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Linear Algebra and Group Theory for Physicists and Engineers

  • Yair Shapira
Textbook

Table of contents

  1. Front Matter
    Pages i-xxxi
  2. Introduction to Linear Algebra

    1. Front Matter
      Pages 1-1
    2. Yair Shapira
      Pages 3-49
    3. Yair Shapira
      Pages 89-101
    4. Yair Shapira
      Pages 103-141
  3. Introduction to Group Theory

    1. Front Matter
      Pages 143-143
    2. Yair Shapira
      Pages 231-264
  4. Polynomials and Basis Functions

    1. Front Matter
      Pages 265-265
    2. Yair Shapira
      Pages 267-297
  5. Finite Elements in 3-D

    1. Front Matter
      Pages 325-326
    2. Yair Shapira
      Pages 327-345
    3. Yair Shapira
      Pages 347-358
    4. Yair Shapira
      Pages 359-367
  6. Advanced Applications in Physics and Chemistry

    1. Front Matter
      Pages 377-377
    2. Yair Shapira
      Pages 379-402
    3. Yair Shapira
      Pages 403-417
  7. Back Matter
    Pages 419-441

About this book

Introduction

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.

Keywords

Group theory Linear algebra High dimensional vectors Fourier matrices Markov chain Quantum mechanics Mesh generation

Authors and affiliations

  • Yair Shapira
    • 1
  1. 1.Department of Computer ScienceTechnion, Israel Institute of TechnologyHaifaIsrael

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