Solving Ordinary Differential Equations I by Wanner

Authors: Hairer, Ernst, Nørsett, Syvert P., Wanner, Gerhard

           "This is the revised version of the first edition of Vol. I published in 1987. ….Vols. I and II (SSCM 14) of Solving Ordinary Differential Equations together are the standard text on numerical methods for ODEs. ...This book is well written and is together with Vol. II, the most comprehensive modern text on numerical integration methods for ODEs. It may serve a a text book for graduate courses, ...and also as a reference book for all those who have to solve ODE problems numerically." Zeitschrift für Angewandte Mathematik und Physik

"… This book is a valuable tool for students of mathematics and specialists concerned with numerical analysis, mathematical physics, mechanics, system engineering, and the application of computers for design and planning…" Optimization

"… This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. It should be in every library, both academic and industrial." Mathematics and Computers

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A First Course in Complex Analysis with Applications by Zill

              A First Course In Complex Analysis With Applications Limits Theoretical Coverage To Only What Is Necessary, And Conveys It In A Student-Friendly Style. Its Aim Is To Introduce The Basic Principles And Applications Of Complex Analysis To Undergraduates Who Have No Prior Knowledge Of This Subject. Contents Of The Book Include The Complex Number System, Complex Functions And Sequences, As Well As Real Integrals; In Addition To Other Concepts Of Calculus, And The Functions Of A Complex Variable. This Text Is Written For Junior-Level Undergraduate Students Who Are Majoring In Math, Physics, Computer Science, And Electrical Engineering.

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Commutative Algebra with a View Toward Algebraic Geometry

        Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.

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Foxit Reader (PDF Reader)

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Foxit Reader is a lightweight and lightning quick utility for reading PDF files. PDF (Portable Document Format) is now one of the most ubiquitous document formats on the net. The problem is that Adobe Reader is both bulky and slow.

Foxit Reader on the other hand is light and quick. The proof is in the pudding for starters - compare Foxit Reader's installation file of just 12MB against Acrobat's more than 320MB and you can see why it opens documents in a snap. The key is that Foxit Reader doesn't have all those annoying splash-up screens, endless credits lists and plugins.

Foxit Reader's interface been designed with ease of use in mind. You have several toolbars available, which you can show or hide at your will and which give you access to all the available utilities: zoom, text selection, image snapshot, search tool, rotation or full screen view, among others. There is a small ad in the upper right corner, but you can deactivate it by going to the View menu and deselecting the Advertisement option.

One added bonus in Foxit Reader is that you can annotate PDF documents in several ways by highlighting text fragments, underlining them, strike them out or even add personal comments.

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Elementary Geometry of Algebraic Curves

Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.

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Elements of the Theory of Functions and Functional Analysis

Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow.

Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks.

Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.

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