Skills In Mathematics Vectors & 3D Geometry

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Publisher :
ISBN 13 : 9788188222223
Total Pages : 268 pages
Book Rating : 4.2/5 (222 download)

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Book Synopsis Skills In Mathematics Vectors & 3D Geometry by : Amit M. Agarwal

Download or read book Skills In Mathematics Vectors & 3D Geometry written by Amit M. Agarwal and published by . This book was released on with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Skills in Mathematics - Vectors and 3D Geometry for JEE Main and Advanced

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Author :
Publisher : Arihant Publications India limited
ISBN 13 : 9325298686
Total Pages : 282 pages
Book Rating : 4.3/5 (252 download)

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Book Synopsis Skills in Mathematics - Vectors and 3D Geometry for JEE Main and Advanced by : Amit M Agarwal

Download or read book Skills in Mathematics - Vectors and 3D Geometry for JEE Main and Advanced written by Amit M Agarwal and published by Arihant Publications India limited. This book was released on 2021-04-19 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. ‘Skill in Mathematics’ series is prepared for JEE Main and Advanced papers 2. It is a highly recommended textbook to develop a strong grounding in Vectors and 3D Geometry 3. The book covers the entire syllabus into 3 chapters 4. Each chapter includes a wide range of questions that are asked in the examinations Good foundational grip is required in the Vectors and 3D Geometry, while you are preparing for JEE Mains & Advanced or any other engineering. Bringing up the series “Skills in Mathematics for JEE Main & Advanced for Vectors and 3D Geometry” that is carefully revised with the sessionwise theory and exercise; to help candidates to learn & tackle the mathematical problems. The book has 3 Chapters covering the whole syllabus for the JEE Mains and Advanced as prescribed. Each chapter is divided into sessions giving complete clarity to concepts. Apart from sessionwise theory, JEE Type examples and Chapter Exercise contain huge amount of questions that are provided in every chapter under Practice Part. Prepared under great expertise, it is a highly recommended textbook to develop a strong grounding in Algebra to perform best in JEE and various engineering entrances. TOC: Vector Algebra, Product of Vectors, Three Dimensional Coordinate System.

3D Math Primer for Graphics and Game Development, 2nd Edition

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Publisher : CRC Press
ISBN 13 : 1568817231
Total Pages : 848 pages
Book Rating : 4.5/5 (688 download)

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Book Synopsis 3D Math Primer for Graphics and Game Development, 2nd Edition by : Fletcher Dunn

Download or read book 3D Math Primer for Graphics and Game Development, 2nd Edition written by Fletcher Dunn and published by CRC Press. This book was released on 2011-11-02 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.

Skills in Mathematics - Coordinate Geometry for JEE Main and Advanced

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Publisher : Arihant Publications India limited
ISBN 13 : 9325298643
Total Pages : 638 pages
Book Rating : 4.3/5 (252 download)

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Book Synopsis Skills in Mathematics - Coordinate Geometry for JEE Main and Advanced by : Dr. S K Goyal

Download or read book Skills in Mathematics - Coordinate Geometry for JEE Main and Advanced written by Dr. S K Goyal and published by Arihant Publications India limited. This book was released on 2021-04-19 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. ‘Skill in Mathematics’ series is prepared for JEE Main and Advanced papers 2. It is a highly recommended textbook to develop a strong grounding in Coordinate Geometry 3. The book covers the entire syllabus into 7 chapters 4. Each chapter includes a wide range of questions that are asked in the examinations Good foundational grip is required in the Coordinate Geometry, while you are preparing for JEE Mains & Advanced or any other engineering. Bringing up the series “Skills in Mathematics for JEE Main & Advanced for Coordinate Geometry” that is carefully revised with the sessionwise theory and exercise; to help candidates to learn & tackle the mathematical problems. The book has 7 Chapters covering the whole syllabus for the JEE Mains and Advanced as prescribed. Each chapter is divided into sessions giving complete clarity to concepts. Apart from sessionwise theory, JEE Type examples and Chapter Exercise contain huge amount of questions that are provided in every chapter under Practice Part. Prepared under great expertise, it is a highly recommended textbook to develop a strong grounding in Algebra to perform best in JEE and various engineering entrances. TOC: Coordinate Systems and Coordinates, The Straight Lines, Pair of Straight Lines, Circle, Parabola, Ellipse, Hyperbola.

