general

When I started using this textbook for a graduate level engineering mathematics I thought I would "see the light" and had finally come across an author that would help me understand advanced mathematics and its application to real-world problems. Needless to say I was let down. Kreysig offers no explanation for many new and complex concepts and often leaves out helpful background (theory/proofs) necessary to have a full undestanding and skill level necessary to apply the concepts. A case in point is his handling of the Legendre Transforms/Polynomials and Sturm-Liouville Theory. Did I mention that I think it is a bad idea to cover matrices and linear algebra in differnt chapters of the book

When I took ODE/PDE in undergraduate we used the text, Advanced Engineering mathematics by O'neil and at the time I thought this book was difficult and confusing. Althought it was not filled with color figures and graphs it contained many proofs and theorems to explain the concepts. I'm starting to use this book as a reference for those concepts that aren't covered thoroughly enough by Kreysig and now appreciate the O'Neil book more and more everyday.

This book tries to do it all, which is impossible. It covers the basics of a wide, wide variety of engineering problems, including ordinary and partial differential equations, Fourier series, differnetial forms, graph theory, linear algebra, complex variables, probablilty and statistics, vector calculus, numerical and computer methods and so on, and is undoubtedly the best book if you want a wide overview of the problems with less attention paid to theory and much attention paid to problem-solving techniques, but there is so much to cover, that there is not really any roomm left for really advanced topics. Tensors are not even mentioned as are topics in variational calculus, and the discrete math and numerical methods chapters are barely touched upon at all in much depth. So if you want a sophmore-junior level enginerring text, this makes for a great textbook and general reference book, but should not really be considered an "advanced" text. Great for up and coming engineers, but is not enough by itself.

This book does provide students, who have taken a first course in differential equations, a good look at Fourier Analysis, Boundary Value Problems, and partial differential equations; however, you might wish to obtain a working knowledge of linear algebra before using this book for the before-mentioned reasons - the chapters dealing with linear algebra (six and seven) are awesome for review, but horrible for the beginning student.
Other than that, the book is a good resource when it comes to the review chapters on ordinary differential equations, multivariable calculus, probability, etc...
This is a recommended book for the engineer who likes to review math on those boring summer days...