Numerical differentiation

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  • Tham khảo sách 'numerical methods for ordinary differential equations butcher tableau', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • We have attempted to write a concise modern treatment of differential equations emphasizing applications and containing all the core parts of a course in differential equations.Asemester or quarter course in differential equations is taught to most engineering students (and many science students) at all universities, usually in the second year. Some universities have an earlier brief introduction to differential equations and others do not. Some students will have already seen some differential equations in their science classes.We do not assume any prior exposure to differential equations.

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  • The fifth edition of this classic book continues its excellence in teaching numerical analysis and techniques. Interesting and timely applications motivate an understanding of methods and analysis of results. Suitable for students with mathematics and engineering backgrounds, the breadth of topics (partial differential equations, systems of nonlinear equations, and matrix algebra), provide comprehensive and flexible coverage of all aspects of all numerical analysis.

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  • This section attempts to answer some of the questions you might formulate when you turn the first page: What does this toolbox do? Can I use it? What problems can I solve?, etc. What Does this Toolbox Do? The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time. The equations are discretized by the Finite Element Method (FEM). The objectives of the PDE Toolbox are to provide you with tools that: • Define a PDE problem, i.e.

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  • In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.

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  • Classical differential geometry is the approach to geometry that takes full advantage of the introduction of numerical coordinates into a geometric space. This use of coordinates in geometry was the essential insight of Rene Descartes that allowed the invention of analytic geometry and paved the way for modern differential geometry. The basic object in differential geometry (and differential topology) is the smooth manifold. This is a topological space on which a sufficiently nice family of coordinate systems or "charts" is defined.

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  • The goal of this book is to expose the reader to modern computational tools for solving differential equation models that arise in chemical engineering, e.g., diffusion-reaction, mass-heat transfer, and fluid flow. The emphasis is placed on the understanding and proper use of software packages. In each chapter we outline numerical techniques that either illustrate a computational property of interest or are the underlying methods of a computer package. At the close of each chapter a survey of computer packages is accompanied by examples of their use....

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  • The present volume, compiled in honor of an outstanding historian of science, physicist and exceptional human being, Sam Schweber, is unique in assembling a broad spectrum of positions on the history of science by some of its leading representatives. Readers will find it illuminating to learn how prominent authors judge the current status and the future perspectives of their field. Students will find this volume helpful as a guide in a fragmented field that continues to be dominated by idiosyncratic expertise and still lacks a methodical canon.

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  • Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.

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  • The goal of this book is to develop robust, accurate and efficient numerical methods to price a number of derivative products in quantitative finance.We focus on one-factor and multi-factor models for a wide range of derivative products such as options, fixed income products, interest rate products and ‘real’ options. Due to the complexity of these products it is very difficult to find exact or closed solutions for the pricing functions. Even if a closed solution can be found it may be very difficult to compute. For this and other reasons we need to resort to approximate methods.

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  • Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics. CFD techniques are commonly used in the many areas of engineering where fluid behavior is an important factor. Traditional fields of application include aerospace and automotive design, and more recently, bioengineering and consumer and medical electronics.

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  • In addition to Excel's extensive list of worksheet functions and array of calculation tools for scientific and engineering calculations, Excel contains a programming language that allows users to create procedures, sometimes referred to as macros, that can perform even more advanced calculations or that can automate repetitive calculations.

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  • Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial differential equation.

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  • This book presents and develops major numerical methods currently used for solving problems arising in quantitative finance. Our presentation splits into two parts. Part I is methodological, and offers a comprehensive toolkit on numerical methods and algorithms. This includes Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transform-based methods and quadrature techniques. Part II is practical, and features a number of self-contained cases.

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  • This research monograph concerns the design and analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes and Poisson processes or Poisson jump measures. In financial and actuarial modeling and other areas of application, such jump diffusions are often used to describe the dynamics of various state variables. In finance these may represent, for instance, asset prices, credit ratings, stock indices, interest rates, exchange rates or commodity prices.

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  • Numerical Differentiation, Integration, and Solutions of Ordinary Differential EquationsChương này bàn về các phương pháp cơ bản cho số lượng tìm kiếm các giá trị giới hạn của một hình thức không xác định, giá trị của một phái sinh, giá trị của một khoản tiền vô hạn hội tụ, và giá trị của một tích phân xác định.

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  • To introduce the ]orward-backward stochastic differential equations (FBS- DEs, for short), let us begin with some examples. Unless otherwise speci- fled, throughout the book, we let (~, •, {Ft)t_0, P) be a complete filtered probability space on which is defined a d-dimensional standard Brownian motion W(t), such that {5~t }t_0 is the natural filtration of W(t), augmented by...

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  • Mutual funds have been a significant source of investment in both government and corporate securities. Decades it has been the monopoly of the state with UTI being the key player, with invested funds exceeding Rs.300 bn. The state-owned insurance companies also hold a portfolio of stocks. Presently, numerous mutual funds exist, including private and foreign companies and mainly state- owned Banks. Foreign participation in mutual funds and asset management companies (AUM) is permitted on a case-by-case basis.

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  • The numerical treatment of partial differential equations is, by itself, a vast subject. Partial differential equations are at the heart of many, if not most, computer analyses or simulations of continuous physical systems, such as fluids, electromagnetic fields, the human body, and so on.

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  • Trying to meet the requirements in the field, present book treats different fuzzy control architectures both in terms of the theoretical design and in terms of comparative validation studies in various applications, numerically simulated or experimentally developed. Through the subject matter and through the inter and multidisciplinary content, this book is addressed mainly to the researchers, doctoral students and students interested in developing new applications of intelligent control, but also to the people who want to become familiar with the control concepts based on fuzzy techniques....

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