A Student's Guide to Infinite Series and Sequences
| Author | : Bach, Jr. (Bernhard W.) |
| Publisher | : |
| Total Pages | : 202 |
| Release | : 2018 |
| Genre | : |
| ISBN | : 9781107446588 |
Download A Student's Guide to Infinite Series and Sequences Book in PDF, ePub and Kindle
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A Student's Guide to Infinite Series and Sequences
| Author | : Bernhard W. Bach, Jr. |
| Publisher | : Cambridge University Press |
| Total Pages | : 201 |
| Release | : 2018-05-17 |
| Genre | : Science |
| ISBN | : 1108645739 |
Download A Student's Guide to Infinite Series and Sequences Book in PDF, ePub and Kindle
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.
A Student's Guide to Infinite Series and Sequences
| Author | : Bernhard W. Bach, Jr. |
| Publisher | : Cambridge University Press |
| Total Pages | : 201 |
| Release | : 2018-05-17 |
| Genre | : Mathematics |
| ISBN | : 1107059828 |
Download A Student's Guide to Infinite Series and Sequences Book in PDF, ePub and Kindle
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.
Infinite Sequences and Series
| Author | : Konrad Knopp |
| Publisher | : Courier Corporation |
| Total Pages | : 212 |
| Release | : 2012-09-14 |
| Genre | : Mathematics |
| ISBN | : 0486152049 |
Download Infinite Sequences and Series Book in PDF, ePub and Kindle
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.
A Student's Guide to Rotational Motion
| Author | : Effrosyni Seitaridou |
| Publisher | : Cambridge University Press |
| Total Pages | : 184 |
| Release | : 2023-07-31 |
| Genre | : Science |
| ISBN | : 1009213318 |
Download A Student's Guide to Rotational Motion Book in PDF, ePub and Kindle
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.
A Student's Guide to the Ising Model
| Author | : James S. Walker |
| Publisher | : Cambridge University Press |
| Total Pages | : 226 |
| Release | : 2023-04-30 |
| Genre | : Science |
| ISBN | : 1009115510 |
Download A Student's Guide to the Ising Model Book in PDF, ePub and Kindle
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.
A Student's Guide to Special Relativity
| Author | : Norman Gray |
| Publisher | : Cambridge University Press |
| Total Pages | : 232 |
| Release | : 2022-02-03 |
| Genre | : Science |
| ISBN | : 1009003119 |
Download A Student's Guide to Special Relativity Book in PDF, ePub and Kindle
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.
A Student's Guide to Laplace Transforms
| Author | : Daniel Fleisch |
| Publisher | : Cambridge University Press |
| Total Pages | : 222 |
| Release | : 2022-01-13 |
| Genre | : Science |
| ISBN | : 1009115502 |
Download A Student's Guide to Laplace Transforms Book in PDF, ePub and Kindle
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.
A Student's Guide to the Navier-Stokes Equations
| Author | : Justin W. Garvin |
| Publisher | : |
| Total Pages | : 238 |
| Release | : 2023-03-13 |
| Genre | : Mathematics |
| ISBN | : 1009236121 |
Download A Student's Guide to the Navier-Stokes Equations Book in PDF, ePub and Kindle
The Navier-Stokes equations describe the motion of fluids and are an invaluable addition to the toolbox of every physicist, applied mathematician, and engineer. The equations arise from applying Newton's laws of motion to a moving fluid and are considered, when used in combination with mass and energy conservation rules, to be the fundamental governing equations of fluid motion. They are relevant across many disciplines, from astrophysics and oceanic sciences to aerospace engineering and materials science. This Student's Guide provides a clear and focused presentation of the derivation, significance and applications of the Navier-Stokes equations, along with the associated continuity and energy equations. Designed as a useful supplementary resource for undergraduate and graduate students, each chapter concludes with a selection of exercises intended to reinforce and extend important concepts. Video podcasts demonstrating the solutions in full are provided online, along with written solutions and other additional resources.
A Student's Guide to General Relativity
| Author | : Norman Gray |
| Publisher | : Cambridge University Press |
| Total Pages | : 166 |
| Release | : 2019-01-03 |
| Genre | : Science |
| ISBN | : 1316873765 |
Download A Student's Guide to General Relativity Book in PDF, ePub and Kindle
This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and important applications of general relativity are described in an appendix.
