Vectors in Two or Three Dimensions

Author: Ann Hirst

Publisher: Butterworth-Heinemann

ISBN: 0080572014

Category: Mathematics

Page: 144

View: 1558

Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is emphasised throughout. Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to more advanced theories. * Adopts a geometric approach * Develops gradually, building from basics to the concept of isometry and vector calculus * Assumes virtually no prior knowledge * Numerous worked examples, exercises and challenge questions

Vectors in Two Or Three Dimensions

Author: A. E. Hirst

Publisher: Elsevier

ISBN: 0340614692

Category: Mathematics

Page: 134

View: 5035

Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is emphasised throughout. Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to more advanced theories. * Adopts a geometric approach * Develops gradually, building from basics to the concept of isometry and vector calculus * Assumes virtually no prior knowledge * Numerous worked examples, exercises and challenge questions

Two and Three Dimensional Calculus

With Applications in Science and Engineering

Author: Phil Dyke

Publisher: John Wiley & Sons

ISBN: 1119221781

Category: Mathematics

Page: 400

View: 7169

Covers multivariable calculus, starting from the basics and leading up to the three theorems of Green, Gauss, and Stokes, but always with an eye on practical applications. Written for a wide spectrum of undergraduate students by an experienced author, this book provides a very practical approach to advanced calculus—starting from the basics and leading up to the theorems of Green, Gauss, and Stokes. It explains, clearly and concisely, partial differentiation, multiple integration, vectors and vector calculus, and provides end-of-chapter exercises along with their solutions to aid the readers’ understanding. Written in an approachable style and filled with numerous illustrative examples throughout, Two and Three Dimensional Calculus: with Applications in Science and Engineering assumes no prior knowledge of partial differentiation or vectors and explains difficult concepts with easy to follow examples. Rather than concentrating on mathematical structures, the book describes the development of techniques through their use in science and engineering so that students acquire skills that enable them to be used in a wide variety of practical situations. It also has enough rigor to enable those who wish to investigate the more mathematical generalizations found in most mathematics degrees to do so. Assumes no prior knowledge of partial differentiation, multiple integration or vectors Includes easy-to-follow examples throughout to help explain difficult concepts Features end-of-chapter exercises with solutions to exercises in the book. Two and Three Dimensional Calculus: with Applications in Science and Engineering is an ideal textbook for undergraduate students of engineering and applied sciences as well as those needing to use these methods for real problems in industry and commerce.

Vectors in Two and Three Dimensions

Author: Anthony Nicolaides


ISBN: 1872684157

Category: Bivectors

Page: 56

View: 1113

Vectors in Three-Dimensional Space

Author: J. S. R. Chisholm

Publisher: CUP Archive

ISBN: 9780521292894

Category: Mathematics

Page: 293

View: 3274

This book deals with vector algebra and analysis and with their application to three-dimensional geometry and the analysis of fields in three dimensions. While many treatments of the application of vectors have approached the fundamentals of the subject intuitively, assuming some prior knowledge of Euclidean and Cartesian geometry, Professor Chrisholm here bases the subject on the axioms of linear space algebra, which are fundamental to many branches of mathematics. While developing the properties of vectors from axioms, however, he continually emphasizes the geometrical interpretation of vector algebra in order to build up intuitive relations between the algebraic equations and geometrical concepts. Throughout, examples are used to illustrate the theory being developed; several sets of problems are incorporate in each chapter, and outline answers to many of these are given. Written primarily for undergraduate mathematicians in the early part of their courses, this lucidly written book will also appeal to mathematical physicists and to mathematically inclined engineers.

Vector Calculus

Author: William Cox

Publisher: Butterworth-Heinemann

ISBN: 0080572952

Category: Mathematics

Page: 256

View: 9725

Building on previous texts in the Modular Mathematics series, in particular 'Vectors in Two or Three Dimensions' and 'Calculus and ODEs', this book introduces the student to the concept of vector calculus. It provides an overview of some of the key techniques as well as examining functions of more than one variable, including partial differentiation and multiple integration. Undergraduates who already have a basic understanding of calculus and vectors, will find this text provides tools with which to progress onto further studies; scientists who need an overview of higher order differential equations will find it a useful introduction and basic reference.

Geometrical Vectors

Author: Gabriel Weinreich

Publisher: University of Chicago Press

ISBN: 9780226890487

Category: Mathematics

Page: 115

View: 390

Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.