Skills in Mathematics - Differential Calculus for JEE Main and Advanced

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Publisher : Arihant Publications India limited
ISBN 13 : 9325298651
Total Pages : 550 pages
Book Rating : 4.3/5 (252 download)

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Book Synopsis Skills in Mathematics - Differential Calculus for JEE Main and Advanced by : Amit M Agarwal

Download or read book Skills in Mathematics - Differential Calculus for JEE Main and Advanced written by Amit M Agarwal and published by Arihant Publications India limited. This book was released on 2021-04-19 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Skill in Mathematics’ series is prepared for JEE Main and Advanced papers 2. It is a highly recommended textbook to develop a strong grounding in Differential Calculus 3. The book covers the entire syllabus into 8 chapters 4. Each chapter includes a wide range of questions that are asked in the examinations Good foundational grip is required in the Differential Calculus, while you are preparing for JEE Mains & Advanced or any other engineering. Bringing up the series “Skills in Mathematics for JEE Main & Advanced for Differential Calculus” that is carefully revised with the sessionwise theory and exercise; to help candidates to learn & tackle the mathematical problems. The book has 8 Chapters covering the whole syllabus for the JEE Mains and Advanced as prescribed. Each chapter is divided into sessions giving complete clarity to concepts. Apart from sessionwise theory, JEE Type examples and Chapter Exercise contain huge amount of questions that are provided in every chapter under Practice Part. Prepared under great expertise, it is a highly recommended textbook to develop a strong grounding in Algebra to perform best in JEE and various engineering entrances. TOC: Essential Mathematical Tools, Differentiation, Functions, Graphical Transformations, Limits, Continuity and Differentiability, dy/dx As a Rate Measurer & Tangents, Normals, Monotonicity, Maxima and Minima.

Skill in Mathematics - Algebra for JEE Main and Advanced

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Publisher : Arihant Publications India limited
ISBN 13 : 9325298635
Total Pages : 836 pages
Book Rating : 4.3/5 (252 download)

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Book Synopsis Skill in Mathematics - Algebra for JEE Main and Advanced by : Dr. S K Goyal

Download or read book Skill in Mathematics - Algebra for JEE Main and Advanced written by Dr. S K Goyal and published by Arihant Publications India limited. This book was released on 2021-04-19 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. ‘Skill in Mathematics’ series is prepared for JEE Main and Advanced papers 2. It is a highly recommended textbook to develop a strong grounding in Algebra 3. The book covers the entire syllabus into 11 chapters 4. Each chapter includes a wide range of questions that are asked in the examinations Good foundational grip is required in the Algebraic Methods, while you are preparing for JEE Mains & Advanced or any other engineering. Bringing up the series “Skills in Mathematics for JEE Main & Advanced for Algebra” that is carefully revised with the sessionwise theory and exercise; to help candidates to learn & tackle the mathematical problems. The book has 11 Chapters covering the whole syllabus for the JEE Mains and Advanced as prescribed. Each chapter is divided into sessions giving complete clarity to concepts. Apart from sessionwise theory, JEE Type examples and Chapter Exercise contain a huge amount of questions that are provided in every chapter under Practice Part. Prepared under great expertise, it is a highly recommended textbook to develop a strong grounding in Algebra to perform best in JEE and various engineering entrances. TOC: Complex Numbers, Theory of Equations, Sequences and Series, Logarithms and Their Properties, Permutations and Combinations, Binomial Theorems, Determinants, Matrices, Probability, Mathematical Inductions, Sets, Relations and Functions.

Essential Math Skills for Engineers

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Publisher : John Wiley & Sons
ISBN 13 : 1118211103
Total Pages : 246 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Essential Math Skills for Engineers by : Clayton R. Paul

Download or read book Essential Math Skills for Engineers written by Clayton R. Paul and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Just the math skills you need to excel in the study or practice of engineering Good math skills are indispensable for all engineers regardless of their specialty, yet only a relatively small portion of the math that engineering students study in college mathematics courses is used on a frequent basis in the study or practice of engineering. That's why Essential Math Skills for Engineers focuses on only these few critically essential math skills that students need in order to advance in their engineering studies and excel in engineering practice. Essential Math Skills for Engineers features concise, easy-to-follow explanations that quickly bring readers up to speed on all the essential core math skills used in the daily study and practice of engineering. These fundamental and essential skills are logically grouped into categories that make them easy to learn while also promoting their long-term retention. Among the key areas covered are: Algebra, geometry, trigonometry, complex arithmetic, and differential and integral calculus Simultaneous, linear, algebraic equations Linear, constant-coefficient, ordinary differential equations Linear, constant-coefficient, difference equations Linear, constant-coefficient, partial differential equations Fourier series and Fourier transform Laplace transform Mathematics of vectors With the thorough understanding of essential math skills gained from this text, readers will have mastered a key component of the knowledge needed to become successful students of engineering. In addition, this text is highly recommended for practicing engineers who want to refresh their math skills in order to tackle problems in engineering with confidence.

