Problems and Solutions on Vector Spaces for Physicists
From Part I in Mathematical Physics—A Modern Introduction to Its Foundations
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Beschreibung
This book offers supporting material for the comprehensive textbook Mathematical Physics—A Modern Introduction to Its Foundations authored by Sadri Hassani. The book covers mathematical preliminaries and all of Part I in Hassani’s textbook. The subjects covered here include the key topics necessary for physicists to form a solid mathematical foundation: vectors and linear maps, algebras, operators, matrices, and spectral decomposition. In particular, the vector space concept is a central unifying theme in later chapters of Hassani’s textbook. Detailed solutions are provided to one third of the end-of-chapter exercises in the first six chapters of his text.
The present volume helps upper-undergraduate and early postgraduate physics students deepen their understanding of the mathematics that they encounter in physics, learn physics more efficiently, and use mathematics with more confidence and creativity. The content is thus presented rigorously but remains accessible tophysics students.
New exercises are also proposed, some with solutions, some without, so that the total number of unsolved exercises remains unchanged. They are chosen to help explain difficult concepts, amplify key points in Hassani's textbook, or make further connections with applications in physics. Taken together with Hassani's work, the two form a self-contained set and the solutions make detailed reference to Hassani's text. The solutions also refer to other mathematics and physics textbooks, providing entry points to further literature that finds a useful place in the physicist's personal library.
Serves as the perfect accompaniment to Hassani's textbook Mathematical Physics
With about 200 exercises, 90 of which are brand new
Includes proofs left for exercise to students in the Hassani textbook
Detailed index helping instructors and students to find problems related to a given topic
Covers complete solutions to one third of the exercises in the first six chapters of Mathematical Physics by Hassani Offers detailed solutions that help students gain confidence when using mathematics for physics Adds new supplementary exercises to illuminate subtle concepts, emphasize key points, and clarify difficult material
Autor*in
Robert B. Scott
Themen in »Problems and Solutions on Vector Spaces for Physicists«
Finite-Dimensional Vector Spaces Schwarz Inequality Gram-Schmidt Process Total Matrix Algebra Hermitian Operator Unitary Operator Projection Operator Inverse of a Matrix Trace of a Matrix Spectral Decomposition Polar Decomposition Infinite-Dimensional Vector Spaces Hilbert Spaces Orthogonal Polynomials Laguerre Polynomials