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a)I am trying to get a book that would give describe all the coordinate systems and their transformations(e.g. cartesian,polar,spherical,homogeneous,curvilinear,generalized,etc).

b) And I need to know about some good books on multi-variable calculus which exclude vector calculus and operates only on scalar field.

All suggestions are welcome although books on an undergraduate level are preferred.

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closed as off-topic by Mark Fantini, Joonas Ilmavirta, Benoît Kloeckner, Daniel Hast, vonbrand Apr 6 '16 at 19:46

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    $\begingroup$ You'll have difficulty finding just one book to satisfy (a), since coordinate systems are as varied as their applications and are generally presented in very specific contexts. You'll also have difficulty satisfying (b) since vector analysis is considered a central topic in MV calculus. Most decent MV calc texts will fairly treat a variety of coordinate systems. Why do you suspect that one of these will not suit your needs for both (a) and (b)? $\endgroup$ – Andrew Apr 4 '16 at 19:43
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    $\begingroup$ Please edit the title of the post to better indicate the type of book you are looking for. $\endgroup$ – mweiss Apr 4 '16 at 23:15
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    $\begingroup$ In addition to what the others have commented, your two questions seem unrelated. It would therefore be best to ask them separately, not in the same question. (Anyway, welcome to the site!) $\endgroup$ – Joonas Ilmavirta Apr 5 '16 at 6:42
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Related is the math stackexchange question Book on coordinate transformations.

In two comments there I suggested looking at some of the many lengthy treatises on mathematical methods for physicists for beginning graduate students in physics, in particular Morse/Feshbach's 2-volume treatise Methods of Theoretical Physics. You can find reviews at amazon.com for Part I and Part II and Parts I & II.

Kris writes (in part) in a review at the "Parts I & II" page:

These books go into great detail on what are now considered esoteric coordinate systems (elliptical, parabolic, etc); this may be the best place to find material on this topic.

(ADDED A WEEK LATER) I happened to be at a university library this weekend and while there I looked at Morse/Feshbach. Pages 656-666 of Part I has summaries of the following:

Rectangular Coordinates, Circular Cylinder Coordinates, Elliptic Cylinder Coordinates, Parabolic Cylinder Coordinates, Spherical Coordinates, Conical Coordinates, Parabolic Coordinates, Prolate Spheroidal Coordinates, Oblate Spheroidal Coordinates, Ellipsoidal Coordinates, Paraboloidal Coordinates, Bispherical Coordinates, Toroidal Coordinates.

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