# Reference help - Linear Algebra and Calculus

I went through some of the questions asking for reference help but they're not the same (definitely similar though). Maybe i missed something but here goes-

I know there are Gilbert Strang videos, textbooks and other sources that are similar to learn Linear Algebra but what i want to know is - are there any concise (preferably freely available) text books to review the concepts? I say review because I've taken up both Linear Algebra and Calculus 6-7 years ago and they are rusty.

I need to review these for grad school and I'm short of time to re-learn everything from scratch.

I need to brush up the basics for example,

Linear Algebra -

• Vectors, and solving linear equations
• Spaces
• Matrices (Rank, Row/Column operations)
• Determinants
• Eigen values and Eigen vectors.

Calculus

• Limits (and some pre-calculus)
• solving differential equations (ODEs and PDEs et al)
• basic integral calculus

What I'm looking for is review sources and primers that maybe some of you have found really useful.

Edit - Some very helpful links, thank you all. I also found PatrickJMT.com for very basic stuff to solve a few problems and help remember high school learning. And some wandering soul might appreciate this link as well - Additional Resources

• This may not be what you're looking for, but have you tried looking thru Pauls Online Math Notes – enthdegree Dec 24 '13 at 1:12
• you could try is to search for free online lecture notes from some university. – Ragnar Dec 24 '13 at 1:14

I found that anytime I needed to review a topic, I searched lecture/class notes.
Here are a few resources that may be of use for you:

Linear algebra/Analysis and Calculus review (Berkeley lecture notes)

Review of Linear Algebra and  Vector Calculus (Slides adapted from notes by Andrew Rosenberg)

Paul's Online Maths Notes

Links to several relevant topic reviews, practice questions and answers from MIT - it is important to test yourself as you review.

• Wow! I appreciate the links; especially the fourth one. The courseware is pretty concise too. Thank you. Thank you as well as @Kainui for recommending the same. – Raaj Dec 25 '13 at 0:41

Just a note -- if you are in a hurry I recommend against Strang's book. I found it nearly impossible to read -- and I already knew the material.

• I agree. While very engaging, it does not serve one's purpose of getting a good and quick review. – Raaj Dec 25 '13 at 0:37
• To which Strang book are you referring? I tend to agree on the introductory linear algebra book, but I haven't read his more advanced linear algebra book. – joeA Dec 25 '13 at 2:17
• yes, the introductory book -- I haven't read any other linear algebra book by him – Betty Mock Dec 25 '13 at 18:50

I highly recommend Herb Gross's "Calculus Revisited" playlist from either MIT or Youtube. He is incredible and has done videos for linear algebra and differential equations.

Here's a quick google link I found, but I think he covers more than what's presented there.

http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/