Linear Algebra And Analytic Geometry

Linear Algebra and Analytic Geometry

In this book, the topics are presented in the same order as in the textbook. The problems concern two content areas: Linear Algebra, and Analytical Geometry. After reading this book, a student should be ables to solve linear equations and to perform the basic operations on numbers and algebraic expressions. The Linear Algebra tests will reveal readers' knowledge and skills, readers' abilities in interpreting symbols, justifying statements and constructing proofs. Readers should be able to apply the properties of determinants and matrix operations and solve linear systems of equations. The Analytical Geometry topics include different forms of equations of straight lines and planes; angles between simple figures; the curves of the second order. This book will prove definitive and ideal reference tool to research scholars, academicians and educationists.

Linear Algebra and Analytic Geometry for Physical Sciences

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.

Calculus with Analytic Geometry