# Mathematical Methods: For Students of Physics and Related by Sadri Hassani

By Sadri Hassani

Intended to persist with the standard introductory physics classes, this booklet has the original characteristic of addressing the mathematical wishes of sophomores and juniors in physics, engineering and different similar fields. Many unique, lucid, and suitable examples from the actual sciences, difficulties on the ends of chapters, and bins to stress very important suggestions support consultant the coed throughout the material.

Beginning with stories of vector algebra and differential and critical calculus, the e-book maintains with endless sequence, vector research, complicated algebra and research, usual and partial differential equations. Discussions of numerical research, nonlinear dynamics and chaos, and the Dirac delta functionality offer an creation to fashionable issues in mathematical physics.

This new version has been made extra uncomplicated via association into handy, shorter chapters. additionally, it comprises a completely new part on chance and lots of new fabric on tensors and necessary transforms.

Some compliment for the former edition:

"The e-book has many strengths. for instance: each one bankruptcy begins with a preamble that places the chapters in context. usually, the writer makes use of actual examples to inspire definitions, illustrate relationships, or culminate the improvement of specific mathematical strands. using Maxwell's equations to cap the presentation of vector calculus, a dialogue that comes with a few tidbits approximately what led Maxwell to the displacement present, is a very stress-free instance. old touches like this aren't remoted circumstances; the booklet encompasses a huge variety of notes on humans and concepts, subtly reminding the coed that technology and arithmetic are carrying on with and engaging human activities."

--Physics Today

"Very good written (i.e., super readable), rather well particular (mainly to a standard pupil of physics at some degree of simply leaving his/her sophomore point) and intensely good focused (to an author's it sounds as if liked topic of PDE's with purposes and with all their invaluable pedagogically-mathematical background)...The major advantages of the textual content are its readability (achieved through returns and options of the context), stability (building the topic step-by-step) and originality (recollect: the life of the complicated numbers is just admitted a long way within the moment half the text!). final yet no longer least, the scholar reader is inspired through the graphical caliber of the textual content (figures to start with, but additionally bins with the necessities, summarizing reviews within the left column etc.)...Summarizing: good done."

--Zentralblatt MATH

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**Sample text**

This is, of course, not true, because the spherical unit vectors at P1 are completely diﬀerent from those at P2 , and, therefore, contrary to the Cartesian case, we cannot simply subtract components. 11 We should really label everything with P . But, as usual, we assume this labeling to be implied. 3 Vectors in Diﬀerent Coordinate Systems 21 One of the great advantages of vectors is their ability to express results independent of any speciﬁc coordinate systems. Physical laws are always coordinate-independent.

Also note that the range of θ excludes values larger than π. This is because the range of ϕ takes care of points where θ “appears” to have been increased by π. Historical Notes One of the greatest achievements in the development of mathematics since Euclid was the introduction of coordinates. Two men take credit for this development: Fermat and Descartes. These two great French mathematicians were interested in the uniﬁcation of geometry and algebra, which resulted in the creation of a most fruitful branch of mathematics now called analytic geometry.

Show the following vector identities by writing each vector in terms of Cartesian unit vectors and showing that each component of the LHS is equal to the corresponding component of the RHS. (a) a · (b × c) = c · (a × b) = b · (c × a). (b) a × (b × c) = b(a · c) − c(a · b), this is called the bac cab rule. (c) (a × b) · (c × d) = (a · c)(b · d) − (a · d)(b · c). (d) (a × b) × (c × d) = b[a · (c × d)] − a[b · (c × d)]. (e) (a × b) × (c × d) = c[a · (b × d)] − d[a · (b × c)]. (f) (a × b) · (a × b) = |a|2 |b|2 − (a · b)2 .