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Calculus Applications by Larry Joel Goldstein

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1Calculus Of Variations With Applications

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2Matrix And Tensor Calculus, With Applications To Mechanics, Elasticity, And Aeronautics (Galcit Aeronautical Series)

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3Test Item File, Calculus/Brief Calculus And Its Applications

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4Calculus, With Applications To The Management, Social, Behavioral, And Biomedical Sciences

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5Calculus And Its Applications

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6Calculus And Its Applications

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7Calculus & Its Applications

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8Calculus With Applications

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9Student's Solutions Manual To Accompany Finite Mathematics And Calculus With Applications

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10Mathematics And Calculus With Applications

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Includes index

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11Applications Of The Calculus To Mechanics

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12Applications Of The Calculus To Mechanics

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vi, 116 p. 21 cm

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13Elements Of The Differential And Integral Calculus With Examples And Applications

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14Differential And Integral Calculus: With Examples And Applications

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15Calculus : Concepts And Applications : Solutions Manual

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v, 302 pages

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16Calculus, With Applications

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v, 302 pages

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17The Brief Calculus, With Applications In The Social Sciences

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viii, 439 pages 22 x 26 cm

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18Pathwise Functional Calculus And Applications To Continuous-time Finance (PhD Thesis)

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This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic notions. Using the recently developed 'non-anticipative functional calculus', we first develop a pathwise definition of the gain process for a large class of continuous-time trading strategies which include the important class of delta-hedging strategies, as well as a pathwise definition of the self-financing condition. Using these concepts, we propose a framework for analyzing the performance and robustness of delta-hedging strategies for path-dependent derivatives across a given set of scenarios. Our setting allows for general path-dependent payoffs and does not require any probabilistic assumption on the dynamics of the underlying asset, thereby extending previous results on robustness of hedging strategies in the setting of diffusion models. We obtain a pathwise formula for the hedging error for a general path-dependent derivative and provide sufficient conditions ensuring the robustness of the delta hedge. We show in particular that robust hedges may be obtained in a large class of continuous exponential martingale models under a vertical convexity condition on the payoff functional. Under the same conditions, we show that discontinuities in the underlying asset always deteriorate the hedging performance. These results are applied to the case of Asian options and barrier options. The last chapter, independent of the rest of the thesis, proposes a novel method, jointly developed with Andrea Pascucci and Stefano Pagliarani, for analytical approximations in local volatility models with L\'evy jumps. Numerical tests confirm the effectiveness of the method.

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19Calculus Of Variations, With Applications To Physics And Engineering

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This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic notions. Using the recently developed 'non-anticipative functional calculus', we first develop a pathwise definition of the gain process for a large class of continuous-time trading strategies which include the important class of delta-hedging strategies, as well as a pathwise definition of the self-financing condition. Using these concepts, we propose a framework for analyzing the performance and robustness of delta-hedging strategies for path-dependent derivatives across a given set of scenarios. Our setting allows for general path-dependent payoffs and does not require any probabilistic assumption on the dynamics of the underlying asset, thereby extending previous results on robustness of hedging strategies in the setting of diffusion models. We obtain a pathwise formula for the hedging error for a general path-dependent derivative and provide sufficient conditions ensuring the robustness of the delta hedge. We show in particular that robust hedges may be obtained in a large class of continuous exponential martingale models under a vertical convexity condition on the payoff functional. Under the same conditions, we show that discontinuities in the underlying asset always deteriorate the hedging performance. These results are applied to the case of Asian options and barrier options. The last chapter, independent of the rest of the thesis, proposes a novel method, jointly developed with Andrea Pascucci and Stefano Pagliarani, for analytical approximations in local volatility models with L\'evy jumps. Numerical tests confirm the effectiveness of the method.

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20The Elements Of The Integral Calculus: With Its Applications To Geometry And To The Summation Of ...

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21Good Rough Path Sequences And Applications To Anticipating Stochastic Calculus

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We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is assumed. Under a simple condition on the stochastic process, we show that the unique solution of the above SDE understood in the rough path sense is actually a Stratonovich solution. We then show that this condition is satisfied by the Brownian motion. As application, we obtain rather flexible results such as support theorems, large deviation principles and Wong--Zakai approximations for SDEs driven by Brownian motion along anticipating vectorfields. In particular, this unifies many results on anticipative SDEs.

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22A Treatise On Infinitesimal Calculus; Containing Differential And Integral Calculus, Calculus Of Variations, Applications To Algebra And Geometry, And Analytical Mechanics

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We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is assumed. Under a simple condition on the stochastic process, we show that the unique solution of the above SDE understood in the rough path sense is actually a Stratonovich solution. We then show that this condition is satisfied by the Brownian motion. As application, we obtain rather flexible results such as support theorems, large deviation principles and Wong--Zakai approximations for SDEs driven by Brownian motion along anticipating vectorfields. In particular, this unifies many results on anticipative SDEs.

