Partial Differential Equations Help

[lion0001]

Guys i need some advice, for the Spring semester i have to take 2 math courses but there is one that i am not sure if i should take it.
that course is Partial Differential Equations, this is the description for MAP 4401 :

A second course in differential equations. Topics may includeeat Equation, Wave Equation,The Method of Separation of variables. Bessel functions and other special functions arising from classical differential equations, Sturm-Liouville problems, partial differential equations,Fourier series, transform techniques.
Prerequisites: MAP 2302 (Differential Equations )
and MAC 2313 ( Calculus 3)

I have met all the prerequisites but i don't know why is this a senior course, it makes me think that this class must be difficult, i don't have to take it now but i think i have to because this class is only offered in the spring, i will be graduating in Spring 2010 and if for some reason i don't pass that class in spring 2010 then i will have to wait until spring 2011.

THe professor for this class told me that diff. equations and calc 3 are the prerequisites for this class but a knowledge of Advanced calculus would help.
i didnt take Advanced calculus , i took and introduction to proofs which include the first 2 chapters of advanced calculus ( sequences and limits) .

do you think this will be enough to be able to understand MAP 4401 ?

i would like to email you the notes of this course ( there is no book for this class , just online notes at his website ) so you can tell me if the material is ok or too hard based on the prerequisites. Please include your email , or send me an email at jcadi001@fiu.edu with MAP 4401 in the subject and i will email it to you , its not a big file , just 3 Mb.

 

[lurflurf]

Well you have the official prerequisites. For a " serious" course on differential equations calculus would be essential. All indications are that this course is not serious. I assume this course is more about methods and applications than theory. Calculus would allow you to justify things, but if you can accept plausible methods on faith all should be well.
Examples of sketchy thing you may see
-Integrating an infinite series term by term
-Expanding a function in Fourier series
-Interchanging two iterated integrals
-Generalized functions
-contour integration in the complex plane
-residue calculus
-Moving a derivative inside a (possibly improper) integral
-equating mixed partials (ie uxy=uyx)

 

[HallsofIvy]

I think lurflurf meant advanced calculus where he wrote "calculus". I can't imagine differential equation, ordinary or partial, even in a "non-serious" course, making any sense at all if you haven't taken Calculus!

 

[lion0001]

I think lurflurf meant advanced calculus where he wrote "calculus". I can't imagine differential equation, ordinary or partial, even in a "non-serious" course, making any sense at all if you haven't taken Calculus!

yes, he meant adv. calculus , but i am not a pure math major, i am an Applied math major , i don't need to take abstract algebra, number theory , topology etc..

Applied math majors don't take those courses, for grad school, they take i think something similar to take on fluid dynamics, mathematical physics etc.

 

[HallsofIvy]

In your talk with the Professor did he say what would be included in the course? From the fact that he said advanced calculus was not needed (and saying "advanced calculus" alone doesn't really tell us much. Some colleges teach as basically an abstract "introduction to analysis" course while others teach it as an "advanced methods of calculus" class, much more application oriented), it sounds like a "methods" rather than a "theory" class. But one thing I would think would be a pre-requisite would be at least an introduction to ordinary differential equations. Most methods of solving partial differential equation involve "reducing" them to ordinary differential equations. Have you taken an introductory course in differential equations?

 

[elarson89]

Do you know the textbook that will be used?

When your prof told you that advanced calc would be helpful, he probably is just looking for a solid grasp of the calculus that you have taken already, as well as some vector calculus. Derivations of the heat and wave eq, as well as some important results of sturm-lioville equations make use of the divergence theorem, and some properties of the gradient and laplacian operators.

I took a PDE class that sounds similar to yours, and I was in the same standing as you. I had only taken diffy q, and intro to linear algebra, I hadn't taken analysis (adv calc). The class never became something i wasnt able to handle, but I did thoroughly read the text, which was very good imo (Applied PDE and bvps, by richard haberman).

In short, don't be afraid that it will be too hard. The class i took was actually a undergraduate and graduate combined course, and i thought i would be left behind, though nothing was ever too difficult. Even if you didnt know vector calculus, you would do fine. It is mostly used in derivations, but you may need to know qualitatively what is going on.

 

[lion0001]

In your talk with the Professor did he say what would be included in the course? From the fact that he said advanced calculus was not needed (and saying "advanced calculus" alone doesn't really tell us much. Some colleges teach as basically an abstract "introduction to analysis" course while others teach it as an "advanced methods of calculus" class, much more application oriented), it sounds like a "methods" rather than a "theory" class. But one thing I would think would be a pre-requisite would be at least an introduction to ordinary differential equations. Most methods of solving partial differential equation involve "reducing" them to ordinary differential equations. Have you taken an introductory course in differential equations?

I have taken Calculus 1 , 2 , 3 , Differential Equations, Linear Algebra, and Introduction to adv. Math which is just , naive set theory, methods of proof, mathematical induction , infinite sets ( a headache by the way) , and sequences and limits with delta epsilon proofs.
Advanced Calculus comes right after this class but i am not taking it.

 

[lion0001]

Do you know the textbook that will be used?

When your prof told you that advanced calc would be helpful, he probably is just looking for a solid grasp of the calculus that you have taken already, as well as some vector calculus. Derivations of the heat and wave eq, as well as some important results of sturm-lioville equations make use of the divergence theorem, and some properties of the gradient and laplacian operators.

I took a PDE class that sounds similar to yours, and I was in the same standing as you. I had only taken diffy q, and intro to linear algebra, I hadn't taken analysis (adv calc). The class never became something i wasnt able to handle, but I did thoroughly read the text, which was very good imo (Applied PDE and bvps, by richard haberman).

In short, don't be afraid that it will be too hard. The class i took was actually a undergraduate and graduate combined course, and i thought i would be left behind, though nothing was ever too difficult. Even if you didnt know vector calculus, you would do fine. It is mostly used in derivations, but you may need to know qualitatively what is going on.

We are not going to be using a particular book, we are going to use a book he wrote himself , PDF files at his website , i think chapter 1 is the heat equation , then wave equation, sturm louville , Fourier etc etc ,

Elarson can i send you these notes so you can see if they are similar to the class u took ,
my email is jcadi001@fiu.edu , send me an email with MAP4401 in the subject and i will send u the file, its a small file , 3MB
Actually your class and mine are very similar because mine too is a comibined course --> MAP4401 ( my class) and MAP 5317 Advanced Differential Equations for Engineers ---> a graduate class for engineers.

i took the 3 calculus , linear algebra, and intro to adv. math , which is a proof based course which included the first 2 chapters in adv. Calculus, sequences and limits , then comes adv. calculus( which iam not taking) with chapter 3 in continuity and so on.

The thing that i don't like about the applied math degree at my school http://w3.fiu.edu/math/html/urmath.htm
is that they include a lot of Computer Science courses, there is one that is hard , theory of algorithms, I've seen the tests of this course in previous semesters at a website of another prof. and its very weird, , So far I've checked other universities and they don't make u take this course , there is also data structures offered in the electives , its more like 60% applied math , 35% Computer science , and 5 % stats

 

[Vid]

Are you planning on going to grad school in applied math?

If you are, you will most certainly need analysis. The applied math concentration where I am doesn't require analysis either. However, the department recommends that people going to grad school for applied math instead get the more general math degree and take 3 semesters of undergrad analysis as well as a semester of algebra. Though, they can choose between the regular algebra course or an applied algebra course.