Applications Of Calculus In Physics

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Applications Of Calculus In Physics

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Author : Brian K. Saltzer
language : en
Publisher:
Release Date : 2020-02-22

Applications Of Calculus In Physics written by Brian K. Saltzer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-22 with categories.

The purpose of this book is to show students of both math and physics the deep relationship between the areas of physics and calculus. In particular: a) How calculus can deepen our understanding of the physical concepts b) How calculus can link together two or more seemingly unrelated physical concepts c) How calculus can be used to help us apply physical concepts to technology d) How calculus provides a mechanism to do physics in alternative ways Because many students might be seeing calculus for the first time, a basic 100-page Calculus Primer has been included in the text immediately following the applications. The Calculus Primer focuses on giving the students a "crash course" in how to calculate a derivative and an integral quickly, rather than on the deep rigor taught in many calculus courses. Formal mathematical language has been intentionally avoided to help students acquire this useful tool as quickly as possible. Because this material is being included in a physics application book rather than a calculus course, the Calculus Primer includes exercises with full solutions. These step-by-step solutions are important since many students will attempt to learn this material on their own. So that the student can immediately see if he/she has executed the calculus correctly using the given rules and algorithms, the solutions have intentionally been left in an "unsimplified" form. As the student works through the ten applications in the book, Connection Boxes are provided in the margins to map the student to the appropriate section of the Calculus Primer to learn the necessary calculus tool to complete the application. Because the Calculus Primer is designed to provide the necessary calculus tools on an "as needed" basis, both the topics covered and their order is somewhat different from that of a standard introductory calculus text. The applications are organized in terms of physical content rather than by calculus content. Consequently, physical concepts that are introduced early in a standard physics course appear earlier in this section than those introduced later in the course. The following examples of the many applications of calculus in physics are covered in this book: 1. Displacement, Velocity, and Acceleration 2. The Work Done by a Variable Force 3. Force and Potential Energy 4. The Electrical-Mechanical Analogy 5. Impulse and Momentum 6. Kepler's Law of Areas and Conservation of Angular Momentum 7. Shockley's Equation and Thermodynamics 8. Simple Harmonic Oscillators 9. The Velocity of a Transverse Wave 10. Lagrangian Physics: An Alternative Way to do Physics To help both the student and the instructor, each application also ends with a set of exercises related to the topic of the application.

Applications Of Fractional Calculus In Physics

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Author : Rudolf Hilfer
language : en
Publisher: World Scientific
Release Date : 2000-03-02

Applications Of Fractional Calculus In Physics written by Rudolf Hilfer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-02 with Science categories.

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.

Applications Of Calculus In Physics

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Author : Quantum Scientific Publishing
language : en
Publisher: Quantum Scientific Publishing
Release Date : 2023-06-11

Applications Of Calculus In Physics written by Quantum Scientific Publishing and has been published by Quantum Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-11 with Science categories.

The purpose of this book is to show students of both math and physics the deep relationship between the areas of physics and calculus. In particular: a) How calculus can deepen our understanding of the physical concepts b) How calculus can link together two or more seemingly unrelated physical concepts c) How calculus can be used to help us apply physical concepts to technology d) How calculus provides a mechanism to do physics in alternative ways Because many students might be seeing calculus for the first time, a basic 100-page Calculus Primer has been included in the text immediately following the applications. The Calculus Primer focuses on giving the students a “crash course” in how to calculate a derivative and an integral quickly, rather than on the deep rigor taught in many calculus courses. Formal mathematical language has been intentionally avoided to help students acquire this useful tool as quickly as possible. Because this material is being included in a physics application book rather than a calculus course, the Calculus Primer includes exercises with full solutions. These step-by-step solutions are important since many students will attempt to learn this material on their own. So that the student can immediately see if he/she has executed the calculus correctly using the given rules and algorithms, the solutions have intentionally been left in an “unsimplified” form. As the student works through the ten applications in the book, Connection Boxes are provided in the margins to map the student to the appropriate section of the Calculus Primer to learn the necessary calculus tool to complete the application. Because the Calculus Primer is designed to provide the necessary calculus tools on an “as needed” basis, both the topics covered and their order is somewhat different from that of a standard introductory calculus text. The applications are organized in terms of physical content rather than by calculus content. Consequently, physical concepts that are introduced early in a standard physics course appear earlier in this section than those introduced later in the course. The following examples of the many applications of calculus in physics are covered in this book: 1. Displacement, Velocity, and Acceleration 2. The Work Done by a Variable Force 3. Force and Potential Energy 4. The Electrical-Mechanical Analogy 5. Impulse and Momentum 6. Kepler’s Law of Areas and Conservation of Angular Momentum 7. Shockley’s Equation and Thermodynamics 8. Simple Harmonic Oscillators 9. The Velocity of a Transverse Wave 10. Lagrangian Physics: An Alternative Way to do Physics To help both the student and the instructor, each application also ends with a set of exercises related to the topic of the application.

Calculus Of Variations

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Author : Robert Weinstock
language : en
Publisher: Courier Corporation
Release Date : 1974-01-01

Calculus Of Variations written by Robert Weinstock and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-01-01 with Mathematics categories.

This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.

Advances In Fractional Calculus

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Author : J. Sabatier
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-28

Advances In Fractional Calculus written by J. Sabatier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-28 with Technology & Engineering categories.

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Calculus Based Physics I

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Author : Jeffrey W. Schnick
language : en
Publisher: Orange Grove Text Plus
Release Date : 2009-09-24

Calculus Based Physics I written by Jeffrey W. Schnick and has been published by Orange Grove Text Plus this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with Physics categories.

Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students. This item is part 1, for the first semester. Only the textbook in PDF format is provided here. To download other resources, such as text in MS Word formats, problems, quizzes, class questions, syllabi, and formula sheets, visit: http: //www.anselm.edu/internet/physics/cbphysics/index.html Calculus-Based Physics is now available in hard copy in the form of two black and white paperbacks at www.LuLu.com at the cost of production plus shipping. Note that Calculus-Based Physics is designed for easy photocopying. So, if you prefer to make your own hard copy, just print the pdf file and make as many copies as you need. While some color is used in the textbook, the text does not refer to colors so black and white hard copies are viable

Introduction To Stochastic Calculus With Applications

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Author : Fima C. Klebaner
language : en
Publisher: Imperial College Press
Release Date : 2005

Introduction To Stochastic Calculus With Applications written by Fima C. Klebaner and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Projects For Calculus

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Author : Keith D. Stroyan
language : en
Publisher: Elsevier
Release Date : 1998-11-03

Projects For Calculus written by Keith D. Stroyan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-03 with Mathematics categories.

Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology. Subjects including: Medicine, Engineering, Economics, Ecology, Physics, Biology

Applications Of Q Calculus In Operator Theory

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Author : Ali Aral
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-09

Applications Of Q Calculus In Operator Theory written by Ali Aral and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-09 with Mathematics categories.

The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. ​​This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain​ forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.