Analytical Geometry 2D and 3D

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Publisher : Pearson Education India
ISBN 13 : 9332517630
Total Pages : 509 pages
Book Rating : 4.3/5 (325 download)

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Book Synopsis Analytical Geometry 2D and 3D by : Vittal

Download or read book Analytical Geometry 2D and 3D written by Vittal and published by Pearson Education India. This book was released on 2013 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to meet the requirements of UG students, the book deals with the theoretical as well as the practical aspects of the subject. Equal emphasis has been given to both 2D as well as 3D geometry. The book follows a systematic approach with adequate examples for better understanding of the concepts.

Essential Mathematics for Games and Interactive Applications

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Publisher : CRC Press
ISBN 13 : 0123742978
Total Pages : 706 pages
Book Rating : 4.1/5 (237 download)

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Book Synopsis Essential Mathematics for Games and Interactive Applications by : James M. Van Verth

Download or read book Essential Mathematics for Games and Interactive Applications written by James M. Van Verth and published by CRC Press. This book was released on 2008-05-19 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.

Math for Programmers

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Publisher : Manning Publications
ISBN 13 : 1617295353
Total Pages : 686 pages
Book Rating : 4.6/5 (172 download)

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Book Synopsis Math for Programmers by : Paul Orland

Download or read book Math for Programmers written by Paul Orland and published by Manning Publications. This book was released on 2021-01-12 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. Summary To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks

Skills in Mathematics - Play with Graphs for JEE Main and Advanced

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Author :
Publisher : Arihant Publications India limited
ISBN 13 : 9325298694
Total Pages : pages
Book Rating : 4.3/5 (252 download)

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Book Synopsis Skills in Mathematics - Play with Graphs for JEE Main and Advanced by : Amit M Agarwal

Download or read book Skills in Mathematics - Play with Graphs for JEE Main and Advanced written by Amit M Agarwal and published by Arihant Publications India limited. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Textbook of Vector Analysis

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Publisher : S. Chand Publishing
ISBN 13 : 9788121922432
Total Pages : 422 pages
Book Rating : 4.9/5 (224 download)

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Book Synopsis A Textbook of Vector Analysis by : Shanti Narayan | PK Mittal

Download or read book A Textbook of Vector Analysis written by Shanti Narayan | PK Mittal and published by S. Chand Publishing. This book was released on 2010 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Textbook of Vector Analysis

Vectors and Coordinate Geometry

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Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781523688661
Total Pages : 184 pages
Book Rating : 4.6/5 (886 download)

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Book Synopsis Vectors and Coordinate Geometry by : Vladimir Serdarushich

Download or read book Vectors and Coordinate Geometry written by Vladimir Serdarushich and published by Createspace Independent Publishing Platform. This book was released on 2016-02-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: vectors in plane and space, length of vector, magnitude of vector, collinear vectors, opposite vectors, coplanar vectors, addition of vectors, triangle rule and parallelogram rule, zero or null vector, subtraction of vectors, scalar multiplication, multiplication of vector by scalar, unit vector, linear combination of vectors, linear dependence of vectors, vectors and coordinate system , Cartesian vectors, vectors in coordinate plane, vectors two dimensional system of coordinates, radius vector, position vector, vector components, vectors in two-dimensional system examples, vectors in three-dimensional space in terms of Cartesian coordinates, angles of vectors in relation to coordinate axes, directional cosines, scalar components of vector, unit vector of vector, vectors in three-dimensional coordinate system examples, scalar product, dot product, inner product, perpendicularity of vectors, different position of two vectors, values of scalar product, square of magnitude of vector, scalar product of unit vector, scalar or dot product properties, scalar product in coordinate system, angle between vectors in coordinate plane, projection of vector in direction of another vector, scalar and vector components, vector product or cross product, vector product, right-handed system, example of vector product in physics, condition for two vectors to be parallel, condition for two vectors to be perpendicular, vector products of standard unit vectors, vector product in component form, mixed product or scalar triple product definition, mixed product properties, condition for three vectors to be coplanar, mixed product, scalar triple product, mixed product expressed in terms of components, vector product and mixed product use examples,coordinate geometry, points lines and planes in three-dimensional coordinate system represented by vectors, points lines and planes in three-dimensional space, position of two lines in 3D space, coplanar lines, skew lines, line and plane in three-dimensional space, two planes in three-dimensional space, line of intersection of two planes, orthogonality of line and plane and, orthogonal projection of point on plane, distance from point to plane, angle between line and plane, angle between two planes, line in three-dimensional coordinate system, equation of line in space, vector equation of line, parametric equation of line, equation of line defined by direction vector and point, symmetric equation of line, distance between two points, orthogonal projection of line in space on xy coordinate plane, line in 3D space examples, angle between lines, condition for intersection of two lines in 3D space, equations of plane in coordinate space, equations of plane in 3D coordinate system, intercept form of equation of plane, equation of plane through three points, distance between point and plane, angle between two planes, line and plane in space, line of intersection of two planes, projection of line on coordinate planes, two planes of which given line is their intersection, intersection point of line and plane, sheaf or pencil of planes, angle between line and plane, orthogonal projections, point line and plane distances, condition for line and plane to be perpendicular, line perpendicular to given plane, plane perpendicular to given line, projection of point on plane in space, projection of point on line in space, line perpendicular to given line, plane parallel with two skew lines, plane parallel with two parallel lines, distance between point and line in 3D space, distance between point and plane in space example, distance between parallel lines, distance between skew lines,

