Linear Algebra / Vector Calc Text (for CompSci student)

  1. I'm taking a Linear Algebra / Vector Calculus course this semester as part of a maths major for my Comp Sci undergrad. degree. We don't have a prescribed text, but I'd very much like a hard copy of something that I can reference. The course is somewhat compressed compared to what the Maths degree students take, and my experience with these courses so far is that I'm learning stuff, quickly, but not deeply. I smashed a compressed Calc (not sure if we made it to Calc II, we did an awful lot of integration techniques on top of regular differentiation and integration) in a single course last semester and I hung on for dear life and ended up with half decent marks. I took Numerical Methods at the same time and it almost killed me! I don't have much in the way of mathematical maturity and found some of the quadrature techniques, and the like, to be way over my head in terms of the proofs, although I could use them in practise to some extent. We made it to Runge-Kutta and touched on ODEs and I really struggled at that point.

    I've found a few threads in the Linear Algebra forum, and have been looking at these books that were mentioned on Amazon:


    Linear Algebra by G. E. Shilov



    Linear Algebra Done Right by Sheldon Jay Axler


    Which seem like solid texts. It seems I'm going to be seeing a lot of proofs, and my past experience with proofs is really bad, I have a lot of trouble with them. The last one that really messed with me was the Pumping Lemma, which I just couldn't apply properly to the range of problems we were provided. I just don't seem to think in the correct fashion for proofs. With that in mind, I came across this text:

    Linear Algebra: A First Course in Pure and Applied Math by Edgar G. Goodaire

    Which seems to focus on learning how to read proofs, sounds great, but I can't find a review on the text itself.

    As for Vector Calc, this text has very good reviews:

    DIV, Grad, Curl, & All That: An Informal Text on Vector Calculus by Harry M. Schey

    I wonder if anyone has advice and/or other text recommendations for me? :)
     
  2. jcsd
  3. Linear Algebra Done Right might be difficult if you haven't had previous experience with proofs. I recommend a more applications/computational orientated book like Lay's Linear Algebra and Its Applications.

    The book you posted under vector calculus is good if you want to understand how to apply vector calculus to electrodynamics, but not for a first experience. Which book did you use for calculus? It might have chapters on multivariable and vector calculus.
     
  4. Schey is a great book but it is not a vector calculus textbook. Marsden is a full vector calc book and I have enjoyed it a lot.

    Shilov is too advanced I imagine. This is a lower division course yeah? Lay or anton are good LA books.
     
  5. I didn't have a prescribed textbook for calc and vectors/matrices, we relied on printed notes, but I have a copy of "Mathematical Methods For Engineers And Scientists" which is written by two profs at my uni (can't find it on Amazon) that served me pretty well when I got stuck.

    Also, I just borrowed this book from a friend, and it seems to cover my syllabus wrt vector calculus, although the reviews at Amazon are poor.

    Calculus: Single and Multivariable

    The Lay and Anton LA books both look good, thanks for the recommendations there, I'm reading up on Marsden and some other vector calc texts. :)
     
  6. mathwonk

    mathwonk 9,761
    Science Advisor
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