Is Linear Algebra needed for PDEs?

[jessfalling]

Hello, this is my first post!

I am interested in studying PDEs (heat/wave equations, etc.). At my university, the only listed prereq. for PDEs is ODEs, which can be taken after Calc II. So, essentially, one could enroll in PDEs without taking Calc III, but I am not sure if that would be wise?? I am hoping for some insight regarding the proper preparation for the PDEs course. Also, is Linear Algebra needed?

If Calc III is not needed for it I may postpone taking it until after PDEs due to scheduling issues.

Thank you!

Jess

 

[HallsofIvy]

You should consider it a pre-requisite even for ordinary differential equations. For example, you need Calculus III to solve first order "exact" equations.

 

[micromass]

Yes, you usually need calc III for PDE's. The very definition of PDE's requires partial derivatives and this requires calc III.
I have a hard time seeing why your uni doesn't demand it as a prereq.

Could you post the course contents?

 

[genericusrnme]

what exactly is Calc I-III?
I'm not american so I have no idea what's in those courses yet I hear their names thrown about all over the place :(

 

[micromass]

what exactly is Calc I-III?
I'm not american so I have no idea what's in those courses yet I hear their names thrown about all over the place :(

Haha, I feel your pain. It took me a long time to find out what each thing is as well a non-american

I think it is:
- Calc I: limits, continuity, derivatives, basic integrals
- Calc II: Integrals (integration by substitution and parts), series, improper integrals
- Calc III: multivariable thingies

 

[Jorriss]

I think it is:
- Calc I: limits, continuity, derivatives, basic integrals
- Calc II: Integrals (integration by substitution and parts), series, improper integrals
- Calc III: multivariable thingies

That's exactly it basically. Calc III at most universities covers vector calculus too.



I don't know how your school can't require calc III.

1) As micro said, PARTIAL differential equations requires an understanding of partial derivatives.
2) But then, there are multidimensional integrals, directional derivatives, fundamental theorems of vector calc, etc.

You need multivariable and vector calc.

 

[jessfalling]

Could you post the course contents?

Here's the full course description: Partial differential equations, separation of variables, orthogonal sets of functions, Sturm-Liouville problems, Fourier series, boundary value problems for the wave equation, heat equation, and Laplace equation; Bessel functions, Legendre polynomials.

Thank you to everyone who has commented so far! It sounds like I need to take Calc III.

 

[MathWarrior]

You should consider it a pre-requisite even for ordinary differential equations. For example, you need Calculus III to solve first order "exact" equations.

This isn't exactly true, I am doing ODE's right now and I've yet to have Calculus 3. Learning partial derivatives is pretty easy, would be hard to go through ODE's without learning partial derivatives at least once. Treating a variable as a constant while finding a derivative isn't exactly something that requires several hours to learn.

I'd say ODE's is a good prerequisite for Calculus 3, and Calculus 3 is a good prerequisite for ODE's.

ODE's are a good requirement for PDE's, but I would definitely take calculus 3 before PDE's.

 

[ZenOne]

I did ODE's without Cal. III with ease. The overlap was minimal and if someone has done Cal. I and II and does not understand partial derivatives within a matter of minutes there is a deeper underlying problem.

Also, I was able to solve conservative fields as a result of having learned ODE (exact equations). It doesn't matter which you learn first--the process is pretty much the same either way.

 

[romsofia]

Here's the full course description: Partial differential equations, separation of variables, orthogonal sets of functions, Sturm-Liouville problems, Fourier series, boundary value problems for the wave equation, heat equation, and Laplace equation; Bessel functions, Legendre polynomials.

Thank you to everyone who has commented so far! It sounds like I need to take Calc III.

You will need the vector calculus side of calc 3 for sure because you'll be using the gradient a LOT based on that description. Besides vector calc, be sure to know your ODEs. What you will find out is that you will be turning a lot of PDEs into a system of ODEs. For the multivariable calc side, I recall doing a few multivarible integrals, but only a few. Also, be sure to know some linear algebra (eigenvalues/eigenvectors) and a little analysis as you will need to prove some theorems (in my class anyway).

To sum it all up: Know your vector calc (gradients mainly), ODEs, mutlivariable integrals, eigenvalues/vectors and a little analysis.

Good luck.

 

[Hobin]

Haha, I feel your pain. It took me a long time to find out what each thing is as well a non-american

I think it is:
- Calc I: limits, continuity, derivatives, basic integrals
- Calc II: Integrals (integration by substitution and parts), series, improper integrals
- Calc III: multivariable thingies

Micro, out of curiosity, don't people have three courses in calculus in Belgium? I know we have in most uni's in the Netherlands (although I assumed the contents differed by country, what you posted comes pretty close).

 

[micromass]

Micro, out of curiosity, don't people have three courses in calculus in Belgium? I know we have in most uni's in the Netherlands (although I assumed the contents differed by country, what you posted comes pretty close).

In my uni, we had a semester of single variable calculus and a semester of multivariable. So we have 2 calc courses in uni.
Of course, we already saw calculus in high school as well. So the calculus in our uni was more analysis.

 

[20Tauri]

My school requires Calc III for ODEs. As for PDEs, is Calc III when partial derivatives are taught or am I remembering wrong?

 

[nlsherrill]

Yes you usually first see partial derivatives in a multivariable calculus class, which is usually dubbed "calc 3"

And yes, you need to understand multiple integration and partial derivatives to do PDE's.