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| application of derivatives in calculus: Calculus and Its Applications P. Mainardi, H. Barkan, 2014-05-12 Calculus and its Applications provides information pertinent to the applications of calculus. This book presents the trapping technique in defining geometrical and physical entities that are usually regarded as limits of sums. Organized into 20 chapters, this book begins with an overview of the notion of average speed that seems to appear first as a qualitative concept. This text then presents the concepts of external and internal parameters to increase the appreciation of parametric functions. Other chapters consider separable differential equations with more detail than usual with their suitability in describing physical laws. This book discusses as well the study of variable quantities whose magnitude is determined by the magnitudes of several other variables. The final chapter deals with a homogeneous differential equation and auxiliary equations consisting imaginary roots. This book is a valuable resource for mathematicians and students. Readers whose interests span a variety of fields will also find this book useful. |
| application of derivatives in calculus: Active Calculus 2018 Matthew Boelkins, 2018-08-13 Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface. |
| application of derivatives in calculus: Applications Of Fractional Calculus In Physics Rudolf Hilfer, 2000-03-02 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. |
| application of derivatives in calculus: An Introduction to the Mathematics of Financial Derivatives Salih N. Neftci, 2000-05-19 A step-by-step explanation of the mathematical models used to price derivatives. For this second edition, Salih Neftci has expanded one chapter, added six new ones, and inserted chapter-concluding exercises. He does not assume that the reader has a thorough mathematical background. His explanations of financial calculus seek to be simple and perceptive. |
| application of derivatives in calculus: Introduction to Stochastic Calculus with Applications Fima C. Klebaner, 2005 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. |
| application of derivatives in calculus: Advanced Calculus (Revised Edition) Lynn Harold Loomis, Shlomo Zvi Sternberg, 2014-02-26 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. |
| application of derivatives in calculus: Financial Derivatives Jamil Baz, George Chacko, 2004-01-12 Publisher Description |
| application of derivatives in calculus: Calculus For Dummies Mark Ryan, 2016-05-18 Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the how and why in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win. Includes foundations in algebra, trigonometry, and pre-calculus concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can't get away with Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there. |
| application of derivatives in calculus: Calculus With Applications Peter D. Lax, Maria Shea Terrell, 2013-09-21 Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory. |
| application of derivatives in calculus: Calculus Kenneth Kuttler, 2011 This is a book on single variable calculus including most of the important applications of calculus. It also includes proofs of all theorems presented, either in the text itself, or in an appendix. It also contains an introduction to vectors and vector products which is developed further in Volume 2. While the book does include all the proofs of the theorems, many of the applications are presented more simply and less formally than is often the case in similar titles. Supplementary materials are available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com. This book is also available as a set with Volume 2: CALCULUS: Theory and Applications. |
| application of derivatives in calculus: General Fractional Derivatives Xiao-Jun Yang, 2019-05-10 General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science. |
| application of derivatives in calculus: Introduction to Integral Calculus Ulrich L. Rohde, G. C. Jain, Ajay K. Poddar, A. K. Ghosh, 2012-01-20 An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with clear, simple explanations, the authors reinforce new concepts to progressively build skills and knowledge, and numerous real-world examples as well as intriguing applications help readers to better understand the connections between the theory of calculus and practical problem solving. The first six chapters address the prerequisites needed to understand the principles of integral calculus and explore such topics as anti-derivatives, methods of converting integrals into standard form, and the concept of area. Next, the authors review numerous methods and applications of integral calculus, including: Mastering and applying the first and second fundamental theorems of calculus to compute definite integrals Defining the natural logarithmic function using calculus Evaluating definite integrals Calculating plane areas bounded by curves Applying basic concepts of differential equations to solve ordinary differential equations With this book as their guide, readers quickly learn to solve a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to Integral Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner. |
