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Mathematical Methods

For Students of Physics and Related Fields

  • Sadri Hassani

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Coordinates and Calculus

    1. Front Matter
      Pages 1-1
    2. Sadri Hassani
      Pages 3-42
    3. Sadri Hassani
      Pages 43-75
    4. Sadri Hassani
      Pages 77-100
    5. Sadri Hassani
      Pages 101-137
    6. Sadri Hassani
      Pages 139-170
  3. Algebra of Vectors

    1. Front Matter
      Pages 171-171
    2. Sadri Hassani
      Pages 173-214
    3. Sadri Hassani
      Pages 215-236
    4. Sadri Hassani
      Pages 237-255
  4. Infinite Series

    1. Front Matter
      Pages 256-256
    2. Sadri Hassani
      Pages 259-281
    3. Sadri Hassani
      Pages 283-316
    4. Sadri Hassani
      Pages 317-339
  5. Analysis of Vectors

    1. Front Matter
      Pages 340-340
    2. Sadri Hassani
      Pages 343-363
    3. Sadri Hassani
      Pages 365-385
    4. Sadri Hassani
      Pages 387-406
    5. Sadri Hassani
      Pages 407-421
    6. Sadri Hassani
      Pages 423-438
    7. Sadri Hassani
      Pages 439-474
  6. Complex Analysis

    1. Front Matter
      Pages 475-475
    2. Sadri Hassani
      Pages 477-496
    3. Sadri Hassani
      Pages 497-514
    4. Sadri Hassani
      Pages 515-523
    5. Sadri Hassani
      Pages 525-537
  7. Differential Equations

    1. Front Matter
      Pages 539-539
    2. Sadri Hassani
      Pages 541-550
    3. Sadri Hassani
      Pages 551-562
    4. Sadri Hassani
      Pages 563-590
    5. Sadri Hassani
      Pages 591-605
    6. Sadri Hassani
      Pages 607-637
    7. Sadri Hassani
      Pages 639-659
    8. Sadri Hassani
      Pages 661-689
  8. Special Topics

    1. Front Matter
      Pages 690-690
    2. Sadri Hassani
      Pages 693-726
    3. Sadri Hassani
      Pages 727-751
    4. Sadri Hassani
      Pages 753-779
    5. Sadri Hassani
      Pages 781-813
  9. Back Matter
    Pages 815-831

About this book

Introduction

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.

Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics.

This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

Some praise for the previous edition:

"The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities."

--Physics Today

 

"Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done."

--Zentralblatt MATH

Keywords

Algebra Arithmetic Differentiation and integration Dirac delta functions Finite Infinite series Laplace's equation Mathematical physics Nonlinear dynamics calculus equation mathematics numerical analysis partial differential equation

Authors and affiliations

  • Sadri Hassani
    • 1
  1. 1.IIlinois State UniversityNormalUSA

Bibliographic information