Vectors and Coordinate Geometry

Author: Vladimir Serdarushich

Publisher: Createspace Independent Publishing Platform

ISBN: 9781523688661


Page: 184

View: 4317

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,

Vectors and Matrices

Author: Pamela Liebeck

Publisher: Elsevier

ISBN: 1483280438

Category: Mathematics

Page: 192

View: 2070

Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

Fundamental Concepts in Electrical and Computer Engineering with Practical Design Problems

Author: Reza Adhami,Peter M. Meenen,Denis Hite

Publisher: Universal-Publishers

ISBN: 1581129718

Category: Computers

Page: 736

View: 1232

In many cases, the beginning engineering student is thrown into upper-level engineering courses without an adequate introduction to the basic material. This, at best, causes undue stress on the student as they feel unprepared when faced with unfamiliar material, and at worst, results in students dropping out of the program or changing majors when they discover that their chosen field of engineering is not what they thought it was. The purpose of this text is to introduce the student to a general cross-section of the field of electrical and computer engineering. The text is aimed at incoming freshmen, and as such, assumes that the reader has a limited to nonexistent background in electrical engineering and knowledge of no more than pre-calculus in the field of mathematics. By exposing students to these fields at an introductory level, early in their studies, they will have both a better idea of what to expect in later classes and a good foundation of knowledge upon which to build.

The Nature of Code

Author: Daniel Shiffman

Publisher: Nature of Code

ISBN: 9780985930806

Category: Computer programming

Page: 498

View: 5778

How can we capture the unpredictable evolutionary and emergent properties of nature in software? How can understanding the mathematical principles behind our physical world help us to create digital worlds? This book focuses on a range of programming strategies and techniques behind computer simulations of natural systems, from elementary concepts in mathematics and physics to more advanced algorithms that enable sophisticated visual results. Readers will progress from building a basic physics engine to creating intelligent moving objects and complex systems, setting the foundation for further experiments in generative design. Subjects covered include forces, trigonometry, fractals, cellular automata, self-organization, and genetic algorithms. The book's examples are written in Processing, an open-source language and development environment built on top of the Java programming language. On the book's website (http: //, the examples run in the browser via Processing's JavaScript mode.

Mathematical Methods for Scientists and Engineers

Author: Donald Allan McQuarrie

Publisher: University Science Books

ISBN: 9781891389245

Category: Mathematics

Page: 1161

View: 2314

Intended for upper-level undergraduate and graduate courses in chemistry, physics, mathematics and engineering, this text is also suitable as a reference for advanced students in the physical sciences. Detailed problems and worked examples are included.

A History of Vector Analysis

The Evolution of the Idea of a Vectorial System

Author: Michael J. Crowe

Publisher: Courier Corporation

ISBN: 0486679101

Category: Mathematics

Page: 270

View: 8696

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

Elements of Matrix Modeling and Computing with MATLAB

Author: Robert E. White

Publisher: CRC Press

ISBN: 1584886277

Category: Mathematics

Page: 402

View: 8942

As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables. Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applications: circuits, trusses, mixing tanks, heat conduction, data modeling, motion of a mass, and image filters. These applications are developed from very simple to more complex models. To explain the processes, the book explores numerous topics in linear algebra, including complex numbers and functions, matrices, algebraic systems, curve fitting, elements of linear differential equations, transform methods, and tools of computation. For example, the author uses linearly independent vectors and subspaces to explain over- and under-determined systems, eigenvalues and eigenvectors to solve initial value problems, and discrete Fourier transforms to perform image filtering in the frequency domain. Although the primary focus is to cultivate calculation skills by hand, most chapters also include MATLAB to help with more complicated calculations.

Analytical Geometry Of Two & Three Dimensions & Vector Analysis

Author: R.M.Khan

Publisher: New Central Book Agency

ISBN: 9788173810893


Page: 664

View: 9348

Matrix theory has been used to simplify the subject matter. Basic ideas of Vector Algebra and Analysis will be helpful to bridge the modern treatments of different branches.

Learning R

A Step-by-Step Function Guide to Data Analysis

Author: Richard Cotton

Publisher: "O'Reilly Media, Inc."

