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Questions regarding self studying have been asked here before, but those seem to concern mostly school level maths.

My situation: I'm an engineer, before I started that training I flunked out of studying physics because of my math grades. Now, I want to improve my engineering skills in several diverse directions:

  • Fluid Dynamics - I don't speak the language, every statement about fluids somehow involves tensors and a Laplace operator. I've met those before, but I don't handle them well.

  • Process Analysis - anything worth describing (that's simpler than a turbulent fluid) boils down to differential equations. I've forgotten most of what I learned about those, and don't trust the rest.

Of course, I still have my old textbooks. What I need is problems and tests to sharpen my teeth on.

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up vote 2 down vote accepted

Below are some books I know about (I've owned all but one for over 20 years) that I think fit what you're looking for, which also appear to be fairly cheap. You will also want to get a calculus text to look up things that you may have forgotten. I recommend a calculus book written before calculators came into common usage (late 1970s) that isn't an "honors calculus" type of text (many of these appeared in the late 1950s through the mid 1970s, as a result of the new math curriculum), because such a book will probably be better suited for the books below.

Harry M. Schey, DIV, Grad, Curl, & All That: An Informal Text on Vector Calculus, 4th edition, 2005.

Harry F. Davis, Introduction to Vector Analysis, 7th edition, 1995.

Note: I have a hardback version of the 1st (2nd?) edition of Davis, so my recommendation is based on that earlier edition. At least one amazon.com reviewer says that the older editions are better (in ways that sound as they would be better for you also), so you might look for a used copy of the 2nd or 3rd edition.

Harry F. Davis, Fourier Series and Orthogonal Functions, Dover, 1989.

Murray R. Spiegel, various Schaum's Outline of volumes at Spiegel's Wikipedia page

I knew that Spiegel had written a lot of these volumes, but I had not seen a complete list until now. (Assuming this is a complete list.) I happen to have 9 of these Spiegel books, for what it's worth.

Kenneth S. Miller, Engineering Mathematics, Dover, 1956.

Rutherford Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics, Dover, 1990.

I'm hesitant to include this book, but since there is now a cheap Dover edition, I will. I did an independent-study/reading-course out of this book with an engineering faculty member back in Spring 1982 (those who know of my mathematical interests will find this curious; this happened to be during one of my several earlier math incarnations that were later abandoned) and I found it very difficult to follow, but this was likely due to a shortfall in my background rather than a fault of the book. Indeed, my goal in working through this book was to "learn the physics/engineering lingo" of vector and tensor analysis, but I probably should have started with Davis' Introduction to Vector Analysis (listed above) and then gone into the Aris book.

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Thanks! Can you please indicate which of those contain tests for self studying? –  mart Aug 2 '12 at 7:34
    
@mart: They all contain problem sets, but if you want a high ratio of problems to text, you'll want to consider the Schaum's Outline books. I don't know the situation now, but back in the 1970s the Schaum's Outline books were kind of like Cliff's Notes for physics and engineering students (but better, since they weren't aimed at the marginal student trying to avoid assigned literature readings), and pretty much everyone was familiar with them. –  Dave L. Renfro Aug 2 '12 at 20:20
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