Advanced Engineering Mathematics 2nd Edition

This is possibly the best single math book I have come across. I used this book for a graduate-level two-course sequence on engineering math based largely on Greenberg's own courses (there's a lot of faculty from Cornell in my department). I have to say, Greenberg has an amazing capability for communicating mathematics. All of the topics he goes into are presented very lucidly, with several examples that both reinforce ideas as well as continue to teach- not just worked out problems for the sake of working out problems. Don't be afraid of the 1300+ pages- the margins are nice and wide for the author's figures and your own notes, and the font is pretty large.The book covers ODEs, linear algebra and vector space theory, scalar and vector field theory, PDEs, and complex numbers- enough to give any engineer a solid background in the mathematics used to solve the problems that arise in engineering. After going through this book (and the two courses), I fixed many of the holes that were in my mathematical background for whatever reason. The one topic that probably should have been in the book is tensor math (it only has a footnote right now). One thing to be aware of is that the exercises at the end of each section are also filled with knowledge to take away. I didn't realize this right away since my prof never assigned problems from the book.I highly recommend this book to any engineer- not just those are seeking/have sought graduate degrees. I can easily see myself using frequently this text as a reference for the rest of my career.

Used for two graduate engineering analysis classes which I should not have taken together. We covered linear algebra, vector calculus, and complex analysis in one half of the book, and ODE's and PDE's in the second half. Even so, there is still probably 50% of the book we did not cover which goes into more detail on many other subjects. Most of the chapters contain what you need to succeed with hidden gems and derivations hidden in some of the homework problems.This book has clear examples and does a great job of helping you remember all those math courses you took years ago. It may look dated graphically compared to newer books available such as the one by Erwin Kreyszigk. However math like this is the same no matter how old it is, so pick what you need because no text is ever complete.

Table of contents:ORDINARY DIFFERENTIAL EQUATIONS.1. Introduction to Differential Equations.2. Equations of First Order.3. Linear Differential Equations of Second Order and Higher.4. Power Series Solutions.5. Laplace Transform.6. Quantitative Methods: Numerical Solution of Differential Equations.7. Qualitative Methods: Phase Plane and Nonlinear Differential Equations.II. LINEAR ALGEBRA.8. Systems of Linear Algebraic Equations; Gauss Elimination.9. Vector Space.10. Matrices and Linear Equations.11. The Eigenvalue Problem.12. Extension to Complex Case (Optional).III. SCALAR and VECTOR FIELD THEORY.13. Differential Calculus of Functions of Several Variables.14. Vectors in 3-Space.15.Curves, Surfaces, and Volumes.16. Scalar and Vector Field Theory.IV. FOURIER SERIES AND PARTIAL DIFFERENTIAL EQUATIONS.17. Fourier Series, Fourier Integral, Fourier Transform.18. Diffusion Equation.19. Wave Equation.20. Laplace Equation.V. COMPLEX VARIABLE THEORY.21. Functions of a Complex Variable.22. Conformal Mapping.23. The Complex Integral Calculus.24. Taylor Series, Laurent Series, and the Residue Theorem.Appendix A: Review of Partial Fraction Expansions.Appendix B: Existence and Uniqueness of Solutions of Systems of Linear Algebraic Equations.Appendix C: Table of Laplace Transforms.Appendix D: Table of Fourier Transforms.Appendix E: Table of Fourier Cosine and Sine Transforms.Appendix F: Table of Conformal Maps.

It's an OK book, but two things against it:1. Few examples and many of them are based on the theory (meaning they're not using specific examples but just a general example for all cases)2. Black and white book. Bolded words get lost. Needs new formatting.That being said, it's a good book for differential equations and linear algebra but you may want to supplement it with other sources (I recommend Nagle/Saff/Snider Fundamentals of Differential Equations which has more examples and explains better).

Its just a Ok book, the thing I didn't like about this book is that it doesn't have many solved examples

I have been using this book for 2 of my classes. It is really big and heavy with well develop examples. I like the organization.

Using this book for a general applied math course as a prerequisite for my engineering graduate program. Normally I don't like reading math books because the language is not easy to understand, so I only refer to them for example problems, but I like the language in this book. It is more down to earth explanations of the methods and has a nice summary at the end of each chapter.