out of a course given at Berkeley since 1960. Refinement through extensive classroom use and the author’s pedagogical experience and expertise make it an unusually accessible introductory text.



An Introduction To Ordinary Differential Equations Dover Books On Mathematics

Total Download : 8237 | Total Read : 8914 | Total Likes: 6716

Author by : Earl A. Coddington
Languange Used : English
Release Date : 1989-03-01
Publisher by : Dover Publications

Description :

"Written in an admirably cleancut and economical style." — Mathematical Reviews.
This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented.
The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations.
Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student's technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems.



A Combinatorial Introduction To Topology Dover Books On Mathematics

Total Download : 7346 | Total Read : 6478 | Total Likes: 4758

Author by : Michael Henle
Languange Used : English
Release Date : 1994-03-14
Publisher by : Dover Publications

Description :

The creation of algebraic topology is a major accomplishment of 20th-century mathematics. The goal of this book is to show how geometric and algebraic ideas met and grew together into an important branch of mathematics in the recent past. The book also conveys the fun and adventure that can be part of a mathematical investigation.
Combinatorial topology has a wealth of applications, many of which result from connections with the theory of differential equations. As the author points out, "Combinatorial topology is uniquely the subject where students of mathematics below graduate level can see the three major divisions of mathematics — analysis, geometry, and algebra — working together amicably on important problems."
To facilitate understanding, Professor Henle has deliberately restricted the subject matter of this volume, focusing especially on surfaces because the theorems can be easily visualized there, encouraging geometric intuition. In addition, this area presents many interesting applications arising from systems of differential equations. To illuminate the interaction of geometry and algebra, a single important algebraic tool — homology — is developed in detail.
Written for upper-level undergraduate and graduate students, this book requires no previous acquaintance with topology or algebra. Point set topology and group theory are developed as they are needed. In addition, a supplement surveying point set topology is included for the interested student and for the instructor who wishes to teach a mixture of point set and algebraic topology. A rich selection of problems, some with solutions, are integrated into the text.



Control System Design An Introduction To State Space Methods Dover Books On Electrical Engineering

Total Download : 1848 | Total Read : 4351 | Total Likes: 4086

Author by : Bernard Friedland
Languange Used : English
Release Date : 2005-03-24
Publisher by : Dover Publications

Description :

Addressed not only to students but also to professional engineers and scientists, this volume introduces state-space methods for direct applications to control system design, in addition to providing background for reading the periodical literature. Its presentation, therefore, is suitable both for those who require methods for achieving results and those more interested in using results than in proving them.
Topics include feedback control; state-space representation of dynamic systems and dynamics of linear systems; frequency-domain analysis; controllability and observability; and shaping the dynamic response. Additional subjects encompass linear observers; compensator design by the separation principle; linear, quadratic optimum control; random processes; and Kalman filters.
Concrete examples of how state-space methods can be used to advantage in several representative applications are woven into the fabric of the text and the homework problems. Many of the models are drawn from aerospace and inertial instrumentation; other examples are derived from chemical process control, maritime operations, robotics, and energy systems.



Introduction To Graph Theory Dover Books On Mathematics By Richard J Trudeau 2003 03 17

Total Download : 1526 | Total Read : 1992 | Total Likes: 2200

Author by : Richard J. Trudeau
Languange Used :
Release Date :
Publisher by : Dover Publications Inc.

Description :