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PDE w/o ODE?

CGiuliano

Lowly Undergrad
Joined
4/19/09
Messages
234
Points
28
My school does not offer ordinary diffeq... They simply have an introduction to diffeq class, which covers both ODE and PDE in one semester... Or, they have PDE, which obviously covers only PDE... The prerequisites are the same: multivariate and linear. Furthermore, a student can not receive credit for both of these classes. So,

Take Intro to DE (ODE/PDE) or, PDE?

Courses of Study 2009-2010


Courses of Study 2009-2010

Thanks.
 
That's weird. My school offers ODE and PDE separately.

I'm actually really looking forward to PDE.
 
One of the crucial techniques of solving PDE is transforming it into a system of ODEs. I guess they provide a brief intro of ODE and then focus on PDE ;)
 
roni said:
Shouldn't ODE be the prereq for PDE ?
Click to expand...

It should. The methods and insights used for ODEs are helpful (arguably even crucial) for getting to grips with PDEs. ODEs need at least a semester. ODEs are inherently interesting, i.e., not just as a springboard for PDEs.
 
I would recommend both courses (ODE and PDE).
Even if you can not receive credit points for both classes, you should attend both classes.

Nevertheless MATH 3230 Introduction to Differential Equations (MQR) seems to be the better choice. But this is only an introduction that can not be enough!!!
 
Strange right...

They also have engineering diffeq which is both ODE and PDE, but focuses primarily on problems that arise in engineering.

And they have diffeq and dynamical systems which covers all of ODE, but then becomes very applied i.e. bifurcations...?

Then, there is numerical analysis and diffeq which uses ODE and PDE again.

Lastly, they have a graduate sequence of PDE 1 and PDE 2.

Maybe take intro to diffeq, then take numerical diffeq... This would give me two semesters of ODE/PDE and numerical analysis. Although, in that case I would not be taking numerical analysis and linear algebra which is an MFE course...

Any more thoughts?

Thanks.
 
I talked to an advisor and apparently the intro to diffeq covers all the topics generally found in an ODE class, but rather then going "further in depth" it moves on to PDE.
 
CGiuliano said:
I talked to an advisor and apparently the intro to diffeq covers all the topics generally found in an ODE class, but rather then going "further in depth" it moves on to PDE.
Click to expand...

The advisor's response is not credible. A one-semester course on ODEs cannot go "in depth." A second semester devoted to the subject could (e.g., based on Waltman's "A Second Course in Elementary Differential Equations"). Surprising that a major American university cannot offer a proper course on ODEs.
 
i can see what the advisor is saying, but i would still take ODEs before PDEs because just because you can get through the course doesn't mean that you'll truly understand the material, which is ultimately what you want
 
bigbadwolf said:
The advisor's response is not credible. A one-semester course on ODEs cannot go "in depth." A second semester devoted to the subject could (e.g., based on Waltman's "A Second Course in Elementary Differential Equations"). Surprising that a major American university cannot offer a proper course on ODEs.
Click to expand...

It does seem odd to me also, but knowing the courses and professors here.... I wouldn't be surprised if it was a full and complete ODE course with an extra heap of PDE packed in there.

Rankings - Math - Graduate Schools - Education - US News and World Report

Rankings - Best Engineering Schools - Graduate Schools - Education - US News and World Report
 
My school also offers a similar course that gives an intro to both ordinary & partial differential equations:

Differential Equations for Scientists and Engineers
Introduction to ordinary and partial differential equations, including their classification, boundary conditions, and methods of solution. Equations, methods, and solutions relevant to science and engineering are emphasized, and exploration is encouraged with the aid of software.

But for MATH students, this is the first Differential Equations course taken:

Differential Equations
Introduction to differential equations, including a discussion of the formation of mathematical models for real phenomena; solution by special techniques; applications; linear equations; solutions in series; other topics if time permits.

In this course we will study some important types of linear differential equations and their solutions. Topics will include first-order (differential) equations; homogeneous second and higher order equations with constant coefficients; the particular solution of inhomogeneous second-order equations; first-order linear systems, solutions and phase plane; series-form solutions of equations with variable coefficients; solutions by use of Laplace transforms.

