Customer Reviews

Introduction to Linear Algebra and Differential Equations (Dover Books on Mathematics)

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I am a physicist, and as a sophomore in college I was warned by the juniors: "Learn linear algebra!!!! They hardly teach any of it in the required math classes, and you'll die in quantum without it!!!" So I studied this book. Even without doing many of the problems I got a clear grasp of what a vector space is, why it is more than mere formalism, what a linear transformation is, the significance of bases, diagonalization, and how to work with matrices and really understand them. All of this was indispensable in studying quantum mechanics.

Of course, solving the problems will only help your understanding. I HIGHLY recommend this for any physics student who had a bad (or non-existent) linear algebra class.

The book is easy to read. Dettman manages to find an excellent balance between formal proof and informal explanation. The first two chapters on Complex Numbers and Linear Algebraic Equations are particularly good, and this has become the first book I usually reach for if I need to look up something about matrices. Matrix notation is used throughout the book for topics such as linear transformations and systems of equations. There are hints and answers to about half the exercises at the end of the book, making it very helpful for self study.

The first half of this book is good. Although Dettman does occasionally skip nonobvious steps, he does a good job of introducing the reader to complex numbers, matrices, and linear algebra. The second half, though, concerning differential equations is awful. I originally got this book to teach myself these two subjects over the summer and shortly into Chapter 5 I had to give it up and switch material; the explanation is murky and the presentation confusing: it only really makes sense after you go somewhere else and learn differential equations, then come back and look at it again.

If you want to learn linear algebra, you can't go wrong with this book, although there are better choices out there. If you want to learn differential equations, this is not the book for you.