Should i review calculus before taking differential equations/ calc 3?

[Luongo]

I took calc 2 6 months ago... and I am just wondering which parts of calc 1,2 i should review for both diff eqns and calc 3. should i also review linear algebra? which parts? (ie: eigenvectors, eigenspaces, row reduction)? also what content is heavy in diff eqns and/or calc 3? should i review all my integration techniques? (partial fracctions/ by parts/ etc...) as well as diff eqns in calc 2. i really need to know what emphasis to prepare for these two courses as i am very worried because i heard the two courses are hard

Please and thank you.

 

[n!kofeyn]

Well calculus III starts off a little new, and teaches you calculus in higher dimensions. You learn how to do multivariate limits, partial derivatives, multiple integrals in Cartesian, polar, and cylindrical coordinates, vector calculus, etc. So what is important is the ability to differentiate and integrate, as well as solving systems of equations (2 or 3). You will use basic matrix algebra, and you need to know how to find determinants of matrices. Calculus III is only difficult because you have to keep up with a lot of stuff compared to calculus I since you're in 2 or 3 dimensions.

Pretty much the same advice applies to differential equations. Being able to integrate and differentiate well will save you trouble in applying the differential equation theory. The first course in differential equations usually isn't too bad because it is real cookie-cutter type course. You are given a certain type of differential equation, and then you are taught a specific technique that only really applies to that type of differential equation.

 

[PieceOfPi]

For both classes: Definitely review the basics of limits, differentiations and integrations (e.g. what are they? Why are they so important?). You may also want to review some techniques of those (especially the ones with *): Differentiation techniques such as product rule*, quotient rule*, chain rule*, implicit differentiations, etc, and integration techniques such as u-substitution*, integration by parts*, and some techniques using trig identities and possibly trig substitutions.

For Diff Eq, it would be useful to review stuff about eigenvalues (if your class covers a chapter on system of DEs). Determinants also become handy.

For Calc III, it would be useful to review dot products and cross products--you'll see them quite a bit.

 

[planethunter]

I took calc 2 6 months ago... and I am just wondering which parts of calc 1,2 i should review for both diff eqns and calc 3. should i also review linear algebra? which parts? (ie: eigenvectors, eigenspaces, row reduction)? also what content is heavy in diff eqns and/or calc 3? should i review all my integration techniques? (partial fracctions/ by parts/ etc...) as well as diff eqns in calc 2. i really need to know what emphasis to prepare for these two courses as i am very worried because i heard the two courses are hard

Please and thank you.

Definitely. Review methods of integration for ODE. Calc 3 is much easier than calc 2 in my opinion- calc 2 was just integration technique after integration technique. For ODE, you will be solving equations using the integration and differentiation techniques that you learned in Calc 2.

 

[GRB 080319B]

Is linear algebra used extensively in ODE? I will be taking ODE, and linear algebra is not a prerequisite for taking the course at my school. Thanks and sorry for hijacking this thread.

 

[planethunter]

Is linear algebra used extensively in ODE? I will be taking ODE, and linear algebra is not a prerequisite for taking the course at my school. Thanks and sorry for hijacking this thread.

You do not really use linear algebra much in ODE, other than with calculating eigenvalues and eigenvectors- which is a small part of ODE and you probably won't even see that in your first ODE course (you will see it in PDE).