ISBN: 1449357180

Category: Computers

Page: 400

View: 7826

Learn how to perform data analysis with the R language and software environment, even if you have little or no programming experience. With the tutorials in this hands-on guide, you’ll learn how to use the essential R tools you need to know to analyze data, including data types and programming concepts. The second half of Learning R shows you real data analysis in action by covering everything from importing data to publishing your results. Each chapter in the book includes a quiz on what you’ve learned, and concludes with exercises, most of which involve writing R code. Write a simple R program, and discover what the language can do Use data types such as vectors, arrays, lists, data frames, and strings Execute code conditionally or repeatedly with branches and loops Apply R add-on packages, and package your own work for others Learn how to clean data you import from a variety of sources Understand data through visualization and summary statistics Use statistical models to pass quantitative judgments about data and make predictions Learn what to do when things go wrong while writing data analysis code

Vectors and Their Applications

Author: Anthony J. Pettofrezzo

Publisher: Courier Corporation

ISBN: 0486148890

Category: Mathematics

Page: 144

View: 9893

Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of 2- and 3-dimensional space.

Data Science from Scratch

First Principles with Python

Author: Joel Grus

Publisher: "O'Reilly Media, Inc."

ISBN: 1491904402


Page: 330

View: 945

Data science libraries, frameworks, modules, and toolkits are great for doing data science, but they’re also a good way to dive into the discipline without actually understanding data science. In this book, you’ll learn how many of the most fundamental data science tools and algorithms work by implementing them from scratch. If you have an aptitude for mathematics and some programming skills, author Joel Grus will help you get comfortable with the math and statistics at the core of data science, and with hacking skills you need to get started as a data scientist. Today’s messy glut of data holds answers to questions no one’s even thought to ask. This book provides you with the know-how to dig those answers out. Get a crash course in Python Learn the basics of linear algebra, statistics, and probability—and understand how and when they're used in data science Collect, explore, clean, munge, and manipulate data Dive into the fundamentals of machine learning Implement models such as k-nearest Neighbors, Naive Bayes, linear and logistic regression, decision trees, neural networks, and clustering Explore recommender systems, natural language processing, network analysis, MapReduce, and databases

University Physics: Australian edition

Author: Hugh D Young,Roger A Freedman,Ragbir Bhathal

Publisher: Pearson Higher Education AU

ISBN: 1442538015

Category: Science

Page: 1576

View: 3485

This book is the product of more than half a century of leadership and innovation in physics education. When the first edition of University Physics by Francis W. Sears and Mark W. Zemansky was published in 1949, it was revolutionary among calculus-based physics textbooks in its emphasis on the fundamental principles of physics and how to apply them. The success of University Physics with generations of (several million) students and educators around the world is a testament to the merits of this approach and to the many innovations it has introduced subsequently. In preparing this First Australian SI edition, our aim was to create a text that is the future of Physics Education in Australia. We have further enhanced and developed University Physics to assimilate the best ideas from education research with enhanced problem-solving instruction, pioneering visual and conceptual pedagogy, the first systematically enhanced problems, and the most pedagogically proven and widely used online homework and tutorial system in the world, Mastering Physics.



Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120348885

Category: Science

Page: 696

View: 5890

This book [earlier titled as Electromagnetism: Theory and Applications which is bifurcated into two volumes: Electromagnetism: Theory and Electromagnetism: Applications (Magnetic Diffusion and Electromagnetic Waves) has been updated to cover some additional aspects of theory and nearly all modern applications. The semi-historical approach is unchanged, but further historical comments have been introduced at various places in the book to give a better insight into the development of the subject as well as to make the study more interesting and palatable to the students. Key Features • Physical explanations of different types of currents • Concepts of complex permittivity and complex permeability; and anisotropic behaviour of constitute parameters in different media and different conditions • Vector co-ordinate system transformation equations • Halbach magnets and the theory of one-sided flux • Discussion on physical aspects of demagnetization curve of B-H loop for ferromagnetic materials • Extrapolation of Frohlich-Kennely equation used for the design and analysis of permanent magnet applications • Physical aspects of Faraday’s law of electromagnetic induction (i.e., Fourth Maxwell’s field equation) through the approach of special relativity • Extrapolation and elaboration of the concept of electromechanical energy conversion to both magnetic as well as electric field systems Appendices contain in-depth analysis of self-inductance and non-conservative fields (Appendix 6), proof regarding the boundary conditions (Appendix 8), theory of bicylindrical co-ordinate system to provide the physical basis of the circuit approach to the cylindrical transmission line systems (Appendix 10), and properties of useful functions like Bessel and Legendre functions (Appendix 9). The book is designed to serve as a core text for students of electrical engineering. Besides, it will be useful to postgraduate physics students as well as research engineers and design and development engineers in industries.