A Course in Derivative Securities: Introduction to Theory and Computation (Springer Finance)

A Course in Derivative Securities: Introduction to Theory and Computation (Springer Finance)

By Kerry Back

This book aims at a middle ground between the introductory books on derivative securities and those that provide advanced mathematical treatments. It is written for mathematically capable students who have not necessarily had prior exposure to probability theory, stochastic calculus, or computer programming. It provides derivations of pricing and hedging formulas (using the probabilistic change of numeraire technique) for standard options, exchange options, options on forwards and futures, quanto options, exotic options, caps, floors and swaptions, as well as VBA code implementing the formulas. It also contains an introduction to Monte Carlo, binomial models, and finite-difference methods.

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Level Set Methods and Dynamic Implicit Surfaces

Level Set Methods and Dynamic Implicit Surfaces

By Stanley J. Osher, Ronald P. Fedkiw

This book is an introduction to level set methods and dynamic implicit surfaces. These are powerful techniques for analyzing and computing moving fronts in a variety of different settings. While it gives many examples of the utility of the methods to a diverse set of applications, it also gives complete numerical analysis and recipes, which will enable users to quickly apply the techniques to real problems. The book begins with a description of implicit surfaces and their basic properties, then devises the level set geometry and calculus toolbox, including the construction of signed distance functions. Part II adds dynamics to this static calculus. Topics include the level set equation itself, Hamilton-Jacobi equations, motion of a surface normal to itself, re-initialization to a signed distance function, extrapolation in the normal direction, the particle level set method and the motion of co-dimension two (and higher) objects. Part III is concerned with topics taken from the fields of Image Processing and Computer Vision. These include the restoration of images degraded by noise and blur, image segmentation with active contours (snakes), and reconstruction of surfaces from unorganized data points. Part IV is dedicated to Computational Physics. It begins with one phase compressible fluid dynamics, then two-phase compressible flow involving possibly different equations of state, detonation and deflagration waves, and solid/fluid structure interaction. Next it discusses incompressible fluid dynamics, including a computer graphics simulation of smoke, free surface flows, including a computer graphics simulation of water, and fully two-phase incompressible flow. Additional related topics include incompressible flames with applications to computer graphics and coupling a compressible and incompressible fluid. Finally, heat flow and Stefan problems are discussed. A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.

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Numerical Methods

Numerical Methods

By J. Douglas Faires, Richard L. Burden

This book emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. In this book, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the reader that the method is reasonable both mathematically and computationally.

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Microflows and Nanoflows: Fundamentals and Simulation (Interdisciplinary Applied Mathematics)

Microflows and Nanoflows: Fundamentals and Simulation (Interdisciplinary Applied Mathematics)

By George Karniadakis, Ali Beskok, Narayan Aluru

In the last few years there has been significant progress in the development of microfluidics and nanofluidics at the application as well as at the fundamental and simulation levels. This book provides a comprehensive summary of these changes describing fluid flow in micro and nano configurations. Where as in their previous book entitled Microflows: Fundamentals and Simulation the authors covered scales from one hundred nanometers to microns (and beyond), in this new book they discuss length scales from angstroms to microns (and beyond). While still maintaining the emphasis on fundamental concepts with a mix of semianalytical, experimental, and numerical results, this book outlines their relevance to modeling and analyzing functional devices.

The text has been divided into three main subject categories: gas flows; liquid flows; and simulation techniques. The majority of the completely new developments in this book are in liquid flows and simulation techniques chapters with modified information throughout the rest of the book.

This book can be used in a two-semester graduate course. Also, selected chapters can be used for a short course or an undergraduate-level course. The book is suitable for graduate students and researchers in fluid mechanics, physics, and in electrical, mechanical and chemical engineering.

Review of earlier volume:

Applied Mechanics, 2002: "Among recent books that addressed the physics of micro devices, the present one ... is perhaps the best of the bunch. ... Microflows: Fundamentals and Simulation has a lot to offer and is certainly recommended as a good place to start for MEMS students interested in flow physics."

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Numerical Analysis

Numerical Analysis

By Richard L. Burden, J. Douglas Faires

The new Seventh Edition of Burden and Faires' well-respected Numerical Analysis provides a foundation in modern numerical-approximation techniques. Explaining how, why, and when the techniques can be expected to work, the Seventh Edition places an even greater emphasis on building readers' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. Applied problems from diverse areas, such as engineering and physical, computer, and biological sciences, are provided so readers can understand how numerical methods are used in real-life situations. The Seventh Edition has been updated and now addresses the evolving use of technology, incorporating it whenever appropriate.

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Pre-Calculus For Dummies (For Dummies (Math & Science))

Pre-Calculus For Dummies (For Dummies (Math & Science))

By Krystle Rose Forseth, Christopher Burger, Michelle Rose Gilman

Getting ready for calculus, but feel confused? Have no fear! This unintimidating, hands-on guide walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. You'll understand the concepts — not just the number crunching — and see how to perform all tasks, from graphing to tackling proofs.

• Apply the major theorems and formulas


• Graph trig functions like a pro


• Find trig values on the unit circle


• Tackle analytic geometry


• Identify function limits and continuity

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Precalculus: Graphical, Numerical, Algebraic (7th Edition)

Precalculus: Graphical, Numerical, Algebraic (7th Edition)

By Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy

In this new edition of Precalculus, Seventh Edition, the authors encourage graphical, numerical, and algebraic modeling of functions as well as a focus on problem solving, conceptual understanding, and facility with technology. They responded to many helpful suggestions provided by students and teachers in order to create a book that is designed for instructors and written for students. As a result, we believe that the changes made in this edition make this the most effective precalculus text available today.

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