Suggestion for textbook(s) needed

[Phy4life]

I'm a fresher at college, pursuing an honors degree in Physics. I've got Mathematical Methods for my first semester. I've collected a couple of books like Arfken and Weber and M. L. Boas. But none of them quite entirely cover the course material.
Listed below are the topics included in our syllabus which I could not find in any book I've looked up so far:

• Index notation: dummy indices, free and sum indices, symmetric and skew symmetric expressions, summation convention, addition and multiplication of symbols, contraction, special symbols.
• Transformations: Inversion, mirror reflection, True and pseudo vectors and scalars, orthogonal transformations, general spatial notations(passive).
• Surfaces in 3D: Surfaces of revolution, cylindrical surfaces, conical surfaces, standard surfaces of second order(ellipsoids, hyperboloids, paraboloids), the Z-Slice method.

Though Orthogonal transformations has been partly covered in Arfken, it isn't as detailed as I need it to be. For some unknown reasons our professor refuses to recommend any textbook. I feel quite lost when it comes to these topics. Not to mention the utterly helpless feeling that comes when you do not have a loyal book to depend on. So, any help in this matter would make me immensely grateful.

 

[WannabeNewton]

The content of your first bullet point is what one would call Ricci calculus, particularly in the context of ##\mathbb{R}^{3}## if this is for say an introductory electromagnetism (EM) class: http://en.wikipedia.org/wiki/Ricci_calculus.

I personally got acquainted with Ricci calculus through general relativity textbooks (Ricci calculus is a fundamental tool in general relativity), e.g. https://www.amazon.com/dp/0521887054/?tag=pfamazon01-20, but the formalism is also introduced in some EM texts.

You might try the following:
https://www.amazon.com/dp/0486658406/?tag=pfamazon01-20
https://www.amazon.com/dp/0486654931/?tag=pfamazon01-20
http://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf