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This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.
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.
Do you own a TI-89, TI-89 Titanium, TI-92 Plus, or a Voyage 200 graphing calculator? If you do, or if you need to get one for school or your job, then you need to know how it works and how to make the most of its functions. TI-89 For Dummies is the plain-English nuts-and-bolts guide that gets you up and running on all the things your TI-89 can do, quickly and easily. This hands-on reference guides you step by step through various tasks and even shows you how to add applications to your calculator. Soon you’ll have the tools you need to: Solve equations and systems of equations Factor polynomials Evaluate derivatives and integrals Graph functions, parametric equations, polar equations, and sequences Create Stat Plots and analyze statistical data Multiply matrices Solve differential equations and systems of differential equations Transfer files between two or more calculators Save calculator files on your computer Packed with exciting and valuable applications that you can download from the Internet and install through your computer, as well as common errors and messages with explanations and solutions, TI-89 For Dummies is the one-stop reference for all your graphing calculator questions!
This is the first entry-level book on algorithmic (also known as automatic) differentiation (AD), providing fundamental rules for the generation of first- and higher-order tangent-linear and adjoint code. The author covers the mathematical underpinnings as well as how to apply these observations to real-world numerical simulation programs. Readers will find: examples and exercises, including hints to solutions; the prototype AD tools dco and dcc for use with the examples and exercises; first- and higher-order tangent-linear and adjoint modes for a limited subset of C/C++, provided by the derivative code compiler dcc; a supplementary website containing sources of all software discussed in the book, additional exercises and comments on their solutions (growing over the coming years), links to other sites on AD, and errata.
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.
Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.
Rigid Body Dynamics Algorithms presents the subject of computational rigid-body dynamics through the medium of spatial 6D vector notation. It explains how to model a rigid-body system and how to analyze it, and it presents the most comprehensive collection of the best rigid-body dynamics algorithms to be found in a single source. The use of spatial vector notation greatly reduces the volume of algebra which allows systems to be described using fewer equations and fewer quantities. It also allows problems to be solved in fewer steps, and solutions to be expressed more succinctly. In addition algorithms are explained simply and clearly, and are expressed in a compact form. The use of spatial vector notation facilitates the implementation of dynamics algorithms on a computer: shorter, simpler code that is easier to write, understand and debug, with no loss of efficiency.
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).
The development and computational implementation of analytical expres sions for the low-order derivatives of electronic energy surfaces and other molecular properties has undergone rapid growth in recent years. It is now fairly routine for chemists to make use of energy gradient information in locating and identifying stable geometries and transition states. The use of second analytical derivative (Hessian or curvature) expressions is not yet routine, and third and higher energy derivatives as well as property (e.g., dipole moment, polarizability) derivatives are just beginning to be applied to chemical problems. This NATO Advanced Research Workshop focused on analyzing the re lative merits of various strategies for deriving the requisite analyti cal expressions, for computing necessary integral derivatives and wave function parameter derivatives, and for efficiently coding these expres sions on conventional scalar machines and vector-oriented computers. The participant list contained many scientists who have been instrumen tal in bringing this field to fruition as well as eminent scientists who have broad knowledge and experience in quantum chemistry in general.