What are some good books for understanding linear algebra and its applications?

In summary, a student completed a math course on differential equations and linear algebra using Elementary Differential Equations with Linear Algebra by Rabenstein. They found the book difficult to understand and are looking for a book that provides a better explanation of the geometry involved with visual aids. They also prefer a book with application sections and answers to problems in the back. They have found a few options, including Lay's Linear Algebra and its Applications and Poole's Linear Algebra: A Modern Introduction, but are open to other suggestions. They are particularly interested in finding a book that combines both differential equations and linear algebra in a visual and geometric way.
  • #1
member 392791
Hello,

I just completed a math course that had a mixture of differential equations and linear algebra. The book used was Elementary Differential Equations with Linear Algebra by Rabenstein. Since the class covered both topics, of course we couldn't go into a lot of detail for either type of math as a single course on either subject.

https://www.amazon.com/dp/0155209841/?tag=pfamazon01-20

However, the book is very hard to understand. I already have in my possession Differential equations by Boyce and Diprima, and I was looking for something to read about linear algebra.

I am looking for books that show the geometry involved (pictures are great!), I liked Larson and Edwards Calculus
https://www.amazon.com/dp/0547167024/?tag=pfamazon01-20

Basically, I am an engineering student, I have no interest in deep mathematical inductive reasoning or proving theorems, I just want something that gives a good explanation of the geometry involved and gives some good pictures to show what the concepts mean, and if the book has application sections for the chapters, that would be fantastic.

I still have a very bad intuition for any of the concepts of DE/LA, it was very analytical and not geometric. The larson book had very good intuition and I enjoyed it a great deal, so something at that level would be fantastic. Another criteria is that the answers for atleast even or odd problems is shown in the back of the book, or has a solutions manual available to students.

Also, if you got something that meets the same criteria for DE, I would look at that too. And lastly, I would like something that is pretty cheap! Don't want to spend a lot on textbooks!

Again, please nothing like Spivak or anything that is heavily focused towards a math major!
 
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  • #2
how about strang's intro book. he's sort of an engineer's mathematician.
 
  • #3
I went through a similar course (DE/LA) and found myself always asking more questions about LA but the course didn't go deep. After the semester I got this book:

https://www.amazon.com/dp/0534998453/?tag=pfamazon01-20

I love this book because it has lots of pictures, geometry, and applications. Also, it has little sections within the chapters, called "Explorations," which is direct applications of what you just learned. Unlike other books that says applications in the title but then has one application problem at the end of the chapter... like Strang's book.


P.S. - I have the 2nd edition (because it's cheap) so I can't compare it to the 3rd edition. On Amazon, the 3rd edition let's you preview almost the entire book. Check it out.
 
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  • #4
Does that book have answers to the questions in the back?

I just found this one

https://www.amazon.com/gp/product/0201520311/?tag=pfamazon01-20

It's 13 cents, so it is hard to beat that price. Anyone know about it?

The book you suggested DrummingAtom looks exactly like something I want, just want to know if this 13 cent one is just as good, since the one you showed was $23
 
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  • #5
Woopydalan said:
Does that book have answers to the questions in the back?

I just found this one

https://www.amazon.com/gp/product/0201520311/?tag=pfamazon01-20

It's 13 cents, so it is hard to beat that price. Anyone know about it?

The book you suggested DrummingAtom looks exactly like something I want, just want to know if this 13 cent one is just as good, since the one you showed was $23

I'm not familiar with Lay's. Poole's does have answers to all odd problems and the first edition is much less:

https://www.amazon.com/dp/0534341748/?tag=pfamazon01-20

If you find another book that fits your style, please post it on here because I'm always looking for good visual/geometric books. :cool:
 
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  • #6
Thanks, do you know of another geometric/visual DE book?
 

1. What is linear algebra and why is it important?

Linear algebra is a branch of mathematics that deals with linear equations, vector spaces, and matrices. It is important because it provides the foundation for many other areas of mathematics and has a wide range of applications in fields such as physics, computer science, and economics.

2. What are some good books for beginners to learn linear algebra?

Some good books for beginners include "Linear Algebra Done Right" by Sheldon Axler, "Introduction to Linear Algebra" by Gilbert Strang, and "Linear Algebra and Its Applications" by David C. Lay. These books provide a comprehensive introduction to the subject with clear explanations and examples.

3. Are there any online resources for learning linear algebra?

Yes, there are many online resources available for learning linear algebra. Some popular ones include Khan Academy, MIT OpenCourseWare, and Coursera. These resources offer video lectures, practice problems, and other materials to help you understand linear algebra concepts.

4. How can I apply linear algebra in real-life situations?

Linear algebra has numerous applications in real-life situations. For example, it is used in computer graphics to create 3D images, in machine learning for data analysis and prediction, and in engineering for solving systems of equations. It also has applications in economics, physics, and other fields.

5. What are some tips for understanding and mastering linear algebra?

Some tips for understanding and mastering linear algebra include practicing regularly, seeking help from a tutor or online resources, and relating the concepts to real-life situations. It is also important to have a strong foundation in algebra and geometry before diving into linear algebra.

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