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

By Sadri Hassani

Intended to persist with the standard introductory physics classes, this e-book has the original characteristic of addressing the mathematical wishes of sophomores and juniors in physics, engineering and different similar fields. Many unique, lucid, and appropriate examples from the actual sciences, difficulties on the ends of chapters, and containers to stress vital recommendations aid consultant the scholar in the course of the material.

Beginning with stories of vector algebra and differential and critical calculus, the e-book keeps with limitless 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 trendy subject matters in mathematical physics.

This re-creation has been made extra common via association into handy, shorter chapters. additionally, it contains a completely new part on likelihood and lots of new fabric on tensors and fundamental transforms.

Some compliment for the former edition:

"The booklet has many strengths. for instance: each one bankruptcy starts off with a preamble that places the chapters in context. usually, the writer makes use of actual examples to encourage definitions, illustrate relationships, or culminate the advance of specific mathematical strands. using Maxwell's equations to cap the presentation of vector calculus, a dialogue that incorporates a few tidbits approximately what led Maxwell to the displacement present, is a very relaxing instance. old touches like this will not be remoted situations; the booklet encompasses a huge variety of notes on humans and ideas, subtly reminding the scholar that technological know-how and arithmetic are carrying on with and engaging human activities."

--Physics Today

"Very good written (i.e., tremendous readable), rather well specified (mainly to an ordinary scholar of physics at some degree of simply leaving his/her sophomore point) and extremely good targeted (to an author's it sounds as if liked topic of PDE's with purposes and with all their worthy pedagogically-mathematical background)...The major advantages of the textual content are its readability (achieved through returns and recommendations of the context), stability (building the topic step-by-step) and originality (recollect: the lifestyles of the complicated numbers is just admitted a ways within the moment half the text!). final yet no longer least, the coed reader is inspired through the graphical caliber of the textual content (figures to begin with, but additionally containers with the necessities, summarizing reviews within the left column etc.)...Summarizing: good done."

--Zentralblatt MATH

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Example text

Also assume that P lies in the xy-plane, and that q was at the origin at t = 0. Then eρ , r1 = vtˆ ez , r − r1 = ρˆ eρ − vtˆ ez . So v = vˆ ez , r = ρˆ |r − r1 | = (ρˆ eρ − vtˆ ez ) · (ρˆ eρ − vtˆ ez ) = ρ 2 + v 2 t2 and v × (r − r1 ) = vˆ ez × (ρˆ eρ − vtˆ ez ) = ρvˆ eϕ . Therefore, the magnetic field is B= km qv × (r − r1 ) km qρv ˆϕ . = 2 e |r − r1 |3 (ρ + v 2 t2 )3/2 Readers familiar with the relation between magnetic fields and currents in long wires will note that the magnetic field above obeys the right-hand rule.

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 . 16. Convert the following triplets from the given coordinate system to the other two. All angles are in radians. Cartesian: (1, 2, 1), (0, 0, 1), (1, −1, 0), (0, 1, 0), (1, 1, 1), (2, 2, 2), (0, 0, 5), (1, 1, 0), (1, 0, 0). Spherical: (2, π/3, π/4), (5, 0, π/3), (3, π/3, 3π/4), (1, 1, 0), (1, 0, 0), (5, 0, ♣), (3, π, ♥), (0, ♠, ♦). Cylindrical: (0, ♣, 4), (2, π, 0), (0, 217, −18), (1, 3π/4, −2), (1, 2, 3), (1, 0, 0).

According to this interpretation, the Sun, by its mere presence, creates around itself an invisible three dimensional “sheet” such that, if any object is placed in this sheet, it feels the gravitational force. The reason that planets feel the force of gravity of the Sun is because they happen to be located in the gravitational field of the Sun. The reason that an apple falls to the Earth is because it is in the gravitational field of the Earth and not due to some kind of action-at-a-distance ghost.

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