the art of differentiating computer programs an introduction to algorithmic differentiation

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The Art Of Differentiating Computer Programs

Author : Uwe Naumann
ISBN : 1611972078
Genre : Automatic differentiations
File Size : 38. 86 MB
Format : PDF, ePub
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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.

The Art Of Differentiating Computer Programs

Author : Uwe Naumann
ISBN : 9781611972061
Genre : Mathematics
File Size : 41. 8 MB
Format : PDF, Kindle
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In this entry-level book on algorithmic (also known as automatic) differentiation (AD) the author covers the mathematical underpinnings as well as applications to real-world numerical simulation programs. Readers will find many examples and exercises, including hints to solutions. A supplementary website contains software sources, additional exercises, useful links and errata.

Evaluating Derivatives

Author : Andreas Griewank
ISBN : 9780898716597
Genre : Mathematics
File Size : 85. 91 MB
Format : PDF, Mobi
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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.

Understanding Search Engines

Author : Michael W. Berry
ISBN : 0898718163
Genre : Text processing (Computer science)
File Size : 64. 40 MB
Format : PDF, Mobi
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The second edition of Understanding Search Engines: Mathematical Modeling and Text Retrieval follows the basic premise of the first edition by discussing many of the key design issues for building search engines and emphasizing the important role that applied mathematics can play in improving information retrieval. The authors discuss important data structures, algorithms, and software as well as user-centered issues such as interfaces, manual indexing, and document preparation. Readers will find that the second edition includes significant changes that bring the text up to date on current information retrieval methods. For example, the authors have added a completely new chapter on link-structure algorithms used in search engines such as Google, and the chapter on user interface has been rewritten to specifically focus on search engine usability. To reflect updates in the literature on information retrieval, the authors have added new recommendations for further reading and expanded the bibliography. In addition, the index has been updated and streamlined to make it more reader friendly.

The Differentiated Classroom

Author : Carol Ann Tomlinson
ISBN : 9781416618638
Genre : Education
File Size : 85. 87 MB
Format : PDF, Docs
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Although much has changed in schools in recent years, the power of differentiated instruction remains the same--and the need for it has only increased. Today's classroom is more diverse, more inclusive, and more plugged into technology than ever before. And it's led by teachers under enormous pressure to help decidedly unstandardized students meet an expanding set of rigorous, standardized learning targets. In this updated second edition of her best-selling classic work, Carol Ann Tomlinson offers these teachers a powerful and practical way to meet a challenge that is both very modern and completely timeless: how to divide their time, resources, and efforts to effectively instruct so many students of various backgrounds, readiness and skill levels, and interests. With a perspective informed by advances in research and deepened by more than 15 years of implementation feedback in all types of schools, Tomlinson explains the theoretical basis of differentiated instruction, explores the variables of curriculum and learning environment, shares dozens of instructional strategies, and then goes inside elementary and secondary classrooms in nearly all subject areas to illustrate how real teachers are applying differentiation principles and strategies to respond to the needs of all learners. This book's insightful guidance on what to differentiate, how to differentiate, and why lays the groundwork for bringing differentiated instruction into your own classroom or refining the work you already do to help each of your wonderfully unique learners move toward greater knowledge, more advanced skills, and expanded understanding. Today more than ever, The Differentiated Classroom is a must-have staple for every teacher's shelf and every school's professional development collection.

An Integrated Introduction To Computer Graphics And Geometric Modeling

Author : Ronald Goldman
ISBN : 9781439803356
Genre : Computers
File Size : 37. 38 MB
Format : PDF, Kindle
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Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.


Author : Herbert S. Wilf
ISBN : 9781483276632
Genre : Mathematics
File Size : 29. 97 MB
Format : PDF, ePub
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Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

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