Mathematics for 3D Game Programming and Computer Graphics

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Publisher :
ISBN 13 : 9780357671092
Total Pages : pages
Book Rating : 4.6/5 (71 download)

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Book Synopsis Mathematics for 3D Game Programming and Computer Graphics by : Eric Lengyel

Download or read book Mathematics for 3D Game Programming and Computer Graphics written by Eric Lengyel and published by . This book was released on 2020-08 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Sooner or later, all game programmers run into coding issues that require an understanding of mathematics or physics concepts such as collision detection, 3D vectors, transformations, game theory, or basic calculus. Unfortunately, most programmers frequently have a limited understanding of these essential mathematics and physics concepts. MATHEMATICS AND PHYSICS FOR PROGRAMMERS, THIRD EDITION provides a simple but thorough grounding in the mathematics and physics topics that programmers require to write algorithms and programs using a non-language-specific approach. Applications and examples from game programming are included throughout, and exercises follow each chapter for additional practice. The book's companion website provides sample code illustrating the mathematical and physics topics discussed in the book.

Mathematics for Machine Learning

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Publisher : Cambridge University Press
ISBN 13 : 1108569323
Total Pages : 392 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Geometric Algebra for Computer Science

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Publisher : Elsevier
ISBN 13 : 0080553109
Total Pages : 664 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Geometric Algebra for Computer Science by : Leo Dorst

Download or read book Geometric Algebra for Computer Science written by Leo Dorst and published by Elsevier. This book was released on 2010-07-26 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA

Essential 3D Geometry

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Publisher : University Readers
ISBN 13 : 9781609273897
Total Pages : 0 pages
Book Rating : 4.2/5 (738 download)

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Book Synopsis Essential 3D Geometry by : Bernardo Camou

Download or read book Essential 3D Geometry written by Bernardo Camou and published by University Readers. This book was released on 2011-07-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live out our lives in a three dimensional world. However, our understanding of what this means is meager, and the study of 3D Geometry is markedly absent from our educational system. Essential 3D Geometry: Unraveling the Mathematical Wonders bridges the gap between current mathematical knowledge and our fascinating--and unexplored--3D world. Originally developed by and for high school students, the material in Essential 3D Geometry has been successfully developed into a college-level text for pre-service teachers. The book offers an original and unique approach for learning mathematics--iMAT engineering--which is based on the principle that learning mathematics is an integrated activity calling for multi-type presentations of mathematical objects through the use of different technologies. The text begins with a thorough study of the building blocks of spatial structures, the five Platonic Solids. The material integrates 2D and 3D geometry, as well as algebra and trigonometry. Subsequent chapters cover a variety of topics including Thales' Theorem, the volume of the Platonic solids and non-regular tetrahedrons, circumcircles and circum-spheres, Archimedean Bodies, and spatial transformations. Students will learn to produce and make use of three types of representation of 3D objects: solids or lattice models, Cabri 3D or GSP files, and constructions using a straight-edge and compass or free hand drawings. Representations will be developed using paper and pencil, craft technology, and computer technology. Essential 3D Geometry is an excellent tool for introducing math educators to the concepts of 3D geometry, helping them go on to develop similar courses for their own students. Bernardo Camou has 20 years of experience teaching mathematics in secondary education. In 2009, he began work on his Ph.D. in mathematics education at the University of Georgia, graduating in May 2012. His dissertation topic, and his passion, is to help others discover the wonders of 3D Geometry. Graciela García studied economics at the Universidad de la Republica for two years before going on to earn the title of Math Teacher at the Instituto de Profesores Artigas. She currently teaches at the Woodlands School, after having spent 37 years teaching math in public high schools. Maria Margarita Colucci earned the title of Math Teacher at the Instituto de Profesores Artigas. For the past fifteen years she has been a high school math teacher at the Liceo N 15, as well as teaching at the Woodlands School where she is also coordinator of M.I.P. Dr. John Olive is Professor Emeritus of Mathematics Education at the University of Georgia. For over 30 years his research has focused on students' mathematical thinking, and the development and use of technological tools to support that thinking.