Differential Equations and Linear Algebra

by Gilbert Strang

Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.

Genres: Mathematics, Engineering, Textbooks, Algebra

510 pages, Hardcover

First published June 4, 2014

About the author

William Gilbert Strang (born November 27, 1934), usually known as simply Gilbert Strang or Gil Strang, is an American mathematician, with contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra. He has made many contributions to mathematics education, including publishing seven mathematics textbooks and one monograph. Strang is the MathWorks Professor of Mathematics at the Massachusetts Institute of Technology. He teaches Introduction to Linear Algebra and Computational Science and Engineering and his lectures are freely available through MIT OpenCourseWare.

Reviews

[Custard Saga · Rating 4 out of 5]

this is probably the best math textbook I've read so far. most concepts explained fairly clearly, but not with an excessive level of rigor. unlike nearly other academic reference author, Strang isn't afraid to let his personality shine through. he tells the reader about his favorite equations and makes endearing little remarks under the example problems: "This solution makes me realize that the initial value y(0) is like having a delta function at time t = 0. The solution 'jumps' to y(0). I don't know if you agree with that." for a subject that can be so depressing, I like that he's having fun.

the most valuable thing that Differential Equations and Linear Algebra taught me was what kind of mentality to approach a differential equation with. Strang consistently reminds the reader to predict the form of the solution before attempting it, and even though I don't remember all of the formulas now, this backwards-solving method has always stuck with me.

4/5 because there were some notation issues and problems with the answer key that gave me massive headaches. occasionally, parts of the equation are condensed or omitted without warning, and other times, terms appear from seemingly nowhere. I'll admit that in several instances I threw this book against my wall and cried. but that's just the name of the game, so no deduction there.

[Happy Scrappy Hero Pup · Rating 4 out of 5]

I’d rather have my liver eaten daily by an eagle whilst I’m chained to a Caucasus mountain than be forced to read this text. I wouldn’t wish this book upon my worst enemy. While ostensibly written for students, it’s impenetrable to anyone who doesn’t already have a fairly solid understanding of Differential Equations…the very thing Strang is attempting to explain in the opening chapters.

That said, it’s a beautiful book - pure art.
And like art, it is enigma to anyone who doesn’t “get it”.

If you are a pure mathematician - that is, a mathematician who studies math for math’s sake (as opposed to an applied-math scientist) - then you will most certainly love and venerate this extremely well-written book!

But if you are being introduced to differential equations for the first time and lack a strong background in mathematics, then the opening chapters of this book will feel like Prometheus tied to a rock. How dare you attempt to fly so close to the sun that is mathematics! Die you arrogant god.

[Paul Floyd · Rating 3 out of 5]

Good but I read it too quickly whilst tired. So I skimmed the bits that I was familiar with and failed to concentrate on the bits I'd forgotten or didn't know.