Linear Algebra and Group Theory for Physicists and Engineers 2nd Edition Yair Shapira

Linear Algebra and Group Theory for Physicists and Engineers – Ebook Instant Download/Delivery ISBN(s): 9783031224218,9783031224225,9783319147932,3031224213,3319147935,3031224221

Product details:

• ISBN-10 ‏ : ‎ 3031224213
• ISBN-13 ‏ : ‎ 978-3031224218
• Author(s): Yair Shapira

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.

Table contents:

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

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