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Author: Haakon Waadeland
Publisher: Springer Science & Business Media
ISBN: 9491216376
Category : Mathematics
Languages : en
Pages : 321
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Book Description
Continued Fractions consists of two volumes — Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given. This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.
Author: Haakon Waadeland
Publisher: Springer Science & Business Media
ISBN: 9491216376
Category : Mathematics
Languages : en
Pages : 321
Get Book Here
Book Description
Continued Fractions consists of two volumes — Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given. This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.
Author: Bowen Kerins
Publisher: American Mathematical Soc.
ISBN: 1470440644
Category : Education
Languages : en
Pages : 172
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Book Description
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tessellations and packing problems, and Voronoi diagrams in 2 and 3 dimensions. These topics all connect to precollege mathematics, either as core ideas (irrational numbers) or enrichment for standard topics in geometry (polygons, angles, and constructions). But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery—participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Fractions, Tilings, and Geometry is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
Author: Tomas Sauer
Publisher: Springer Nature
ISBN: 3030843602
Category : Mathematics
Languages : en
Pages : 275
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Book Description
Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony’s problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.
Author: Remedia Publications
Publisher: Remedia Publications
ISBN: 9781596396999
Category : Education
Languages : en
Pages : 32
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Book Description
Grade Level: 3-6 CCSS Level: 4-6 Making fractions make sense! This 23-lesson learning unit is packed with hundreds of sequential fraction activities featuring both computation and word problems. As the third book in a series – following Adding Fractions and Subtracting Fractions – these exercises are designed to build upon what students have already learned. From “writing reciprocals of fractions, whole numbers, and mixed numbers,” to “multiplying a proper fraction by a proper fraction,” and on to “using a banana bread recipe to multiply fractions,” the activities in this book progress from learning basic concepts to mastering an understanding of how to multiply fractions. A Post Test and Answer Key are included.
Author: Mohammad Farshadnia
Publisher: Springer
ISBN: 9811087083
Category : Technology & Engineering
Languages : en
Pages : 266
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Book Description
This book focuses on the analytical modeling of fractional-slot concentrated-wound (FSCW) interior permanent magnet (IPM) machines and establishes a basis for their magnetic and electrical analysis. Aiming at the precise modeling of FSCW IPM machines’ magnetic and electrical characteristics, it presents a comprehensive mathematical treatment of the stator magneto-motive force (MMF), the IPM rotor non-homogeneous magnetic saturation, and its airgap flux density. The FSCW stator spatial MMF harmonics are analytically formulated, providing a basis on which a novel heuristic algorithm is then proposed for the design of optimal winding layouts for multiphase FSCW stators with different slot/pole combinations. In turn, the proposed mathematical models for the FSCW stator and the IPM rotor are combined to derive detailed mathematical expressions of its operational inductances, electromagnetic torque, torque ripple and their respective subcomponents, as a function of the machine geometry and design parameters. Lastly, the proposed theories and analytical models are validated using finite element analysis and experimental tests on a prototype FSCW IPM machine.
Author: Stephen Siklos
Publisher:
ISBN: 9781783747764
Category : Mathematics
Languages : en
Pages : 188
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Book Description
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.
Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595
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Book Description
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486696300
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces.
Author: Stan Collins
Publisher:
ISBN: 9780931993213
Category : Arithmetic
Languages : en
Pages : 0
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Book Description
Higher level skills with addition, subtraction, multiplication, and division of fractions. Practice, review, and testing included.
Author: Remedia Publications
Publisher: Remedia Publications
ISBN: 9781596390287
Category : Education
Languages : en
Pages : 32
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Book Description
Grade Level: 1-2 CCSS Math Level: 3 An introduction to fractions! Easy-to-grasp, graphically illustrated shapes are used to begin teaching the concept of fractions. Example: A half-moon shape is divided into two even parts and students are asked to color the fraction «. In all, there are 25 lessons in this teaching unit. As they work through the exercises, students will enjoy identifying, drawing, coloring, and dividing the basic shapes into fractions of 1/2, 1/4, 1/8, 1/3 and on and on.
