Tell me about multivariable calculus/calculus 3...

Classes started on Friday and I have a mini-math section on Fridays, so I got to meet my teacher. What do I think of his teaching abilities? Well, let's just say I think I'm going to be pretty much on my own this semester. :lol:

I'd feel better if I got a little advice, and since a ton of you are math whizzes, I figure this is easier than going around campus asking people. Basically, I just want to know about any specific tips, memorization aids, study strategies and anything else at all that helped you with the course that you think might help me. Also, warnings about any particularly brutal sections of the material that I'm going to run into.

Also, I'm curious: IYO, how much harder was calc 3 than calc 1/2, and which was harder: calc 1 or 2?

Hmm you're gonna have to clarify what you mean by "calc 1" and "calc 2". In my university, calc 1 included multivariables.

Just don't be overly worried about the class and you'll be fine.

My TAs for those types of classes have always been foreign and with really hard to understand accents. :P I have also been on my own sometimes.

Calc 1: differential calculus
Calc 2: integral calculus

Learn how to do partial derivatives, it's not that hard. I can't tell you how because I honestly forget.

With multiple variables you will never get a concrete answer like you do with basic calculus, you may end up with a range of answers, which results in an undefined function.

http://upload.wikimedia.org/math/d/2...77e5d609b2.png
The limit as the line approaches zero is zero, except with it comes it from the parabola x squared. In that case the limit is one half. With two different possible values for the limits, this makes it undefined.


I took that straight from wikipedia, I think it's obvious, but then again I already know how to do it. If you'd like ask and I'll solve it in detail for you.

Calc 1 is harder than calc 2 simply because when you first learn calculus it's a completely knew way of looking at mathematics and once you have the calc 1 basis then calc 2 should be fairly easy. After all, integrals are just differentials in reverse :P Calc 3 is much much harder.

If you want to do well on math, ditch the idea of memorizing stuff. That's the worst way to go about it. The only memory stuff that should happen is the automatic development of some pattern recognition (common integrals, etc.) that happens with lots of problems.

Multivar calculus is not that bad. If you did well on calc 1 and 2, 3 is just an extension of the previous theory, with some new notation (gradients, partial diff eqs, etc.)

Where you did area under the curve, you'll probably do lots of volumes (volume under the surface is exactly area under the curve, but with a double integral). Same kind of analogy can go into curve length --> surface area.

You might have to delve into the world of vector spaces (which is usually taught in linear algebra classes), but it's not that bad. I got a 98% in that class. :D

If you post your course outline, I can give you a better idea of what's hard and what's easier.

I learned Calculus by myself around 10th grade and then took AP Calculus the year after. It's easy.

Quote:

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Originally Posted by Replicon

If you post your course outline, I can give you a better idea of what's hard and what's easier.

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Section Topics Suggested lecture hours
13.1 Coordinates in space .25
13.2 Vectors in space .25
13.3 Dot product .5
13.4 Cross product 1
13.5 Lines and planes 2
13.6 Quadric surfaces 1.5
13.7 Cylindrical and spherical coordinates 2
14.1 Curves in space .5
14.2 Derivatives of vector functions (omit integrals) .5
15.1 Functions of several variables 1.5
15.2 Limits and continuity 2
15.3 Partial derivatives 1.5
15.4 Tangent planes, differentials 2
15.5 Chain rule 2
15.6 Directional derivative, gradient 2
15.7 Extrema 2
16.1 Double integrals over rectangles 1
16.2 Iterated integrals 1
16.3 Double integrals over non-rectangles 2
16.4 Double integrals in polar coordinates 1.5
16.5 Applications of double integrals (omit inertia, probability) 1
16.6 Surface area 1.5
16.7 Triple integrals (omit charge, inertia, probability) 2
16.8 Triple integrals in cylindrical and spherical 2
12.1 Sequences 1
12.2 Series 1
12.3 Integral test, estimates 1.5
12.4 Comparison tests 2
12.5 Alternating series 1.5
12.6 Absolute convergence, ratio test (omit root test) 1.5
12.7 Strategy for testing series .5
12.8 Power series 1.5
12.9 Representing functions as power series 1
12.10 Taylor series, Maclaurin series 2
12.11 Binomial series 1
12.12 Applications of Taylor polynomials 1

Haha, I don't expect you to comment on all this stuff, but if any sections jump out at you and you remember some specific tips and tricks that you couldn't have done without, spill the beans! There are always a bunch of good ones that the teachers don't seem to be aware of.

Quote:

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Originally Posted by M-Cat

I learned Calculus by myself around 10th grade and then took AP Calculus the year after. It's easy.

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So you're saying you want to lend me your brain for the semester?

Is Calc 3 pretty much only about implicit functions? I'm in Calc 2 right now...

Ok, so it doesn't look like they take you deep into vector space theory (which they sometimes do, but that's more for differential equations, etc.) If you did well on calc 1 and 2, you should have no trouble with 3. It's all the same stuff, just extended.

I like how they shoved sequences and series in at the end. They always do that... It's kind of a segway...

Just do the assigned problems, and you'll have no trouble getting through that (again, assuming you're generally good at calculus hehe).