Linear Algebra and Group Theory for Physicists and Engineers, 2nd Edition
- Length: 601 pages
- Edition: 2
- Language: English
- Publisher: Springer
- Publication Date: 2023-01-17
- ISBN-10: 3031224213
- ISBN-13: 9783031224218
- Sales Rank: #12000486 (See Top 100 Books)
This textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience. Being approached together at the same time, these two topics complete one another, allowing students to attain a deeper understanding of both subjects. The opening chapters introduce linear algebra with applications to mechanics and statistics, followed by group theory with applications to projective geometry. Then, high-order finite elements are presented to design a regular mesh and assemble the stiffness and mass matrices in advanced applications in quantum chemistry and general relativity.
This text is ideal for undergraduates majoring in engineering, physics, chemistry, computer science, or applied mathematics. It is mostly self-contained―readers should only be familiar with elementary calculus. There are numerous exercises, with hints or full solutions provided. A series of roadmaps are also provided to help instructors choose the optimal teaching approach for their discipline.
The second edition has been revised and updated throughout and includes new material on the Jordan form, the Hermitian matrix and its eigenbasis, and applications in numerical relativity and electromagnetics.
Cover Front Matter Part I. Part I 1. Vectors and Matrices 2. Determinant and Vector Product and Their Applications in Geometrical Mechanics 3. Markov Matrix and Its Spectrum: Toward Search Engines 4. Special Relativity: Algebraic Point of View Part II. Part II 5. Groups and Isomorphism Theorems 6. Projective Geometry with Applications in Computer Graphics 7. Quantum Mechanics: Algebraic Point of View Part III. Part III 8. Polynomials and Their Gradient 9. Basis Functions: Barycentric Coordinates in 3-D Part IV. Part IV 10. Automatic Mesh Generation 11. Mesh Regularity 12. Numerical Integration 13. Spline: Variational Model in 3-D Part V. Part V 14. Permutation Group and the Determinant 15. Electronic Structure in the Atom: The Hartree–Fock System Part VI. Part VI 16. The Jordan Form 17. Jordan Decomposition of a Matrix 18. Algebras and Their Derivations and Their Jordan Form Part VII. Part VII 19. Einstein Equations and their Linearization Back Matter
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