| application of derivatives in calculus: Matrix Differential Calculus with Applications in Statistics and Econometrics Jan R. Magnus, Heinz Neudecker, 2019-03-15 A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology. |
| application of derivatives in calculus: Fractional Dynamics Carlo Cattani, Hari M. Srivastava, Xiao-Jun Yang, 2015-01-01 The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science. |
| application of derivatives in calculus: APEX Calculus Gregory Hartman, 2015 APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back). |
| application of derivatives in calculus: Fractional Calculus and Fractional Processes with Applications to Financial Economics Hasan Fallahgoul, Sergio Focardi, Frank Fabozzi, 2016-10-06 Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization. - Provides the necessary background for the book's content as applied to financial economics - Analyzes the application of fractional calculus and fractional processes from deterministic and stochastic perspectives |
| application of derivatives in calculus: Calculus for the Life Sciences James L. Cornette, Ralph A. Ackerman, 2015-12-30 Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text. The students should have studied algebra, geometry, and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses. |
| application of derivatives in calculus: Fractional Derivatives for Physicists and Engineers Vladimir V. Uchaikin, 2013-07-09 The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular. Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy. |
| application of derivatives in calculus: Advances in Fractional Calculus J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado, 2010-10-19 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. |
| application of derivatives in calculus: Derivatives Keith Cuthbertson, Dirk Nitzsche, Niall O'Sullivan, 2019-12-16 Three experts provide an authoritative guide to the theory and practice of derivatives Derivatives: Theory and Practice and its companion website explore the practical uses of derivatives and offer a guide to the key results on pricing, hedging and speculation using derivative securities. The book links the theoretical and practical aspects of derivatives in one volume whilst keeping mathematics and statistics to a minimum. Throughout the book, the authors put the focus on explanations and applications. Designed as an engaging resource, the book contains commentaries that make serious points in a lighthearted manner. The authors examine the real world of derivatives finance and include discussions on a wide range of topics such as the use of derivatives by hedge funds and the application of strip and stack hedges by corporates, while providing an analysis of how risky the stock market can be for long-term investors, and more. To enhance learning, each chapter contains learning objectives, worked examples, details of relevant finance blogs technical appendices and exercises. |
| application of derivatives in calculus: The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974-09-05 In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering |
| application of derivatives in calculus: University Calculus Joel Hass, Maurice D. Weir, George Brinton Thomas, 2008 Calculus hasn't changed, but your students have. Many of today's students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. University Calculus: Alternate Edition responds to the needs of today's students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course. The Alternate Edition is the perfect alternative for instructors who want the same quality and quantity of exercises as Thomas' Calculus, Media Upgrade, Eleventh Edition but prefer a faster-paced presentation. University Calculus: Alternate Edition is now available with an enhanced MyMathLab(t) course-the ultimate homework, tutorial and study solution for today's students. The enhanced MyMathLab(t) course includes a rich and flexible set of course materials and features innovative Java(t) Applets, Group Projects, and new MathXL(R) exercises. This text is also available with WebAssign(R) and WeBWorK(R). |
| application of derivatives in calculus: Fractional Calculus and Its Applications B. Ross, 2006-11-15 |
| application of derivatives in calculus: Calculus Stanley I. Grossman, 1977 Revised edition of a standard textbook for a three-semester (or four- to five-quarter) introduction to calculus. In addition to covering all the standard topics, it includes a number of features written to accomplish three goals: to make calculus easier through the use of examples, graphs, reviews, etc.; to help students appreciate the beauty of calculus through the use of applications in a wide variety of fields; and to make calculus interesting by discussing the historical development of the subject. Annotation copyright by Book News, Inc., Portland, OR |
