Studying for PDEs: Advice & Strategies

[Tony11235]

My second test in my partial differential equations class is coming up in a few days and I truly have no idea how to study for it. The first test I bombed, so I really need to do much better this time. It is the toughest math course I have encountered so far. I mean ODEs are a joke when compared. A decent amount of questions will be proofs that involve a bit of analysis, and I have not yet taken real analysis. My teacher rarely asks us just to solve an equation. And like I said before, I have trouble when it comes to studying or how to study. I am easily distracted not by tv or games, not by people or friends, but by wanting to study something else, which I do not even have a class in, althought usualy related to math/physics.

Any advice? I don't expect to many responses. I will probably have to figure out a way myself.

 

[leon1127]

My second test in my partial differential equations class is coming up in a few days and I truly have no idea how to study for it. The first test I bombed, so I really need to do much better this time. It is the toughest math course I have encountered so far. I mean ODEs are a joke when compared. A decent amount of questions will be proofs that involve a bit of analysis, and I have not yet taken real analysis. My teacher rarely asks us just to solve an equation. And like I said before, I have trouble when it comes to studying or how to study. I am easily distracted not by tv or games, not by people or friends, but by wanting to study something else, which I do not even have a class in, althought usualy related to math/physics.
Any advice? I don't expect to many responses. I will probably have to figure out a way myself.

my way is to understand all the example that is handy, and then do it.

 

[2k5 yzf-r1]

For hard math classes like that I try to over learn the material. I do the homeworks over and over. I do as many examples that I can and if there are theorems in the book that have proofs, I usually do them over and over until I can prove them without looking. Even if the theorem looks daunting and you think he won't ask a question in that much detail, it is still very good if you can prve the theorem because you will have a much deeper understanding of the material. Another thing I do is search online for exams from other professors that use the same textbook. Just google the name of your text or the name of your class and you will find other professors that have posted their old exams on their website, I usually do them too. I know this sounds like overkill and it probably is, but it works everytime I have took 19 math classes at the university and I am usually the first one done. At my school we have 15 week semester and tests are usually given on week 8 and week 14 so I have plenty of time do all this, I don't just sit down and do this in one night, I usually start a week and a half before the test.

 

[Tony11235]

For hard math classes like that I try to over learn the material. I do the homeworks over and over. I do as many examples that I can and if there are theorems in the book that have proofs, I usually do them over and over until I can prove them without looking. Even if the theorem looks daunting and you think he won't ask a question in that much detail, it is still very good if you can prve the theorem because you will have a much deeper understanding of the material. Another thing I do is search online for exams from other professors that use the same textbook. Just google the name of your text or the name of your class and you will find other professors that have posted their old exams on their website, I usually do them too. I know this sounds like overkill and it probably is, but it works everytime I have took 19 math classes at the university and I am usually the first one done. At my school we have 15 week semester and tests are usually given on week 8 and week 14 so I have plenty of time do all this, I don't just sit down and do this in one night, I usually start a week and a half before the test.

Sounds like a great idea. Memorization and experience through tons of problems is probably the best method. I just wish that the solutions to problems given in course books would be shown in detail and not just one line answers.

 

[Astronuc]

Try the tutorial and webpages listed here.
https://www.physicsforums.com/showthread.php?p=818026#post818026

Where have you studied so far, and what seems to be giving you difficulty?

There is also a differential equations section in the Math Forum - https://www.physicsforums.com/forumdisplay.php?f=74 , but this is mix of ODE and PDE topics.

 

[Tony11235]

I copied this out of our review sheet. This is just one of the sections we have to know.

"• Theory behind separation of variables. Fourier series. Fourier sine series (odd functions). Fourier cosine series (even functions). Theorem on pointwise convergence of a Fourier series to (1/2) ((f(x+)+f(x−)). Definition of pointwise convergence of an infinite series of functions. Definition of uniform convergence. Theorem on when it’s legal to termwise differentiate an infinite series of functions. Weierstrass M-test. Using M-test on series solution to heat equation to show it can be differentiated. Using M-test on Fourier series through integration by parts on Fourier coefficients."

The above is what is mostly bothering me. It is also not in our textbook. Our class notes do not help. I just need to find something decent to read on the subject to understand it better.

 

[Astronuc]

That helps. Now I need to dig up my course notes from ~30 years ago.

Perhaps Schaum's Outline on PDE's might help - https://www.amazon.com/gp/product/0070178976/?tag=pfamazon01-20

Introduction.
Classification and Characteristics.
Qualitative Behavior of Solutions to Elliptic Equations.
Qualitative Behavior of Solutions to Evolution Equations.
First-Order Equations.
Eigenfunction Expansions and Integral Transforms: Theory.
Eigenfunction Expansions and Integral Transforms: Applications.
Green's Functions.
Difference Methods for Parabolic Equations.
Difference and Characteristic Methods for Parabolic Equations.
Difference Methods for Hyperbolic Equations.
Difference Methods for Elliptic Equations.
Variational Formulation of Boundary Value Problems.
The Finite Element Method: An Introduction.
Answers to Supplementary Problems.

And definitely check out - http://www.physics.miami.edu/nearing/mathmethods/pde.pdf

 

[Lonewolf]

Sounds like a review of necessary background in functional analysis. Have you taken such a course? It might explain why the material is not in your textbook, especially if the book is geared towards PDEs.

 

[Tony11235]

That is what me and a lot of other students think. But our professor insists that it won't be so bad. Oh well, I will just have to teach myself.

 

[Eratosthenes]

My second test in my partial differential equations class is coming up in a few days and I truly have no idea how to study for it. The first test I bombed, so I really need to do much better this time. It is the toughest math course I have encountered so far. I mean ODEs are a joke when compared. A decent amount of questions will be proofs that involve a bit of analysis, and I have not yet taken real analysis. My teacher rarely asks us just to solve an equation. And like I said before, I have trouble when it comes to studying or how to study. I am easily distracted not by tv or games, not by people or friends, but by wanting to study something else, which I do not even have a class in, althought usualy related to math/physics.
Any advice? I don't expect to many responses. I will probably have to figure out a way myself.

I happen to also be studying PDE's currently. This is how I study. I read the book, sometimes rereading certain parts several times, and do the homework problems. I also work through all the proofs in the book, and so far, it's working. When I get stuck, I try harder and reference different books if needed. If I get stuck for a long time though I move on and come back to whatever I was doing later. Just don't neglect anything and learn to teach yourself. If you can learn something on your own it helps. The lectures/course notes are just an added bonus. Anyways this might be good idea for you. Goodluck.

 

[Tony11235]

I happen to also be studying PDE's currently. This is how I study. I read the book, sometimes rereading certain parts several times, and do the homework problems. I also work through all the proofs in the book, and so far, it's working. When I get stuck, I try harder and reference different books if needed. If I get stuck for a long time though I move on and come back to whatever I was doing later. Just don't neglect anything and learn to teach yourself. If you can learn something on your own it helps. The lectures/course notes are just an added bonus. Anyways this might be good idea for you. Goodluck.

I can teach myself, that's what I usually depend on, I never feel like I learn anything in class. It's just the latest stuff that we've covered isn't handy in our book. Oh and I hardly ever take notes. I HATE hand writing, I'm also a computer science guy. The notes really do not help anyway. My real problem, which I just realized, might be that I don't study for the class everyday. That could help, lol.

Thanks for the advice.