# Tag Info

### How would you explain what a PDE is to a very educated layman with no math background?

I would say something like this: "Often in complicated systems one needs to study multiple quantities, each of which varies at rates that depend on the other quantities and on how fast they are ...
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### Should I teach Laplace Transforms? How much?

Consider something besides an "all or nothing" approach. Here's what I did a couple of times when the topic was optional and I didn't have much time, but I still wanted to give students an ...
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### Diagram of Methods to Solve Differential Equations

I would just like to mention that other similar flowcharts have been developed, of varying degrees of generality, which you might consult. Here is one (by Adam Monahan). And another (by Jeremy ...

### Why do we study ordinary differential equations?

ODEs are used in many models to determine how the state of this model is changing (regarding time or another variable). […] Am I missing another application […]? This may be somewhat pedantic, but I ...
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### Why do we study ordinary differential equations?

Of course I agree that one motivation for studying ODEs is that they have applications. But it might be useful to also point out another fact that students do not always think about: ODEs are often ...
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### Why aren't integral equations often taught "back to back" with differential equations?

While there is a logical symmetry between differential equations and integral equations, it seems that (as they say) "laws of nature" are written in differential equations, not integral equations. As ...
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### What mathematical topics are important for succeeding in an undergrad PDE course?

They must understand the quadratic equation and how to factor it, solve it and manipulate it formally in both the real and complex case. Also, how to solve simple trigonometric equation and knowledge ...
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### How much prior math should I review in teaching a graduate-level course?

Even for math grad students, I'd forcefully review much more than many traditions seem to indicate. That is, I would not presume perfect recall of the standard curriculum, especially either in detail ...
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### Why do we study ordinary differential equations?

Echoing many of the points made in the other excellent answers... but just to focus on one (to me very significant) aspect: differential equations characterize functions in (physically?) operationally ...
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### Differential equations - definitions

One reason that calculus solution concepts didn't necessarily have labels of this kind is that such things are fairly ad-hoc. But all of the terms you listed - "linear", "homogeneous", etc. - have ...
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### Online homework systems for ordinary differential equations

MyOpenMath is free. It doesn't look like it has a full course, but it has something, and you could add to it. Here's what I found: Covers chapters 1-6 and 8-10 from the Trench text (Elementary ...
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### Differential equations - definitions

I'll give you the big picture of the differential equations course I've taught for a few years, I'm not sure what the curriculum is at your university, but, odds are we have much in common. First, ...
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### Why do we study ordinary differential equations?

We should study Ordinary Differential Equations because it is beautiful mathematics which clearly illustrates the wondrous connection between analysis and algebra. Linear algebra, or perhaps matrix ...
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### A good way to learn differential equations rigorously

A classic book is Coddington & Levinson, Theory of Ordinary Differential Equations. Probably tough going for most students. Coddington, An Introduction to Ordinary Differential Equations. Much ...
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### What mathematical topics are important for succeeding in an undergrad PDE course?

I would say that a good knowledge of linear algebra is paramount (for many reasons). About equally important is the full mastery of the differential and integral calculus of one variable. With these ...
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### What is the right way to order the topics in a first ODEs course?

Your desire for some beautiful integrated thematic math person version of course shows not thinking about two important things: Your students and what they need. How people learn best. For number 1, ...
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### Why do we study ordinary differential equations?

My slant is more tactical than the general idea of modeling. An ODE course is useful for students in engineering and physics because they will need the concepts to follow derivations and work ...
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### How would you explain what a PDE is to a very educated layman with no math background?

Imagine a surface, for example, a horse saddle. Note that the "curvature" of the surface differs not only when you measure it at different points, but also when you measure it along different ...
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### Refreshing math knowledge

Don't underestimate how much your knowledge and skills can fade when unused, even after a couple of years, let alone twenty. I've experienced this personally when trying to study advanced topics for ...
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### Why are "homogeneous differential equations" in the standard ODE curriculum?

Introduction This is some sort of “apology” for teaching homogeneous ODEs. I think there’s a certain beauty and simplicity to them. That beauty is overlooked in most textbooks, which Rota sourly ...
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