Greenberg M. Advanced Engineering Mathematics

Pearson, 1998. – 1324 p. – 2nd ed. – ISBN: 0133214311, 9780133214314This clear, pedagogically rich book develops a strong understanding of the mathematical principles and practices that today's engineers need to know. Equally as effective as either a textbook or reference manual, it approaches mathematical concepts from an engineering perspective, making physical applications more vivid and substantial. Its comprehensive instructional framework supports a conversational, down-to-earth narrative style, offering easy accessibility and frequent opportunities for application and reinforcement.
We used this text in an introductory math for engineers course that I took for fun (I can see the smirk on your face already :) Anyway, the book integrates different parts of applied mathematics very well, particularly drilling into your head the wonderful properties of linearity, and how linear algebra in general makes life much simpler. The only (minor) drawback to this book I would say is it's "lack of color", i.e., this is not a book you buy for the pictures. The diagrams are black and white, and very simple. Kreyszig's book is much more visually appealing, but does not have the mathematical depth that Greenberg can get across. If you are more of a visual learner (as I actually am), you may prefer Kreyszig, as he puts important results/theorems in colored boxes, and his style is more casual than Greenberg. It is not hard to see why mathematicians (including several professors I know) prefer Greenberg, as his presentation is more crisp, and it definitely flows. Some of the material requires deep thought, but is well worth the effort. His material on PDEs (mostly 2nd order linear equations) is very engaging, and expertly written. You get a nice overview of the subject (a branch of mathematics highly applicable in today's world), but he doesn't get bogged down in unnecessary detail. My verdict is this: if you want a reference book to refer to from time to time, Kreyszig may be better. However, if you want a text to learn the material from, I would definitely go with Greenberg. If you have the money, get both titles, they complement each other well. But if you can only afford one, get Greenberg.