Introduction To Finite And Infinite Series And Related Topics
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| Author | : J. H. Heinbockel |
| Publisher | : Trafford Publishing |
| Total Pages | : 531 |
| Release | : 2010-12 |
| Genre | : Mathematics |
| ISBN | : 1426949545 |
An introduction to the analysis of finite series, infinite series, finite products and infinite products and continued fractions with applications to selected subject areas. Infinite series, infinite products and continued fractions occur in many different subject areas of pure and applied mathematics and have a long history associated with their development. The mathematics contained within these pages can be used as a reference book on series and related topics. The material can be used to augment the mathematices found in traditional college level mathematics course and by itself is suitable for a one semester special course for presentation to either upper level undergraduates or beginning level graduate students majoring in science, engineering, chemistry, physics, or mathematics. Archimedes used infinite series to find the area under a parabolic curve. The method of exhaustion is where one constructs a series of triangles between the arc of a parabola and a straight line. A summation of the areas of the triangles produces an infinite series representing the total area between the parabolic curve and the x-axis.
| Author | : Edwin Herman |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2016-03-30 |
| Genre | : Calculus |
| ISBN | : 9781947172838 |
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
| Author | : Charles H. C. Little |
| Publisher | : Springer Nature |
| Total Pages | : 258 |
| Release | : 2022-01-10 |
| Genre | : Mathematics |
| ISBN | : 3030906469 |
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.
| Author | : Konrad Knopp |
| Publisher | : Courier Corporation |
| Total Pages | : 212 |
| Release | : 2012-09-14 |
| Genre | : Mathematics |
| ISBN | : 0486152049 |
Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
| Author | : Konrad Knopp |
| Publisher | : |
| Total Pages | : 596 |
| Release | : 1928 |
| Genre | : Series, Infinite |
| ISBN | : |
Trans from the 2nd German ed , pub 1923.
| Author | : Leonhard Euler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210216 |
From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."
| Author | : Neelacanta Sthanumoorthy |
| Publisher | : Academic Press |
| Total Pages | : 514 |
| Release | : 2016-04-26 |
| Genre | : Mathematics |
| ISBN | : 012804683X |
Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. - Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory - Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities - Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras - Focuses on Kac-Moody algebras
| Author | : Granino A. Korn |
| Publisher | : Courier Corporation |
| Total Pages | : 1154 |
| Release | : 2013-04-26 |
| Genre | : Technology & Engineering |
| ISBN | : 0486320235 |
Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.
| Author | : Robert G. Mortimer |
| Publisher | : Elsevier |
| Total Pages | : 406 |
| Release | : 2005-06-10 |
| Genre | : Science |
| ISBN | : 0080492886 |
Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. - Numerous examples and problems interspersed throughout the presentations - Each extensive chapter contains a preview, objectives, and summary - Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory - Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics
| Author | : Robert C. Wrede |
| Publisher | : McGraw Hill Professional |
| Total Pages | : 460 |
| Release | : 2002-02-20 |
| Genre | : Mathematics |
| ISBN | : 9780071375672 |
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