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  • Title: ➤  A Treatise On Infinitesimal Calculus; Containing Differential And Integral Calculus, Calculus Of Variations, Applications To Algebra And Geometry, And Analytical Mechanics
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23A Treatise On The Integral Calculus And Its Applications: With Numerous Examples

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24A Treatise On Infinitesimal Calculus, Containing Differential And Integral Calculus, Calculus Of Variations, Applications To Algebra And Geometry, And Analytical Mechanics

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25Second-order Subdifferential Calculus With Applications To Tilt Stability In Optimization

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The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of frst-order subdifferential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal secondorder chain rule for strongly and fully amenable compositions. The calculus results obtained in this way and computing the second-order subdifferentials for piecewise linear-quadratic functions and their major specifications are applied then to the study of tilt stability of local minimizers for important classes of problems in constrained optimization that include, in particular, problems of nonlinear programming and certain classes of extended nonlinear programs described in composite terms.

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26Elements Of The Differential And Integral Calculus, With Examples And Applications

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xiii, 236 p. 21 cm

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27Fractional Calculus Of Variations In Terms Of A Generalized Fractional Integral With Applications To Physics

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We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to Physics discussed.

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28Essential Calculus With Applications

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We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to Physics discussed.

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29Elements Of The Integral Calculus; With Its Applications To Geometry And To The Summation Of Infinite Series

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14

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30The Elements Of The Integral Calculus: With Its Applications To Geometry And To The Summation Of ...

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31The Elements Of The Integral Calculus: With Its Applications To Geometry And ...

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32Fundamentals Of Calculus With Applications And Companion To Calculus

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33Correspondence Principle For Idempotent Calculus And Some Computer Applications

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This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar constructions and results over idempotent semirings in the spirit of N. Bohr's correspondence principle in Quantum Mechanics. Some problems nonlinear in the traditional sense (for example, the Bellman equation and its generalizations) turn out to be linear over a suitable semiring; this linearity considerably simplifies the explicit construction of solutions. The theory is well advanced and includes, in particular, new integration theory, new linear algebra, spectral theory and functional analysis. It has a wide range of applications. Besides a survey of the subject, in this paper the correspondence principle is used to develop an approach to object-oriented software and hardware design for algorithms of idempotent calculus.

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34Poisson Process Partition Calculus With Applications To Exchangeable Models And Bayesian Nonparametrics

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This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.

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35Differential Calculus, With Applications And Numerous Examples; An Elementary Treatise

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This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.

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36A Treatise On Infinitesimal Calculus, Containing Differential And Integral Calculus, Calculus Of Variations, Applications To Algebra And Geometry, And Analytical Mechanics

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This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.

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37A Treatise On Infinitesimal Calculus, Containing Differential And Integral Calculus, Calculus Of Variations, Applications To Algebra And Geometry, And Analytical Mechanics

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This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.

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38Instructor's Resource Manual Calculas And Its Applications Brief Calculus And Its Applications

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This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.

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39Calculus : A Short Course With Applications

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This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.

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40Calculus: A Short Course With Applications

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This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.

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41Differential And Integral Calculus: With Applications

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43Calculus & Its Applications

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44The Differential And Integral Calculus, Containing Differentiation, Integration, Development, Series, Differential Equations, Differences, Summation, Equations Of Differences, Calculus Of Variations, Definite Integrals,--with Applications To Algebra, Plane Geometry, Solid Geometry, And Mechanics. Also, Elementary Illustrations Of The Differential And Integral Calculus

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First issued in 25 parts, July 15, 1836, to June 1, 1842

“The Differential And Integral Calculus, Containing Differentiation, Integration, Development, Series, Differential Equations, Differences, Summation, Equations Of Differences, Calculus Of Variations, Definite Integrals,--with Applications To Algebra, Plane Geometry, Solid Geometry, And Mechanics. Also, Elementary Illustrations Of The Differential And Integral Calculus” Metadata:

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45College Mathematics And Calculus : With Applications To Management, Life, And Social Sciences

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First issued in 25 parts, July 15, 1836, to June 1, 1842

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46Local Malliavin Calculus For Lévy Processes And Applications

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In this paper a Malliavin calculus for L\'evy processes based on a family of true derivative operators is developed. The starting point is an extension to L\'evy processes of the pioneering paper by Carlen and Pardoux [8] for the Poisson process, and our approach includes also the classical Malliavin derivative for Gaussian processes. We obtain a sufficient condition for the absolute continuity of functionals of the L\'evy process. As an application, we analyze the absolute continuity of the law of the solution of some stochastic differential equations.

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47Study Guide To Accompany Brief Calculus With Applications, Fourth Edition, Larson, Hostetler, Edwards

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384 p. ; 28 cm

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48Elements Of The Differential And Integral Calculus With Examples And Applications

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384 p. ; 28 cm

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49Elements Of The Differential Calculus With Examples And Applications

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384 p. ; 28 cm

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50Elements Of The Differential Calculus, With Examples And Applications

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xv, 258 p. 22 cm

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1Test item file, Calculus/Brief calculus and its applications

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  • Number of Pages: Median: 143
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  • First Year Published: 1987
  • Is Full Text Available: Yes
  • Is The Book Public: No
  • Access Status: Borrowable

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