John H. Hubbard's Books

MacMath 9.0

A Dynamical Systems Software Package for the Macintosh TM

By: John H. Hubbard,Beverly H. West

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MacMath 9.0

A Dynamical Systems Software Package for the Macintosh TM

By: John H. Hubbard,Beverly H. West

An updated collection of twelve interactive graphics programs for the Macintosh computer, addressing differential equations and iteration. These versatile programs greatly enhance the understanding of the mathematics in these topics. Qualitative analysis of the pictures leads to quantitative results and even to new mathematics. The MacMath programs encourage experimentation and vastly increase the number of examples to which a student may be quickly exposed. The are also ideal for exploring applications of differential equations and iteration, which roughly speaking form the interface between mathematics and the realworld. This is how mathematics models a changing situation, whether it be physical forces or predator-prey populations. MacMath permits easy investigation of various models, particularly in showing the effects of a change in parameters on ultimate behavior of the system.

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Page Count

174

Publisher

Springer

Published Date

ISBN 10

1468403907

ISBN 13

9781468403909

Differential Equations: A Dynamical Systems Approach

A Dynamical Systems Approach. Part II: Higher Dimensional Systems

By: John H. Hubbard,Beverly Henderson West

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Differential Equations: A Dynamical Systems Approach

A Dynamical Systems Approach. Part II: Higher Dimensional Systems

By: John H. Hubbard,Beverly Henderson West

This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as in the life sciences, physics, and economics. After an introduction, there follow chapters on systems of differential equations, of linear differential equations, and of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The whole is rounded off with an appendix containing important theorems from parts I and II, as well as answers to selected problems.

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Page Count

622

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387943773

ISBN 13

9780387943770

Wilkes County, NC, P&Q Minutes, 1860-1868

By: John A. McGeachy

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Wilkes County, NC, P&Q Minutes, 1860-1868

By: John A. McGeachy

These volumes contains a verbatim transcription of the Wilkes County Court minutes. Two individuals have abstracted the earliest Wilkes County court minutes, those for the period 1778 to 1797. First, in 1974-1975 by Mrs. W.O. Absher, and in 2014 as 2nd edition by James Alan Williams.

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Page Count

292

Publisher

Lulu.com

Published Date

ISBN 10

1794774750

ISBN 13

9781794774759

MacMath 9.2

A Dynamical Systems Software Package for the MacintoshTM

By: John H. Hubbard,Beverly H. West

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MacMath 9.2

A Dynamical Systems Software Package for the MacintoshTM

By: John H. Hubbard,Beverly H. West

MacMath is a scientific toolkit for the Macintosh computer consisting of twelve graphics programs. It supports mathematical computation and experimentation in dynamical systems, both for differential equations and for iteration. The MacMath package was designed to accompany the textbooks Differential Equations: A Dynamical Systems Approach Part I & II. The text and software was developed for a junior-senior level course in applicable mathematics at Cornell University, in order to take advantage of excellent and easily accessible graphics. MacMath addresses differential equations and iteration such as: analyzer, diffeq, phase plane, diffeq 3D views, numerical methods, periodic differential equations, cascade, 2D iteration, eigenfinder, jacobidraw, fourier, planets. These versatile programs greatly enhance the understanding of the mathematics in these topics. Qualitative analysis of the picture leads to quantitative results and even to new mathematics. This new edition includes the latest version of the Mac Math diskette, 9.2.

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Page Count

173

Publisher

Springer

Published Date

ISBN 10

1461383781

ISBN 13

9781461383789

Manchester

By: John B. Clarke

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Manchester

By: John B. Clarke

Reprint of the original, first published in 1875.

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Page Count

582

Publisher

BoD – Books on Demand

Published Date

ISBN 10

3385236207

ISBN 13

9783385236202

Newton's Method Applied to Two Quadratic Equations in $\mathbb {C}^2$ Viewed as a Global Dynamical System

By: John H. Hubbard,Peter Papadopol

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Newton's Method Applied to Two Quadratic Equations in $\mathbb {C}^2$ Viewed as a Global Dynamical System

By: John H. Hubbard,Peter Papadopol

The authors study the Newton map $N:\mathbb{C}^2\rightarrow\mathbb{C}^2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things: The Russakovksi-Shiffman measure does not change the points of indeterminancy. The lines joining pairs of roots are invariant, and the Julia set of the restriction of $N$ to such a line has under appropriate circumstances an invariant manifold, which shares features of a stable manifold and a center manifold. The main part of the article concerns the behavior of $N$ at infinity. To compactify $\mathbb{C}^2$ in such a way that $N$ extends to the compactification, the authors must take the projective limit of an infinite sequence of blow-ups. The simultaneous presence of points of indeterminancy and of critical curves forces the authors to define a new kind of blow-up: the Farey blow-up. This construction is studied in its own right in chapter 4, where they show among others that the real oriented blow-up of the Farey blow-up has a topological structure reminiscent of the invariant tori of the KAM theorem. They also show that the cohomology, completed under the intersection inner product, is naturally isomorphic to the classical Sobolev space of functions with square-integrable derivatives. In chapter 5 the authors apply these results to the mapping $N$ in a particular case, which they generalize in chapter 6 to the intersection of any two conics.

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Page Count

160

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821840568

ISBN 13

9780821840566

Book's by John H. Hubbard

MacMath 9.0

MacMath 9.0

Differential Equations: A Dynamical Systems Approach

Differential Equations: A Dynamical Systems Approach

Wilkes County, NC, P&Q Minutes, 1860-1868

Wilkes County, NC, P&Q Minutes, 1860-1868

MacMath 9.2

MacMath 9.2

Manchester

Manchester

Newton's Method Applied to Two Quadratic Equations in $\mathbb {C}^2$ Viewed as a Global Dynamical System

Newton's Method Applied to Two Quadratic Equations in $\mathbb {C}^2$ Viewed as a Global Dynamical System

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