Linear Algebra and Analytic Geometry for Physical Sciences

Linear Algebra and Analytic Geometry for Physical Sciences

Author: Giovanni Landi

Publisher: Springer

Published: 2018-05-12

Total Pages: 348

ISBN-13: 3319783610

DOWNLOAD EBOOK

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises.Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number.The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.


Linear Algebra and Analytic Geometry for Physical Sciences

Linear Algebra and Analytic Geometry for Physical Sciences

Author: Giovanni Landi

Publisher: Springer

Published: 2018-05-22

Total Pages: 345

ISBN-13: 9783319783604

DOWNLOAD EBOOK

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises.Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number.The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.


Linear Algebra and Geometry

Linear Algebra and Geometry

Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

Published: 2012-08-23

Total Pages: 536

ISBN-13: 3642309941

DOWNLOAD EBOOK

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.


Algebraic and Analytic Geometry

Algebraic and Analytic Geometry

Author: Amnon Neeman

Publisher: Cambridge University Press

Published: 2007-09-13

Total Pages: 433

ISBN-13: 0521709830

DOWNLOAD EBOOK

Modern introduction to algebraic geometry for undergraduates; uses analytic ideas to access algebraic theory.


A First Course in Calculus

A First Course in Calculus

Author: Serge Lang

Publisher: Springer Science & Business Media

Published: 2012-09-17

Total Pages: 741

ISBN-13: 1441985328

DOWNLOAD EBOOK

This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.


Linear Algebra Through Geometry

Linear Algebra Through Geometry

Author: Thomas Banchoff

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 316

ISBN-13: 1461243904

DOWNLOAD EBOOK

This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.


A Vector Space Approach to Geometry

A Vector Space Approach to Geometry

Author: Melvin Hausner

Publisher: Courier Dover Publications

Published: 2018-10-17

Total Pages: 417

ISBN-13: 0486835391

DOWNLOAD EBOOK

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.


Complex Geometry

Complex Geometry

Author: Daniel Huybrechts

Publisher: Springer Science & Business Media

Published: 2005

Total Pages: 336

ISBN-13: 9783540212904

DOWNLOAD EBOOK

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)


Basic Linear Algebra

Basic Linear Algebra

Author: T.S. Blyth

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 242

ISBN-13: 1447106814

DOWNLOAD EBOOK

Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.