Steven G. Krantz – författare

Here''s the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more.

If you''re interested in learning the fundamentals of discrete mathematics but can''t seem to get your brain to function, then here''s your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts.

Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains this challenging topic in an effective and enlightening way. You will learn about logic, proofs, functions, matrices, sequences, series, and much more. Concise explanations, real-world examples, and worked equations make it easy to understand the material, and end-of-chapter exercises and a final exam help reinforce learning.

This fast and easy guide offers:

Simple enough for a beginner, but challenging enough for an advanced student, Discrete Mathematics Demystified is your integral tool for mastering this complex subject.

Calculate this: learning CALCULUS just got a whole lot easier!

Stumped trying to understand calculus? Calculus Demystified, Second Edition, will help you master this essential mathematical subject.

Written in a step-by-step format, this practical guide begins by covering the basics--number systems, coordinates, sets, and functions. You''ll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key concepts.

It''s a no-brainer! You''ll get:

Simple enough for a beginner, but challenging enough for an advanced student, Calculus Demystified, Second Edition, is one book you won''t want to function without!

Krantz takes the reader on a journey around the globe and through centuries of history , exploring the many transformations that mathematical proof has undergone from its inception at the time of Euclid and Pythagoras to its versatile, present-day use . The author elaborates on the beauty, challenges and metamorphisms of thought that have accompanied the search for truth through proof.

The first two chapters examine the early beginnings of concept of proof and the creation of its elegant structure and language, touching on some of the logic and philosophy behind these developments. The history then unfolds as the author explains the changing face of proofs. The more well-known proofs , the mathematicians behind them, and the world that surrounded them are all highlighted . Each story has its own unique past; there was often a philosophical, sociological, technological or competitive edge that restricted or promoted progress. But the author''s commentary and insights create a seamless thread throughout the many vignettes.

Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. This is shown in noting some of the more prominent discussions currently underway, such as Gorenstein''s effort to classify finance groups, Thomas Hale''s resolution of the Kepler sphere-packing problem, and other modern tales. Most of the proofs are discussed in detail with figures and

Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme.

This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis –and also to spark the interest of seasoned workers in the field – the book imparts a solid education both in complex analysis and in how modern mathematics works.

This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces.

The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.