Students will use the symbolic computational computer language Maple to study the behaviour of differential equations.



And this is the PDE course:

Partial Differential Equations
Partial differential equations of mathematical physics and their solutions in various coordinates, separation of variables in Cartesian coordinates, application of boundary conditions; Fourier series and eigenfunction expansions; generalized curvilinear coordinates; separation of variables in spherical and polar coordinates.
The course will be based on the three archetypical equations from mathematical physics: the wave equation, Laplace's equation, and the heat equation. Using these equations in various contexts as examples and motivation, the basic mathematical techniques for solving second order partial differential equations will be developed.
 
MATH 323(3230) Introduction to Differential Equations (MQR)

Fall. 4 credits. Prerequisites: multivariable calculus and linear algebra (e.g., MATH 221 222, 223 224, or 192 and 294), or permission of instructor.

Intended for students who want a one-semester introduction to the theory and techniques of both ordinary and partial differential equations. Topics for ordinary differential equations include initial-value and two-point boundary value problems, the basic existence and uniqueness theorems, continuous dependence on data, stability of fix-points, numerical methods, special functions. Topics for partial differential equations include the Poisson, heat and wave equations, boundary and initial-boundary value problems, maximum principles, continuous dependence on data, separation of variables, Fourier series, Green's functions, numerical methods, transform methods.

MATH 293(2930) Differential Equations for Engineers (MQR)

Fall, spring, summer. 4 credits. Prerequisite: MATH 192. Taking MATH 293 and 294 simultaneously is not recommended.

Introduction to ordinary and partial differential equations. Topics include: first-order equations (separable, linear, homogeneous, exact); mathematical modeling (e.g., population growth, terminal velocity); qualitative methods (slope fields, phase plots, equilibria, and stability); numerical methods; second-order equations (method of undetermined coefficients, application to oscillations and resonance, boundary-value problems and eigenvalues); Fourier series; linear partial differential equations (heat flow, waves, the Laplace equation); and linear systems of ordinary differential equations.

MATH 4200 Differential Equations and Dynamical Systems (MQR)

Fall. 4 credits. Prerequisite: high level of performance in MATH 2210–2220, 2230–2240, 1920 and 2940, or permission of instructor.

Covers ordinary differential equations in one and higher dimensions: qualitative, analytic, and numerical methods. Emphasis is on differential equations as models and the implications of the theory for the behavior of the system being modeled and includes an introduction to bifurcations.

MATH 428(4280) Introduction to Partial Differential Equations (MQR)

Spring. 4 credits. Prerequisite: MATH 221 222, 223 224, or 192 and 294, or permission of instructor.

Topics are selected from first-order quasilinear equations, classification of second-order equations, with emphasis on maximum principles, existence, uniqueness, stability, Fourier series methods, approximation methods.
 
DanM said:
My school also offers a similar course that gives an intro to both ordinary & partial differential equations:

Differential Equations for Scientists and Engineers
Introduction to ordinary and partial differential equations, including their classification, boundary conditions, and methods of solution. Equations, methods, and solutions relevant to science and engineering are emphasized, and exploration is encouraged with the aid of software.
Click to expand...

That's a "mathematical methods" course for engineering and physics types -- a bit of this, a bit of that. Not appropriate for math majors, who need coherence and depth.
 
bigbadwolf said:
That's a "mathematical methods" course for engineering and physics types -- a bit of this, a bit of that. Not appropriate for math majors, who need coherence and depth.
Click to expand...

I know, I'll be taking the other two courses I posted.
 
CGiuliano said:
I might just go with intro to DE's and a grad PDE course

Apparently Harvard doesn't offer an ODE course either. They group diffeqs with linear algebra (Cornell also has this) and have an ODE/PDE course.
Click to expand...

Linear algebra + ODEs is okay. A lot of the charm of the subject of ODEs comes from its interaction with linear algebra (for a simple example, the solution space of y" + y = 0 has as a basis sin x and cos x).
 
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