Multivariable calculus

[ashramsoji]

Hi all,

I am going to start a Multivariable Calculus on Monday. It's a summer course in a compressed schedule so it will be complete in just about 5 weeks -- we meet Monday through Thursday for 2 hours.

I've been reviewing the lectures from MIT's OCW on Single Calc, but I was wondering what particular areas I should focus on in preparation for MVC. It's been a while since I took a Math course and given the compressed schedule and I'll be working full-time as well.

I have two chapters of review left on infinite series, but I almost think I should skip those and just focus on doing a lot more integration problems. I haven't really covered polar coordinates because I didn't do that in my college Calculus course and MIT really only does one lecture on it, but if it's really important I'd appreciate a heads-up.

 

[ParanoidAndroid]

Basic linear algebra will definitely help. Review linear transformations, matrices, determinants and analytic geometry. 

Edited May 14, 2014 by ParanoidAndroid

[33andathirdRPM]

Which textbook will you be using for the course?

[ashramsoji]

Thanks for the replies! I'll be using Stewart's version

 

http://www.prioritytextbook.com/products/Calculus%3A-Early-Transcendentals-%287th-Edition%29-Stewart.html

 

I haven't really taken linear algebra yet although I'm familiar with determinants and matrices. Is there anything from the calculus sides of things that you all would recommend I be really sharp on?

[bsharpe269]

I took linear algebra after multivariable. Really, if you have a good understanding of derivatives and integrals then you will be in good shape.

[33andathirdRPM]

You will not need to know matrix multiplication on the way in the door for the material covered in Stewart's text. You'll develop the necessary basics of linear algebra - euclidean distance, inner product, cross product, etc - during the course. Do go back and review differentiation and antidifferentiation. For now, you can set aside the material on sequences and series, although I *highly* recommend that you review that because it will come back farther along in your studies. I highly encourage you to review implicit differentiation, the chain and product rules of differentiation, 'u-substitions,' integration by parts, trig substitutions and polar coordinates now.

[ashramsoji]

You will not need to know matrix multiplication on the way in the door for the material covered in Stewart's text. You'll develop the necessary basics of linear algebra - euclidean distance, inner product, cross product, etc - during the course. Do go back and review differentiation and antidifferentiation. For now, you can set aside the material on sequences and series, although I *highly* recommend that you review that because it will come back farther along in your studies. I highly encourage you to review implicit differentiation, the chain and product rules of differentiation, 'u-substitions,' integration by parts, trig substitutions and polar coordinates now.

 

 

Thank you, this is really helpful. I feel really solid on integration except the trig substitution (too many weird identities and integrals).

 

I think I'll prioritize this weekend with the infinite series and polar coordinates.

[ashramsoji]

For the record, I'm pursuing a MS in Statistics starting in the Fall, and I am trying to clear some of the pre-requisites. I don't intend on taking any more of the standard math courses after MVC and Linear Algebra, though I'm sure I'll have my hands full with probability and math statistics.

[mf161]

Pay attention to the Jacobian matrix (useful for function transformations) and double integrals (useful for cintinuous probability functions).

[ashramsoji]

Pay attention to the Jacobian matrix (useful for function transformations) and double integrals (useful for cintinuous probability functions).

Well i have no idea what those are but I certainly will! 

[TakeruK]

Stewart is on its 7th edition already??

 

I took Multivariable Calculus with this book too (5th edition). We also did single variable calculus with the same book so I felt it was a good transition. I agree with what 33andathirdRPM said in terms of what to review. I definitely agree that Stewart expects you to be comfortable with different coordinate systems because it's fairly often that a change of coordinates is exactly what you need to make the problem reduce to something you can solve.

[mf161]

Well i have no idea what those are but I certainly will! 

Well, I did make things unnecessarily difficult by spelling continuous as "cintinuous".

A double integral is what it sounds like (integrating a function over two variables/dimensions, usually x and y). The Jacobian matrix uses partial derivatives to transform a function from one variable to another--I didn't go over this in great extent during MVC, but I was able to apply what I knew when studying Probability.

[ashramsoji]

Thanks all. Looks like I have a pretty busy weekend ahead with polar coordinates and series. I'm a little bummed because the MIT lectures only do one class on Polar Coordinates and I'd really like to learn more about it in an efficient fashion.

[33andathirdRPM]

If you already have the Stewart textbook, you can use it as a resource to get you up to speed with polar coordinates. It's a very well written resource.

[reinhard]

I TA'd this course two times as an undergrad. I can tell you, most people have a lot of trouble with basic algebraic manipulation. Be fluent in those otherwise Lagrange Multipliers will haunt you at night.

[ashramsoji]

I TA'd this course two times as an undergrad. I can tell you, most people have a lot of trouble with basic algebraic manipulation. Be fluent in those otherwise Lagrange Multipliers will haunt you at night.

 

 

Can you be more specific in terms of what you meant by basic algebraic manipulation? Are we talking about things like square roots and exponents?

[reinhard]

Can you be more specific in terms of what you meant by basic algebraic manipulation? Are we talking about things like square roots and exponents?

Know basic rules as in

 

1. (a + ^2 = a^2 + 2ab + b^2 and not (a + ^2 = a^2 + b^2. Similarly idea for (a+^n

 

2. If you have two equations, let's say both are nonlinear $x^2 + y^2 = 1$ and $xy = 1$, know how to  solve for x and y. I actually made this one up on the fly.

 

3. Yes exponent rules, know them very well. Even with fractional ones. I can't think of any examples.

[Stat Assistant Professor]

A large number of the "trickier" stats problems I've encountered involve completing the square, integration by parts, change of variables, and/or u-substitution. It'd be a good idea to know these thoroughly well.

Edited June 2, 2014 by Applied Math to Stat

[ashramsoji]

Thanks everyone. I'm almost done with the course and it's been pretty smooth thus far. The Stewart textbook is pretty good and finding a solutions manual was REALLY helpful.

 

The course is really compressed so we don't have a lot of time to practice/ask questions, etc. I feel like I understand the concepts (except triple integrals in polar coordinates), but I do wish we had more time to work out problems together with the professor and do more than just learn to solve these.

 

I think the most important thing was to remember derivatives, integration, geometry, and trig. So many of the concepts seem to rely on a solid understanding of integrals, areas, and spaces.

[brettmullga]

If you already have the Stewart textbook, you can use it as a resource to get you up to speed with polar coordinates. It's a very well written resource.

 

I second this! I used the Stewart book for Calc I & II. I transferred schools and used the Salas, Hille, and Etgen book for Calc III. It was much worse all the way around, especially the amount of errors. Just know that with the Stewart book you're in good hands and that you could be much worse off.