The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus.

This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph

This book is a compilation of all basic topics on functions of Several Variables and is primarily meant for undergraduate and post graduate students. Topics covered are: Limits, continuities and differentiabilities of functions of several variables. Properties of Implicit functions and Jacobians. Extreme values of multivariate functions. Various types of integrals in planes and surfaces and their related theorems including Dirichlet and Liouville's extension to Dirichlet. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan)

From one of today's most accomplished and trusted mathematics authors comes a new textbook that offers unmatched support for students taking the AP (R) Calculus exam, and comes with additional resources for the teachers helping them prepare for it.Sullivan and Miranda's Calculus for the AP Course covers every Big Idea, Essential Knowledge statement, Learning Objective, and Math Practice described in the 2016-2017 redesigned College Board (TM) Curriculum Framework. It is concise and its focused narrative and integrated conceptual and problem-solving tools give students just the help they need as they learn calculus and prepare for the redesigned AP (R) Exam. Its accompanying Teacher's Edition provides an in depth correlation and abundant tips, examples, projects, and resources to ensure close adherence the new Curriculum Framework.

Suitable for graduate students and professional researchers in operator theory and/or analysis Numerous applications in related scientific fields and areas.

Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not—and that is the advantage these books offer the astute reader. Published under the collective title of Foundations of Quantitative Finance, this set of ten books presents the advanced mathematics finance professionals need to advance their careers. These books develop the theory most do not learn in Graduate Finance programs, or in most Financial Mathematics undergraduate and graduate courses. As a high-level industry executive and authoritative instructor, Robert R. Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial industry and two decades in education where he taught in highly respected graduate programs. Readers should be quantitatively literate and familiar with the developments in the first books in the set. The set offers a linear progression through these topics, though each title can be studied independently since the collection is extensively self-referenced. Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes, develops several approaches to an integration theory. The first two approaches were introduced in the Chapter 1 of Book I to motivate measure theory. The general theory of integration on measure spaces will be developed in Book V, and stochastic integrals then studies on Book VIII. Book III Features: Extensively referenced to utilize materials from earlier books. Presents the theory needed to better understand applications. Supplements previous training in mathematics, with more detailed developments. Built from the author's five decades of experience in industry, research, and teaching. Published and forthcoming titles in the Robert Reitano Quantitative Finance Series: Book I: Measure Spaces and Measurable Functions. Book II: Probability Spaces and Random Variables, Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes Book IV: Distribution Functions and Expectations Book V: General Measure and Integration Theory Book VI: Densities, Transformed Distributions, and Limit Theorems Book VII: Brownian Motion and Other Stochastic Processes Book VIII: Itô Integration and Stochastic Calculus 1 Book IX: Stochastic Calculus 2 and Stochastic Differential Equations Book 10: Applications and Classic Models

Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not—and that is the advantage these books offer the astute reader. Published under the collective title of Foundations of Quantitative Finance, this set of ten books presents the advanced mathematics finance professionals need to advance their careers. These books develop the theory most do not learn in Graduate Finance programs, or in most Financial Mathematics undergraduate and graduate courses. As a high-level industry executive and authoritative instructor, Robert R. Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial industry and two decades in education where he taught in highly respected graduate programs. Readers should be quantitatively literate and familiar with the developments in the first books in the set. The set offers a linear progression through these topics, though each title can be studied independently since the collection is extensively self-referenced. Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes, develops several approaches to an integration theory. The first two approaches were introduced in the Chapter 1 of Book I to motivate measure theory. The general theory of integration on measure spaces will be developed in Book V, and stochastic integrals then studies on Book VIII. Book III Features: Extensively referenced to utilize materials from earlier books. Presents the theory needed to better understand applications. Supplements previous training in mathematics, with more detailed developments. Built from the author's five decades of experience in industry, research, and teaching. Published and forthcoming titles in the Robert Reitano Quantitative Finance Series: Book I: Measure Spaces and Measurable Functions. Book II: Probability Spaces and Random Variables, Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes Book IV: Distribution Functions and Expectations Book V: General Measure and Integration Theory Book VI: Densities, Transformed Distributions, and Limit Theorems Book VII: Brownian Motion and Other Stochastic Processes Book VIII: Itô Integration and Stochastic Calculus 1 Book IX: Stochastic Calculus 2 and Stochastic Differential Equations Book 10: Applications and Classic Models

G.H. Hardy's text is a good single volume refresher course for work in analysis and more advanced algebra, including number theory. Not quite as modern as Birkhoff and MacLane's text, or Manes' work, this volume forms the underpinnings of both works. If you have a good understanding of the preliminary work required in algebra and geometry, Hardy can be read directly and with pleasure. If you have a desire to understand the basis of what is presented in most first-year calculus texts, then Hardy's text is for you.

Sir Horace Lamb (1849 1934) the British mathematician, wrote a number of influential works in classical physics. A pupil of Stokes and Clerk Maxwell, he taught for ten years as the first professor of mathematics at the University of Adelaide before returning to Britain to take up the post of professor of physics at the Victoria University of Manchester (where he had first studied mathematics at Owens College). As a teacher and writer his stated aim was clarity: 'somehow to make these dry bones live'. The first edition of this work was published in 1897, the third revised edition in 1919, and a further corrected version just before his death. This edition, reissued here, remained in print until the 1950s. As with Lamb's other textbooks, each section is followed by examples.

Yes, this is another Calculus book. However, it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one - it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide - because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between these two extremes. It is best used as a companion to a traditional text or as a refresher - with its conversational tone, its 'get right to it' content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.Exercises are structured in three sets to force multiple encounters with each topic. Solved examples in the text are accompanied by 'You Try It' problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are 'Practice Problems': more problems similar to the 'You Try It' problems, but given all at once. Finally, each section has Challenge Problems - these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.The goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. The target audience is STEM students including those in engineering and meteorology programs.

The Gradient Test: Another Likelihood-Based Test presents the latest on the gradient test, a large-sample test that was introduced in statistics literature by George R. Terrell in 2002. The test has been studied by several authors, is simply computed, and can be an interesting alternative to the classical large-sample tests, namely, the likelihood ratio (LR), Wald (W), and Rao score (S) tests. Due to the large literature about the LR, W and S tests, the gradient test is not frequently used to test hypothesis. The book covers topics on the local power of the gradient test, the Bartlett-corrected gradient statistic, the gradient statistic under model misspecification, and the robust gradient-type bounded-influence test.

This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the "fractional community" is growing rapidly there is a pressing need for the exchange of scientific results. The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:* Mathematical foundations* Fractional systems analysis and synthesis* System modelingSeven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.

Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.This book is the first to introduce fractal calculus and provides a basis for the research and development of this framework. It is suitable for undergraduate and graduate students in mathematics and physics who have mastered general mathematics, quantum physics, and statistical mechanics, as well as researchers dealing with fractal structures in various disciplines.

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.

Calculus of variations has a long history. Its fundamentals were laid down by icons of mathematics like Euler and Lagrange. It was once heralded as the panacea for all engineering optimization problems by suggesting that all one needed to do was to state a variational problem, apply the appropriate Euler-Lagrange equation and solve the resulting differential equation. This, as most all encompassing solutions, turned out to be not always true and the resulting differential equations are not necessarily easy to solve. On the other hand, many of the differential equations commonly used in various fields of engineering are derived from a variational problem. Hence it is an extremely important topic justifying the new edition of this book. This third edition extends the focus of the book to academia and supports both variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.

This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer. It is an integrated resource with theory and applications for those interested in hydrology, hydraulics and fluid mechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications.

This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items,  generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc.