This tried-and-true book of differential equations expands upon the authors' Differential Computing and Modeling , 2nd Edition. It covers the core concepts and techniques of elementary linear algebra—matrices and linear systems, vector spaces, eigensystems, and matrix exponentials—that are needed for a careful introduction to linear equations. Complimenting this solid foundation, the book emphasizes mathematical modeling of real-world phenomena, and offers a fresh new computational flavor evident in figures, examples, problems, and projects throughout. Chapter topics first order differential equations, mathematical models and numerical methods, linear systems and matrices, vector spaces, linear equations of higher order, eigenvalues and eigenvectors, linear systems of differential equations, matrix exponential methods, and nonlinear systems and phenomena. A geometric visualization for those interested in science and engineering.
This sucked. I crammed a bunch of this on the bathroom floor before my exam freshman year of college and it was also the first time I started experimenting with black eyeliner, so I was trying to figure out what the fuck dual space is, tearing up, came out of the bathroom with it smudged all over my face, "took" the exam, walked out and my buddy went "Oooh I like the goth look!" with 100% sincerity and I just said "Thanks." absentmindedly because my brain had just been melted down and recast inside of a Moron Mold (thanks for NOTHING Prof. Leslie!!!!) then I got home, looked in the mirror, and came face-to-face with Raccoon Sophia. Horrifying.
This book was simply one of the best math textbooks I've ever come across. It was quite straightforward and easy to understand both in terms of explanations and, refreshingly, in the homework problems it posed. It similarly used several worked-out example problems that allowed the student to really grasp the quite novel concepts it was putting across.