A Student's Guide to Infinite Series and Sequences PDF Download
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Author: Bernhard W. Bach, Jr.
Publisher: Cambridge University Press
ISBN: 1108645739
Category : Science
Languages : en
Pages : 201
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Book Description
Why study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area.
Author: Bernhard W. Bach, Jr.
Publisher: Cambridge University Press
ISBN: 1108645739
Category : Science
Languages : en
Pages : 201
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Book Description
Why study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area.
Author: Bernhard W. Bach, Jr.
Publisher: Cambridge University Press
ISBN: 1107059828
Category : Mathematics
Languages : en
Pages : 201
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Book Description
An informal and practically focused introduction for undergraduate students exploring infinite series and sequences in engineering and the physical sciences. With a focus on practical applications in real world situations, it helps students to conceptualize the theory with real-world examples and to build their skill set.
Author: Ludmila Bourchtein
Publisher: Springer Nature
ISBN: 3030794318
Category : Mathematics
Languages : en
Pages : 388
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Book Description
This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.
Author: Bach, Jr. (Bernhard W.)
Publisher:
ISBN: 9781107446588
Category :
Languages : en
Pages : 202
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Book Description
Author: Konrad Knopp
Publisher:
ISBN:
Category : Series, Infinite
Languages : en
Pages : 596
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Book Description
Trans from the 2nd German ed , pub 1923.
Author: David Rush
Publisher: SIU Press
ISBN: 9780809326099
Category : Drama
Languages : en
Pages : 324
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Book Description
With the skills of a playwright, the vision of a producer, and the wisdom of an experienced teacher, David Rush offers a fresh and innovative guide to interpreting drama in A Student Guide to Play Analysis, the first undergraduate teaching tool to address postmodern drama in addition to classic and modern. Covering a wide gamut of texts and genres, this far-reaching and user-friendly volume is easily paired with most anthologies of plays and is accessible even to those without a literary background. Contending that there are no right or wrong answers in play analysis, Rush emphasizes the importance of students developing insights of their own. The process is twofold: understand the critical terms that are used to define various parts and then apply these to a particular play. Rush clarifies the concepts of plot, character, and language, advancing Aristotle's concept of the Four Causes as a method for approaching a play through various critical windows. He describes the essential difference between a story and a play, outlines four ways of looking at plays, and then takes up the typical structural devices of a well-made play, four primary genres and their hybrids, and numerous styles, from expressionism to postmodernism. For each subject, he defines critical norms and analyzes plays common to the canon. A Student Guide to Play Analysis draws on thoughtful examinations of such dramas as The Cherry Orchard, The Good Woman of Setzuan, Fences, The Little Foxes, A Doll House, The Glass Menagerie, and The Emperor Jones. Each chapter ends with a list of questions that will guide students in further study.
Author: Effrosyni Seitaridou
Publisher: Cambridge University Press
ISBN: 1009213318
Category : Science
Languages : en
Pages : 184
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Book Description
Rotational motion is of fundamental importance in physics and engineering, and an essential topic for undergraduates to master. This accessible yet rigorous Student's Guide focuses on the underlying principles of rotational dynamics, providing the reader with an intuitive understanding of the physical concepts, and a firm grasp of the mathematics. Key concepts covered include torque, moment of inertia, angular momentum, work and energy, and the combination of translational and rotational motion. Each chapter presents one important aspect of the topic, with derivations and analysis of the fundamental equations supported by step-by-step examples and exercises demonstrating important applications. Much of the book is focused on scenarios in which point masses and rigid bodies rotate around fixed axes, while more advanced examples of rotational motion, including gyroscopic motion, are introduced in a final chapter.
Author: James S. Walker
Publisher: Cambridge University Press
ISBN: 1009115510
Category : Science
Languages : en
Pages : 226
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Book Description
The Ising model provides a detailed mathematical description of ferromagnetism and is widely used in statistical physics and condensed matter physics. In this Student's Guide, the author demystifies the mathematical framework of the Ising model and provides students with a clear understanding of both its physical significance, and how to apply it successfully in their calculations. Key topics related to the Ising model are covered, including exact solutions of both finite and infinite systems, series expansions about high and low temperatures, mean-field approximation methods, and renormalization-group calculations. The book also incorporates plots, figures, and tables to highlight the significance of the results. Designed as a supplementary resource for undergraduate and graduate students, each chapter includes a selection of exercises intended to reinforce and extend important concepts, and solutions are also available for all exercises.
Author: Norman Gray
Publisher: Cambridge University Press
ISBN: 1009003119
Category : Science
Languages : en
Pages : 232
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Book Description
This compact yet informative Guide presents an accessible route through Special Relativity, taking a modern axiomatic and geometrical approach. It begins by explaining key concepts and introducing Einstein's postulates. The consequences of the postulates – length contraction and time dilation – are unravelled qualitatively and then quantitatively. These strands are then tied together using the mathematical framework of the Lorentz transformation, before applying these ideas to kinematics and dynamics. This volume demonstrates the essential simplicity of the core ideas of Special Relativity, while acknowledging the challenges of developing new intuitions and dealing with the apparent paradoxes that arise. A valuable supplementary resource for intermediate undergraduates, as well as independent learners with some technical background, the Guide includes numerous exercises with hints and notes provided online. It lays the foundations for further study in General Relativity, which is introduced briefly in an appendix.
Author: Daniel Fleisch
Publisher: Cambridge University Press
ISBN: 1009115502
Category : Science
Languages : en
Pages : 222
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Book Description
The Laplace transform is a useful mathematical tool encountered by students of physics, engineering, and applied mathematics, within a wide variety of important applications in mechanics, electronics, thermodynamics and more. However, students often struggle with the rationale behind these transforms, and the physical meaning of the transform results. Using the same approach that has proven highly popular in his other Student's Guides, Professor Fleisch addresses the topics that his students have found most troublesome; providing a detailed and accessible description of Laplace transforms and how they relate to Fourier and Z-transforms. Written in plain language and including numerous, fully worked examples. The book is accompanied by a website containing a rich set of freely available supporting materials, including interactive solutions for every problem in the text, and a series of podcasts in which the author explains the important concepts, equations, and graphs of every section of the book.