| application of derivatives in calculus: Derivative with a New Parameter Abdon Atangana, 2015-09-18 Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives. Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies. - Introduce the new parameters for the local derivative, including its definition and properties - Provides examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases - Includes definitions of beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, their properties, and methods for partial differential using beta derivatives - Explains how the new parameter can be used in multiple methods |
| application of derivatives in calculus: Applications of Calculus Philip D. Straffin, 1993 This book explains how calculus can be used to explain and analyze many diverse phenomena. |
| application of derivatives in calculus: The Hitchhiker's Guide to Calculus Michael Spivak, 2019-01-24 The Hitchhiker's Guide to Calculus begins with a rapid view of lines and slope. Spivak then takes up non-linear functions and trigonometric functions. He places the magnifying glass on curves in the next chapter and effortlessly leads the reader to the idea of derivative. In the next chapter he tackles speed and velocity, followed by the derivative of sine. Maxima and minima are next. Rolle's theorem and the MVT form the core of Chapter 11, Watching Experts at Play. The Hitchhiker's Guide to Calculus closes with a chapter on the integral, the fundamental theorem, and applications of the integral. |
| application of derivatives in calculus: Teaching and Learning of Calculus David Bressoud, Imène Ghedamsi, Victor Martinez-Luaces, Günter Törner, 2016-06-14 This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions. |
| application of derivatives in calculus: Yet Another Calculus Text Dan Sloughter, 2009-09-24 |
| application of derivatives in calculus: Stochastic Calculus and Financial Applications J. Michael Steele, 2012-12-06 Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book. --ZENTRALBLATT MATH |
| application of derivatives in calculus: Analysis with Ultrasmall Numbers Karel Hrbacek, Olivier Lessmann, Richard O'Donovan, 2014-12-01 Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon–delta methods. Students can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book is suitable for a calculus course at the undergraduate or high school level or for self-study with an emphasis on nonstandard methods. The first part of the text offers material for an elementary calculus course while the second part covers more advanced calculus topics. The text provides straightforward definitions of basic concepts, enabling students to form good intuition and actually prove things by themselves. It does not require any additional black boxes once the initial axioms have been presented. The text also includes numerous exercises throughout and at the end of each chapter. |
| application of derivatives in calculus: Calculus from the Ground Up Jonathan Laine Bartlett, 2018-11 Calculus from the Ground Up invites readers to become active participants in mathematics-making numbers and symbols the servants of their imaginations in ways they didn't think possible. It is a guidebook for learning not only the bare subject of calculus, but also to discover how its artistry can be applied everywhere else. |
| application of derivatives in calculus: Theory and Applications of Fractional Differential Equations A.A. Kilbas, H. M. Srivastava, J.J. Trujillo, 2006-02-16 This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations. |
| application of derivatives in calculus: Fractional Differential Equations Anatoly Kochubei, Yuri Luchko, 2019-02-19 This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations. |
| application of derivatives in calculus: Calculus for Computer Graphics John Vince, 2019-03-12 Students studying different branches of computer graphics have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems. In this 2nd edition, the author extends the scope of the original book to include applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature. The author draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function’s derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with numerous worked examples, and over a hundred and seventy colour illustrations. This book complements the author’s other books on mathematics for computer graphics, and assumes that the reader is familiar with everyday algebra, trigonometry, vectors and determinants. After studying this book, the reader should understand calculus and its application within the world of computer graphics, games and animation. |
