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

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Discussion Overview

The discussion revolves around the preparation needed before taking differential equations and calculus III, focusing on which topics from calculus I and II, as well as linear algebra, should be reviewed. Participants express concerns about the difficulty of these courses and seek advice on essential content to study.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant suggests reviewing the basics of limits, differentiation, and integration, emphasizing the importance of techniques such as the product rule, quotient rule, chain rule, and various integration methods.
  • Another participant notes that calculus III introduces higher-dimensional calculus, including multivariate limits, partial derivatives, and vector calculus, and stresses the need for proficiency in basic matrix algebra and determinants.
  • Some participants propose that reviewing eigenvalues and determinants may be beneficial for differential equations, particularly if the course covers systems of differential equations.
  • One participant expresses the opinion that calculus III is easier than calculus II, attributing this to the nature of the content covered.
  • There is a question regarding the extent to which linear algebra is used in differential equations, with some participants indicating that it is not heavily relied upon, except for specific topics like eigenvalues and eigenvectors.

Areas of Agreement / Disagreement

Participants generally agree on the importance of reviewing foundational calculus concepts and techniques. However, there is some uncertainty regarding the necessity and extent of linear algebra in differential equations, with differing opinions on its relevance.

Contextual Notes

Some participants mention specific techniques and topics that may be emphasized in differential equations and calculus III, but there is no consensus on a definitive list of what to review.

Luongo
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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.
 
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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.
 
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.
 
Luongo said:
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.
 
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.
 
GRB 080319B said:
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).
 

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