What to brush up on before taking Differential Equations?

In summary, it is recommended to review integration techniques from Calculus II, such as integration by parts, trig integration, partial fractions, and series, for an introductory differential equations class. Additionally, understanding eigenvalues and linear algebra concepts may also be helpful. It is important to review these techniques thoroughly as they are the foundation for differential equations.
  • #1
Shackleford
1,656
2
Unfortunately, I'll probably have to wait until the Fall to take it. I've taken Cal I-III and took Linear Algebra this past fall.

What specifically in Calculus (besides the short differential equations) should I review?
 
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  • #2
Eigenvalue problems, vector valued functions, and taking derivatives/integrals. That's pretty much all differential equations is based on. Most of the techniques you'd actually use in the class will be new to you.
 
  • #3
pde's or ode's? I can see eigenvalue stuff in the pde's but if it's just an intro diffy q class you won't see a lot of linear algebra (you will see some, like linear independence/dependence and matrix determinants and a few other things), you'll want to review a lot of integral methods from calculus II
 
  • #4
MATH 3331: Differential Equations
Cr. 3. (3-0). Prerequisites: MATH 2433 and MATH 2331 (formerly 2431). Systems of ordinary differential equations; existence, uniqueness and stability of solutions; initial value problems; bifurcation theory; Jordan form; higher order equations; Laplace transforms. Computer assignments are required.
 
  • #5
What they don't tell you shackel is you want to know your integration techniques from Calc 2. Know that like the back of your hand.

edit: I'm taking the class right now, also clope said this first :)
 
  • #6
djeitnstine said:
What they don't tell you shackel is you want to know your integration techniques from Calc 2. Know that like the back of your hand.

Looks like I'll have to bust out my notes. All the integration techniques or a few in particular?
 
  • #7
Shackleford said:
Looks like I'll have to bust out my notes. All the integration techniques or a few in particular?

integration by parts, trig integration, and partial fractions you'll probably see the most; be able to recognize when one is done too cause the steps aren't always shown; oh also series
 
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  • #8
clope023 said:
pde's or ode's? I can see eigenvalue stuff in the pde's but if it's just an intro diffy q class you won't see a lot of linear algebra (you will see some, like linear independence/dependence and matrix determinants and a few other things), you'll want to review a lot of integral methods from calculus II

Well, I guess it depends on your school. We used eigenvalues extensively in my intro diff eqs class, to linearize nonlinear systems.
 
  • #9
I'm pretty much at the same point having taken Calculus I-III and Linear Algebra, but I'm taking Diff-EQ now. Our teacher went over a list of techniques that we should review the first day of class. One that caught my eye was partial fractions - something we spent 1/2 a lecture on in Calculus II that I had to review. It's really just algebraic manipulation, but funny how many people said they had to review the process the following class.
 

Related to What to brush up on before taking Differential Equations?

1. What is the prerequisite knowledge for Differential Equations?

The main prerequisite for Differential Equations is a strong understanding of Calculus, including derivatives and integrals. It is also helpful to have a solid foundation in algebra and trigonometry.

2. Are there any specific topics within Calculus that I should review?

Yes, it is important to have a good understanding of limits, derivatives, and integrals. It is also helpful to be familiar with techniques such as integration by parts, partial fractions, and integration by substitution.

3. Do I need to know any specific programming languages for Differential Equations?

While not necessary, having some experience with a programming language such as MATLAB or Python can be beneficial. These languages can be used to solve and visualize differential equations.

4. Is it helpful to have knowledge of linear algebra?

Yes, linear algebra is often used in solving systems of differential equations. It is helpful to have an understanding of matrices, eigenvalues, and eigenvectors.

5. How can I prepare for Differential Equations?

In addition to reviewing prerequisite knowledge, it can be helpful to practice solving various types of differential equations. There are many resources available, such as textbooks, online tutorials, and practice problems. It can also be beneficial to work on developing critical thinking and problem-solving skills.

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