How hard is Partial Differential Equation or Mathematical Optimization?

[BamBam215]

Introduction to Partial Differential Equation : First and second order equations, characteristics. Cauchy problems, elliptic, hyperbolic, and parabolic equations. Introduction to boundary and initial value problems and their applications.



Making my schedule and I get to pick an upper division math elective. This is the only elective that seems to fit my schedule. Should I even attempt this class? Oh yeah, it's pre-requisite is Intro to Differential Equation. I am enrolled in that class next semester so I would be taking both classes at the same time. In my experience, a lot of pre-req requirements are kinda bull because you barely use what you learn in the pre-req class. But do you guys think I'll be okay taking both classes at the same time?


EDIT:

How about

Mathematical Optimization: Linear and nonlinear programming: simplex methods, duality theory, theory of graphs, Kuhn-Tucker theory, gradient methods, and dynamic programming.

Sounds like a lot of programming junk which I really have no experience. The last programming class I took was Pascal back in high school. But the pre-req for this class I've fulfilled.

 

[Anubis]

i wouldent do it. yull need that info from teh Diff EQ class to do teh second order one

 

[BamBam215]

Originally posted by: TheEvil1
i wouldent do it. yull need that info from teh Diff EQ class to do teh second order one

You don't think there's anyway I can wing it? I'm not shooting for an A. A lot of the times you just need the really basic stuff from a pre-req.

 

[vtqanh]

Depends on how good you are in math. And also among those who are good in math, there are also two kinds: one being good at reasoning (number theory, combinatorics...), one being good at stuff like calculus and statistic. If you are good at calculus stuff, then it should be okay

 

[Anubis]

Originally posted by: BamBam215

Originally posted by: TheEvil1
i wouldent do it. yull need that info from teh Diff EQ class to do teh second order one

You don't think there's anyway I can wing it? I'm not shooting for an A. A lot of the times you just need the really basic stuff from a pre-req.

trust me. im just took Diff EQ and its not easy. i wouldent think about dooin second order ones with out this first. i have done second order diffe eqs in physics and they are a bitch unless you know exactly what they are and teh solution

 

[BamBam215]

Yeah I see myself as being good at computational math. I'm still struggling in theoretical math mainly because I haven't yet grasped the language.

 

[dullard]

A good portion of ordinary differential equations (ODEs) can be solved analytically. There are a few tried and true methods that will solve most of them for you. And even if you can't remember them, often you can solve an ordinary differential equation by guessing an answer and checking to see if it is true. For the few equations you will see that cannot be solved analytically - you will learn methods to graph the result without ever finding the equation that solves it. That is a very useful course and relatively easy. Expect a typical homework assignment to take 1-2 hours (depending on the professor of course).

Partial differential equations (PDEs) have just one small change from ordinary differential equations - but it makes it significantly harder. In general the vast majority cannot be solved analytically. But a small class of special partial differential equations can be solved analytically. I've been taught maybe 5 tricks to solve them - in a typical partial differential equations course you will learn maybe 3 of them - meaning you will spend a good month on each trick to even begin to understand their use. All of these solutions are tricks that convert a PDE into an ODE then you solve the resulting ODE. If you don't know how to solve the ODE after applying the trick you will not do well. So I would highly recommend taking an ODE course before a PDE course (but since many ODEs can be solved by trial and error - if you spend enough time I guess you could wing it - but I wouldn't recommend it). In fact to really understand PDEs, I'd recommend taking 2 or 3 courses on them (since the first one will not cover all the tricks). Expect a typical homework assignment to take 8-16 hours (depending on the professor of course) and double that if you have to guess every answer with trial and error.

Optimization can be quite useful as well. The term "programming" is a misnomer though. A Kuhn-Tucker "program" is a problem that looks like this:

• Minimize f(x)
  Subject to the constraints g1(x)<=0, g2(x)<=0, ... , gn(x)<=0.