| application of derivatives in calculus: Functional Differential Equations A.V. Kim, 2013-04-17 Beginning with the works of N.N.Krasovskii [81, 82, 83], which clari fied the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional approach, different aspects of time-delay system theory have been developed with almost the same completeness as the corresponding field of ODE (ordinary differential equations) the ory. The term functional differential equations (FDE) is used as a syn onym for systems with delays 1. The systematic presentation of these re sults and further references can be found in a number of excellent books [2, 15, 22, 32, 34, 38, 41, 45, 50, 52, 77, 78, 81, 93, 102, 128]. In this monograph we present basic facts of i-smooth calculus ~ a new differential calculus of nonlinear functionals, based on the notion of the invariant derivative, and some of its applications to the qualitative theory of functional differential equations. Utilization of the new calculus is the main distinction of this book from other books devoted to FDE theory. Two other distinguishing features of the volume are the following: - the central concept that we use is the separation of finite dimensional and infinite dimensional components in the structures of FDE and functionals; - we use the conditional representation of functional differential equa tions, which is convenient for application of methods and constructions of i~smooth calculus to FDE theory. |
| application of derivatives in calculus: MATH 221 FIRST Semester Calculus Sigurd Angenent, 2014-11-26 MATH 221 FIRST Semester CalculusBy Sigurd Angenent |
| application of derivatives in calculus: Kronecker Products and Matrix Calculus with Applications Alexander Graham, 2018-06-13 Enhanced by many worked examples, problems, and solutions, this in-depth text is suitable for undergraduates and presents a great deal of information previously only available in specialized and hard-to-find texts. 1981 edition. |
| application of derivatives in calculus: Algorithms for Optimization Mykel J. Kochenderfer, Tim A. Wheeler, 2019-03-12 A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals. |
| application of derivatives in calculus: MVT: A Most Valuable Theorem Craig Smorynski, 2017-04-07 This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mathematics majors as well as graduate students. Unlike other books, the present monograph treats the mathematical and historical aspects in equal measure, providing detailed and rigorous proofs of the mathematical results and even including original source material presenting the flavour of the history. |
软件（software）和应用程序（application）有什么区别？ - 知乎
App 其实是 Application Software （应用程序）的简称。 因为在之前的计算机时代，人们不但需要懂软件层的Software，也要关心硬件层的 Hardware 是否支持、是否兼容，所以用软件来与硬 …
你们说的ABI，Application Binary Interface到底是什么东西？
ABI（Application Binary Interface）是编译器和链接器遵守的一组规则，使编译后的程序可以正常工作。
epub怎么打开？ - 知乎
在iPhone上面看，epub的格式用什么软件打开呢，电脑上呢
WPS 如何卸载干净？ - 知乎
7、打开我的电脑，C盘，依次打开Documents and Settings\Administrator\Application Data\Kingsoft\。注意上述Administrator是计算机管理员的用户名，如果你的电脑管理员用户名 …
win11内存完整性打不开，显示PassGuard_x64.sys驱动不兼容，这 …
sys 是驱动程序的可执行代码，扩展名为.sys,一般是在C:\Windows\System32\drivers里面，找到之后就可以删除啦。
Edge浏览器主页被360劫持怎么办 - 知乎
2021年7月21日实测有效： 右击快捷方式，属性，将目标中的内容替换为 "C:\Program Files (x86)\Microsoft\Edge\Application\msedge_proxy.exe"
如何打开mobi为后缀的文件？ - 知乎
我补充个PC上的软件，借用其首页上的介绍. Sumatra PDF is a PDF, ePub, MOBI, CHM, XPS, DjVu, CBZ, CBR reader for Windows
如何解决Windows更新导致AMD Radeon Software等软件无法正常 …
每次Windows更新之后（Advanced micro devices, inc, -Display -27.20.11028.5001），双击AMD Radeon Sof…
expert systems with applications这个期刊怎么样 ？有投过的么。 …
《expert systems with applications》学术影响力没得说，if=7.5，位于中科院1区，jcr q1，但审核速度在14个月左右，将近1年多的时间，周期太不稳定，时间紧迫的学者千万不要投稿，否则 …
F12如何查看cookie? - 知乎
May 4, 2023 · 在F12开发者工具中，切换到“ Application ”（或“应用程序”）选项卡； 在左侧的菜单中，点击“ Cookies ”（或“Cookie”）选项； 在右侧的面板中，可以查看当前网站的Cookie信 …
软件（software）和应用程序（application）有什么区别？ - 知乎
App 其实是 Application Software （应用程序）的简称。 因为在之前的计算机时代，人们不但需要懂软件层的Software，也要关心硬件层的 Hardware 是否支持、是否兼容，所以用软件来与硬 …
你们说的ABI，Application Binary Interface到底是什么东西？
ABI（Application Binary Interface）是编译器和链接器遵守的一组规则，使编译后的程序可以正常工作。
epub怎么打开？ - 知乎
在iPhone上面看，epub的格式用什么软件打开呢，电脑上呢
WPS 如何卸载干净？ - 知乎
7、打开我的电脑，C盘，依次打开Documents and Settings\Administrator\Application Data\Kingsoft\。注意上述Administrator是计算机管理员的用户名，如果你的电脑管理员用户名 …
win11内存完整性打不开，显示PassGuard_x64.sys驱动不兼容，这 …
sys 是驱动程序的可执行代码，扩展名为.sys,一般是在C:\Windows\System32\drivers里面，找到之后就可以删除啦。
Edge浏览器主页被360劫持怎么办 - 知乎
2021年7月21日实测有效： 右击快捷方式，属性，将目标中的内容替换为 "C:\Program Files (x86)\Microsoft\Edge\Application\msedge_proxy.exe"
如何打开mobi为后缀的文件？ - 知乎
我补充个PC上的软件，借用其首页上的介绍. Sumatra PDF is a PDF, ePub, MOBI, CHM, XPS, DjVu, CBZ, CBR reader for Windows
如何解决Windows更新导致AMD Radeon Software等软件无法正常 …
每次Windows更新之后（Advanced micro devices, inc, -Display -27.20.11028.5001），双击AMD Radeon Sof…
expert systems with applications这个期刊怎么样 ？有投过的么。 …
《expert systems with applications》学术影响力没得说，if=7.5，位于中科院1区，jcr q1，但审核速度在14个月左右，将近1年多的时间，周期太不稳定，时间紧迫的学者千万不要投稿，否则 …
F12如何查看cookie? - 知乎
May 4, 2023 · 在F12开发者工具中，切换到“ Application ”（或“应用程序”）选项卡； 在左侧的菜单中，点击“ Cookies ”（或“Cookie”）选项； 在右侧的面板中，可以查看当前网站的Cookie信 …
