Analytic Geometry And Linear Algebra For Physical Sciences
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Analytic Geometry and Linear Algebra for Physical Sciences
Dive into the essential mathematical tools with "Analytic Geometry and Linear Algebra for Physical Sciences." This comprehensive guide is tailored for undergraduate students pursuing degrees in the physical sciences, including physics, chemistry, and engineering. Our book seamlessly integrates theoretical concepts with practical applications, fostering a deep understanding of linear algebra and analytic geometry. Each chapter is designed to build from fundamental concepts to advanced topics, reinforced by real-world examples that highlight the relevance of these mathematical principles. Key features include a progressive learning approach, numerous exercises ranging from basic to challenging, and practical applications that develop problem-solving skills. This book not only supports academic success but also cultivates the analytical mindset crucial for future scientific endeavors. Aspiring scientists will find in this book a valuable companion that demystifies mathematical complexities, making the journey through linear algebra and analytic geometry engaging and empowering.
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.
Linear Algebra for Physics
Author: Nikolaos A. Papadopoulos
language: en
Publisher: Springer Nature
Release Date: 2024-10-13
This textbook provides a full treatment of Linear Algebra devoted to undergraduate and graduate physics students. Although the mathematical level is similar to the corresponding mathematical textbooks in regard to definitions, propositions and proofs, it adopts a language and approach more attuned to the reader’s familiarity with physics lectures and physics textbooks. A distinctive feature is the emphasis placed on the significance of bases within a vector space. As a result, students gain a deeper understanding of how vector indices, despite their abundance, serve not as enemies but as friends since they give additional information about the mathematical objects being used, and facilitate access to tensor formalism. The book offers numerous worked examples and exercises with solution hints to deepen this knowledge.