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Author: Gilbert de B. Robinson Publisher: Courier Corporation ISBN: 0486321045 Category : Mathematics Languages : en Pages : 194
Book Description
Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.
Author: Gilbert de B. Robinson Publisher: Courier Corporation ISBN: 0486321045 Category : Mathematics Languages : en Pages : 194
Book Description
Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.
Author: Melvin Hausner Publisher: Courier Dover Publications ISBN: 0486835391 Category : Mathematics Languages : en Pages : 417
Book Description
A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.
Author: Gabriel Weinreich Publisher: University of Chicago Press ISBN: 9780226890487 Category : Mathematics Languages : en Pages : 132
Book Description
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.
Author: Miroslav Josipović Publisher: Springer Nature ISBN: 3030017567 Category : Mathematics Languages : en Pages : 258
Book Description
This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.
Author: Serge Lang Publisher: Springer Science & Business Media ISBN: 1461210682 Category : Mathematics Languages : en Pages : 624
Book Description
This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.
Author: D. E. Rutherford Publisher: Courier Corporation ISBN: 048615453X Category : Mathematics Languages : en Pages : 148
Book Description
This text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. 1957 edition.
Author: Anthony J. Pettofrezzo Publisher: Courier Corporation ISBN: 0486148890 Category : Mathematics Languages : en Pages : 146
Book Description
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 two- and three-dimensional space. Its rigorous development includes a complete treatment of the algebra of vectors in the first two chapters. Among the text's outstanding features are numbered definitions and theorems in the development of vector algebra, which appear in italics for easy reference. Most of the theorems include proofs, and coordinate position vectors receive an in-depth treatment. Key concepts for generalized vector spaces are clearly presented and developed, and 57 worked-out illustrative examples aid students in mastering the concepts. A total of 258 exercise problems offer supplements to theories or provide the opportunity to reinforce the understanding of applications, and answers to odd-numbered exercises appear at the end of the book.
Author: Vladimir Serdarushich Publisher: Createspace Independent Publishing Platform ISBN: 9781523688661 Category : Languages : en Pages : 184
Book Description
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,
Author: Gilbert de B. Robinson
Author: Gilbert de B. Robinson
Author: Melvin Hausner
Author: Gabriel Weinreich
Author: Seymour Schuster
Author: Miroslav Josipović
Author: Serge Lang
Author: David Carruthers Murdoch
Author: D. E. Rutherford
Author: Anthony J. Pettofrezzo
Author: Vladimir Serdarushich