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Multivariate Calculus & Linear Algebra In 3 Weeks

  1. Aug 6, 2010 #1
    I wish to master Multivariate Calculus(to the extent required to get an A with a ridiculously difficult professor) and Linear Algebra in 3 weeks so I can breeze through both classes in the Fall semester.

    I've self studied both of my textbooks that I will be using for the two courses, but I'd like to know if anyone has any advice for the most efficient method for mastering the material in these books.
    ______________________________________________________________________________
    My Multivariate Calculus course will be from Calculus by James Stewart 6th Edition:
    We will cover section 11.3-11.6 + everything in chapter 13, 14, 15, and 16. So far I've been watching MIT lecture videos and doing the example problems in each section.

    My Linear Algebra course will be from Introduction to Linear Algebra by Strang International Edition: We will cover everything from chapter 1-7. Much like with Multivariate Calculus, I'm watching the appropriate MIT lecture videos(which sync very well since the author of the text is also the lecturer on the MIT videos).

    My Discrete Mathematics course will be from Discrete Mathematics and Its Applications (6th Edition) by Kenneth H. Rosen:
    We will cover chapters 1.1-1.7, 2.1-2.4, 3.1-3.8, 4.1-4.4, and 5.1-5.3.
    ______________________________________________________________________________

    I know my Linear Algebra and Discrete Mathematics teachers have a very fair grading policy so I can get an A in their classes very easily. I'm also very good with proofs so that won't be any problem, at least in the case of Linear Algebra and Discrete Maths(which is basically an intro to proofs). However, I will have the same teacher I did for Calculus III as I did for Calculus II. The problem is, I was the only person in the entire class to get a grade higher than a B(I got a B+) for Calculus II and my teacher is very unfair with his exams(he gives the hardest questions you'll see for a computational course) and he required us to do many proofs(which caused many students to fail) in a non-proof based class. By the time school starts, I want to know Multivariate Calculus well enough where I would get an A in almost any comparable course with the most difficult professors.

    I'm really worried about the professor I have for Calculus III because he says he never gives out A's(in fact, he told people that were looking for A's to drop the course immediately), but on the flip side, anyone who can get a C in his class can probably get an A in a comparable course with any other professor. However, I'm aiming for an A, being the madman I am. I plan to study non-stop between now and 3 weeks from now when school starts so I can get the most out of my Calculus III class(and of course, so I can get the highest grade possible).

    As I mentioned before, my Linear Algebra and Discrete mathematics courses won't be any issue since the professors are very relaxed with grading compared to my Calculus III professor.
     
    Last edited: Aug 6, 2010
  2. jcsd
  3. Aug 6, 2010 #2
    Well you could always try to find Apostol's book. I believe Volume 2 of his book gives a treatment of Multivariable and Linear Algebra together. If you could clear that...especially in 3 weeks...I would bet you would be ready for anything. Not a cheap book though, so if you don't have it in your school's library, that is not really the best thing.

    https://www.amazon.com/Calculus-Vol...plications/dp/0471000078/ref=pd_bxgy_b_text_b

    I would wait for someone else's advice though. I'm just an undergraduate myself.
     
    Last edited by a moderator: Apr 25, 2017
  4. Aug 6, 2010 #3


    Are you skipping chapter 9 and 10? You can't do chapter 10 and 12 without chapter 9. Why are you skipping chapter 12 in the first place? Multiple Integration is important. I am not even sure how you can do chapter 13 without chapter 12.
     
  5. Aug 6, 2010 #4
    I have that book already. I'm currently running through Calculus by Spivak(single variable) to make sure I'm ready for Multivariate Calculus.

    I also have Calculus on Manifolds by Michael Spivak.
    We did chapter 9, 10, part of 11, and 12.1-12.11 in Calculus II.
     
    Last edited by a moderator: Apr 25, 2017
  6. Aug 6, 2010 #5
    You don't need to learn all of the material ahead of time to breeze through the class. It's enough to familiarize yourself with the concepts and basic results. If you know the "big picture" going into the class, you can focus on filling in the details during lectures and on the homework.
     
  7. Aug 6, 2010 #6
    I believe you can master all the subject, even in such short time. You seem pretty motivated to study enough for a perfect score.

    I wouldn't, however, expect for an A. Unfortunately, there are professors who simply can't admit it - and he seems to be one of them.
     
  8. Aug 6, 2010 #7
    I'd say I'm pretty motivated, but the thing is, I studied a lot for Calculus II, and was able to do all the practice exam questions I could find online, but even then, I still didn't get perfect scores on my professor's exams. I think I could cover all the material for Calculus III in 3 weeks since I'm home everyday, and I don't have any other priorities.
     
  9. Aug 6, 2010 #8
    FWIW I didn't think calc III was any easier than II. In fact, there were quite a few people in my class that thought it was harder.
     
  10. Aug 6, 2010 #9
    Let me explain. Calculus II material is easy. My professor is difficult. He could turn a basic algebra test into a nightmare. That being said, I plan to complete an entire syllabus worth of homework before school starts again in a few weeks.
     
  11. Aug 8, 2010 #10
    OK there are a lot of misconceptions floating around, but I'll point out one or two and then you guys can generalize or say 'whatever'. Reading through a difficult math book such as Apostol Volume II in 3 weeks as a first exposure to the subject is pretty much the easiest way to ensure that you really don't know the subject. If you don't believe me try it yourself, taking care to do the most difficult problems in the book.

    Also if the OP's professor really does make difficult exams, then doing practice exam questions online is not enough. If the practice exam problems weren't from the professor, then they're probably of less use. If they were from the professor, then they're still useless because you know your professor is a difficult dude and probably won't have you do something you can already do. In fact this notion of just being able to 'do' practice questions in a really difficult class is STUPID. In a truly difficult course, you have to do the most difficult questions. If you are breezing through them, I guarantee you there are a harder problems out there requiring the same basic background knowledge. Difficult exams require thinking and creativity and the more you do that with difficult problems, the better you fare.
     
  12. Aug 8, 2010 #11
    I used Calculus by Stewart for single variable calculus(and it will also be the standard text for my multivariate course this Fall). Do you think I would be better off using a different book? I heard that Apostal has quite a few errors.

    I'm currently using Calculus by Spivak and I must say, it makes single variable calculus look like a different subject from what I learned from the Stewart text. When I finish Spivak's single variable text, would I be able to continue with his Calculus on Manifolds or Apostol's volume II(I own both already so price isn't a concern)?
     
    Last edited: Aug 8, 2010
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