# 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 ...

### Commonly taught method divides by zero

The method is mathematically incorrect, but whether it is wrong or not, depends on whether people know what they're doing or not. The possible division by zero is a mistake, yes. But it is a mistake ...

### 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 ...
Accepted

### 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?

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 ...

### 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 ...
Accepted

### 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 ...

### 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 ...

### 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 ...

### 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 ...

### 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, ...

### 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 ...

### 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 ...

### In what order should I teach methods for solving (linear) ODEs?

You left out linear first order ODE's, with their integrating factors. I use this often, compared to the other techniques. This probably should be done just after separation of variables, though I ...

### 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, ...