Differential Equations and Linear Algebra (Gilbert Strang) by Gilbert Strang (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “As with Strang’s linear algebra books, now in their fourth edition, this text is destined to have a big impact on differential equations courses and applied math education. Its conversational presentation, breadth, and provocative problems will even appeal to students, who typically read little of the book assigned. Those who teach differential equations should definitely give Strang’s approach serious consideration. Once again, he’s making us think!” Robert E. O’Malley, Jr. SIAM Review vol. 56, ISSUE 4 Book Description An innovative textbook that allows the fundamental topics of differential equations and linear algebra to be taught together or separately. About the Author Gilbert Strang is a professor of mathematics at the Massachusetts Institute of Technology, where his research focuses on analysis, linear algebra and PDEs. In addition, he is the author of many textbooks and his service to the mathematics community is extensive, having spent time as President of SIAM, Chair of the Joint Policy Board for Mathematics as well as membership of various other committees and boards. The awards that Professor Strang has received for his research and teaching include the Chauvenet Prize (1976), the Award for Distinguished Service (SIAM, 2003), the Graduate School Teaching Award (MIT, 2003) and the Von Neumann Prize Medal of the US Association for Computational Mechanics (2005), among others. He is a Member of the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences and an Honorary Fellow of Balliol College, Oxford. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am a surgeon by profession and have been using this text in my “hobby”, a serious self-study of mathematics and modern physics, in conjunction with MIT’s Open Courseware and edx.org. I started off with just high school calculus from decades ago, and have made it to the mid-undergraduate maths covered in this volume. Although I’m giving it five stars, I have to add the caveat that at first it was hard to get started with this book. Professor Strang fills the text with all sorts of glimpses of more advanced topics that will be unfamiliar to new students. For example, some of the very first examples involve step and Dirac delta input, with a heavy emphasis on impulse response concepts to explain the time evolution of solutions. This really confused me at first. However, once I started to feel more familiar with ODEs, this presentation was very helpful to get me to “get it” at a deeper level than the mere methodology of finding and writing out solutions.Also, the book does not follow the OCW differential equations course (18.03) very closely, at least the version currently online, even though it supposedly grew out of a rewrite of the 18.03 syllabus. Hopefully MIT will put up an updated version of 18.03 at some point (though I do love Prof. Mattuck’s lectures in the current one).I still have a decent chunk of the material ahead of me (matrix methods for ODE systems, eigenvalues, etc.) but I now find the book very easy to follow.

⭐This refers to the Kindle version:While I was looking forward to the content, my immediate reaction is that the equation layout is poorly done. That, in turn, makes reading comprehension difficult. There are also blank white squares on many of the pages, and I can’t tell if they were meant to be images or not.I’m not going to be able to read this book until a revised version is released. The poor equation formatting is too much of a distraction.

⭐an interesting attempt to put these two topics together

⭐Best out of the 3 books i have but there are not enough example problems and he skips so many steps it is very hard to follow. It became a habit to youtube the section title before even trying to follow what he writes and that has proven most succesful in getting through this book. There are no answers to the problem sets either so this may be an issue for the self taught.

⭐A great undergraduate book, but if you already own Straang’s linear algebra text, you’d do better to buy a different diff eq book since there’s a few chapters of overlap.

⭐Perhaps this book is a good reference for those who are already versed in the subjects, but for the student in my home I find the book hard to follow and lacking in sufficient walkthrough examples for the student to gain a grasp on a systematic methodology for solving the problems.

⭐Prof. Gilbert Strangs text is Excellent as you would expect from such a brilliant Mathematician!

⭐There are a few strangers that have benefited me in my life. Elizabeth Taylor, Richard Burton, obviously some others, and Dr. Strang. Combine this textbook (and his others) with his lectures available online, and you’re hooked up with everything that an independent learner needs.

⭐One can only have the utmost respect for Gilbert Strang. If there were more mathematics teachers like him the world would be a better place.

⭐I really like Gilbert Strang, I would give another star, if it wasn’t so expensive. I’m sure it’s not the author’s fault, but books for students should be a lot cheaper than that. I’ve decided to buy it anyway just because I like this author.

⭐Simply excellent (as all of Dr. Strang’s books are. As always, he presents otherwise difficult material in an intuitive fashion making itcrystal clear. I have read several of his books on linear algebra and computational science and found the presentation of thecalculus involved in differential equations to be an excellent addition to his previous material on linear algebra. This is a book that should be read (even if one has read several booksbefore on related topics (as I have).The video presentations available at ocw.mit.edu are a valuable addition to the book.

⭐I always appreciated Gilbert Strang style of teaching watching his video lectures at MIT.ocw. When this book came out I was curious how he would be able to translate his effective teaching methods into the writing. After half of the book, I can say this is an high-quality book that explains concisely, clearly and easily differential equations and linear algebra. Often, the equations and reasonings are surrounded with real and practical example which further clearify the concepts previously illustrated. FIVE STARS

⭐Uso esse produto em minhas atividades de ensino.

⭐

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