That is a "program". It has nothing at all to do with computers. I suppose you could use a computer to help you solve that problem, but it really isn't required (depends on the professor). In my optimization classes it was heavilly theoretical - memorize this theorem, prove that theorem, etc. I found it boring since I like to do computations, not memorize proofs. Maybe your professor will be different. I'd highly suggest taking a matrix theory class before taking optimization - but it isn't required if you've had matrices in other courses.

 

[ajayjuneja]

easy class. Try taking a speech recognition class if you want some real fun, or a controls class if you like this diff. eq. stuff

 

[RaynorWolfcastle]

I haven't taken either class but I do know PDE is one of the most feared classes at my university. Very, very few people get A's and A LOT of people fail it

 

[Spamela]

Originally posted by: BamBam215
Introduction to Partial Differential Equation : First and second order equations, characteristics. Cauchy problems, elliptic, hyperbolic, and parabolic equations. Introduction to boundary and initial value problems and their applications.



Making my schedule and I get to pick an upper division math elective. This is the only elective that seems to fit my schedule. Should I even attempt this class? Oh yeah, it's pre-requisite is Intro to Differential Equation. I am enrolled in that class next semester so I would be taking both classes at the same time. In my experience, a lot of pre-req requirements are kinda bull because you barely use what you learn in the pre-req class. But do you guys think I'll be okay taking both classes at the same time?


EDIT:

How about

Mathematical Optimization: Linear and nonlinear programming: simplex methods, duality theory, theory of graphs, Kuhn-Tucker theory, gradient methods, and dynamic programming.

Sounds like a lot of programming junk which I really have no experience. The last programming class I took was Pascal back in high school. But the pre-req for this class I've fulfilled.

i've taken both. be prepared to work your @ss off.

"programming," in the latter case, does not mean "programming" in the computer sense.

i know a "duality theory" joke, btw, but it's not funny until you've studied it.

 

[oboeguy]

Originally posted by: Spamela

Originally posted by: BamBam215
Mathematical Optimization: Linear and nonlinear programming: simplex methods, duality theory, theory of graphs, Kuhn-Tucker theory, gradient methods, and dynamic programming.

Sounds like a lot of programming junk which I really have no experience. The last programming class I took was Pascal back in high school. But the pre-req for this class I've fulfilled.

i've taken both. be prepared to work your @ss off.

"programming," in the latter case, does not mean "programming" in the computer sense.

i know a "duality theory" joke, btw, but it's not funny until you've studied it.

Yes, everyone who has mentioned it is correct: "programming" in this context does not mean "coding". It's a term that originated with the field of Operations Research, back int he days of WWII. It should have been called "planning"; in fact, a friend of mine used to call it "linear planning" or some such thing.

Anyhow, I am an expert in this field so I can tell you whatever you want to know. It's excellent stuff. The suggestion of a linear algebra class is a good one. Even if LA is not an official prereuisite for the course, it's very useful to know a little ahead of time. I would very strongly recommend you get your hands on a syllabus before choosing the course, because some professors will call upon the students to code (program in the current sense of the word), because nearly all practical problems in this field are solved by computer.

If you ask me, the Optimization course will be better for you when you try to get a job. It's very, very, very (one more, very!!!) useful in the business/industrial world. It's everywhere, let me tell you.

 

[fizmeister]

I did stuff like that freshman year in a non-PDE course. It was easy, so I'm sure you'll be fine. I'm taking PDEs next year, and this is the course description:

"Laplace transform: inverse transform, applications to constant coefficient
differential equations. Boundary value problems: Fourier series, Bessel
functions, Legendre polynomials."

You'll be okay taking both classes at the same time...I've done it before.

 

[BamBam215]

It looks like PDE are out of the question. So now it's a toss up between Mathematical Optimization and Multivariable Calculus (how is this one? ehe).

 

[dullard]

Originally posted by: BamBam215
It looks like PDE are out of the question. So now it's a toss up between Mathematical Optimization and Multivariable Calculus (how is this one? ehe).

Well if you haven't even had multivariable calculus, I'd take that before anything listed in this thread. At my school you couldn't even take ODEs before multivariable calculus. Honestly that is a very easy class - with just minor extensions to what you learned in the first calculus classes.

 

[BamBam215]

Originally posted by: dullard

Originally posted by: BamBam215
It looks like PDE are out of the question. So now it's a toss up between Mathematical Optimization and Multivariable Calculus (how is this one? ehe).

Well if you haven't even had multivariable calculus, I'd take that before anything listed in this thread. At my school you couldn't even take ODEs before multivariable calculus. Honestly that is a very easy class - with just minor extensions to what you learned in the first calculus classes.

I don't think it's the same Calculus you're thinking of. I've already taken 3 yrs of Calculus. Here's the course description for Multivariable Calculus.

Topology of Euclidean spaces. Partial derivatives. Derivatives as linear transofrmations. Inverse and implicit function theorems. Jacobians, vector calculus. Green's and Stoke's theorems. Variational problems.

 

[oboeguy]

That sounds like a nice course. What are your goals for this slot you wish to fill? I already told you what I think is good about Optimization, but we still don't know what you are trying to get out of this class.

 

[ryzmah]

Definitely take the Multivariable calculus before PDE - the optimization course will be some pseudocode, and use linear algebra and basic vector knowledge. I would take the optimization, because I think it's useful and interesting, but if you didn't like matrix theory you might not like this either.

 

[BamBam215]

I am going to teach. Most likely middle school. I'm just trying to get by with the easiest elective!

So Mathematical Optimization or Multivariable Calculus? Hmm. hehe. Which one has the least amount of theories and more computation?

 

[oboeguy]

Guaranteed that the Optimization course, if at the undergrad level, will have more computation. It's a computational field, after all. PM me if you want some more info.

 

[cchen]

Originally posted by: BamBam215

Originally posted by: dullard

Originally posted by: BamBam215
It looks like PDE are out of the question. So now it's a toss up between Mathematical Optimization and Multivariable Calculus (how is this one? ehe).

Well if you haven't even had multivariable calculus, I'd take that before anything listed in this thread. At my school you couldn't even take ODEs before multivariable calculus. Honestly that is a very easy class - with just minor extensions to what you learned in the first calculus classes.

I don't think it's the same Calculus you're thinking of. I've already taken 3 yrs of Calculus. Here's the course description for Multivariable Calculus.

Topology of Euclidean spaces. Partial derivatives. Derivatives as linear transofrmations. Inverse and implicit function theorems. Jacobians, vector calculus. Green's and Stoke's theorems. Variational problems.

Yeaaaa you definitely should take the multivariable calc before taking PDE, ODE, or even Optimization. ODE uses some multivariable stuff....

 

[BamBam215]

Originally posted by: cchen

Originally posted by: BamBam215

Originally posted by: dullard

Originally posted by: BamBam215
It looks like PDE are out of the question. So now it's a toss up between Mathematical Optimization and Multivariable Calculus (how is this one? ehe).

Well if you haven't even had multivariable calculus, I'd take that before anything listed in this thread. At my school you couldn't even take ODEs before multivariable calculus. Honestly that is a very easy class - with just minor extensions to what you learned in the first calculus classes.

I don't think it's the same Calculus you're thinking of. I've already taken 3 yrs of Calculus. Here's the course description for Multivariable Calculus.

Topology of Euclidean spaces. Partial derivatives. Derivatives as linear transofrmations. Inverse and implicit function theorems. Jacobians, vector calculus. Green's and Stoke's theorems. Variational problems.

Yeaaaa you definitely should take the multivariable calc before taking PDE, ODE, or even Optimization. ODE uses some multivariable stuff....

Really. ODE is listed as a lower course than Multivariable Calculus at my university.