# Questions tagged [differential-equations]

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23 questions
882 views

### Should I teach Laplace Transforms? How much?

My question is in the title. Let me elaborate and give some context: I'm teaching a first differential equations course, essentially for engineers, at the university. I'm developing the syllabus ...
692 views

### What is the motivation for characterizing second order linear PDEs as hyperbolic, elliptic, or parabolic?

I'm teaching an Intro to PDEs course (I'm an analyst, but PDEs are a bit outside my bailiwick) and I'm covering the basic examples: Heat, Wave, and Laplace. How should I move from these examples to ...
510 views

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

Is every mathematical concept, even the complex ones, explainable? As someone who will be needing to explain my line of work for a position to a committee who is very, very, educated, just not in ...
229 views

### How to teach ordinary differential equations to good students?

I am TA-ing a introductory course on ODEs and PDEs this year. At my university most introductory math courses can be taken at "basic" and "extended" levels. This one is the extended one. My students ...
647 views

### What is the right way to order the topics in a first ODEs course?

This question is long but I am asking for educated opinions on a question of math education and for this reason I'd like it not to be closed on the grounds that it invites subjective discussion. ...
322 views

### Theme of a Differential Equations Course

I am tasked with teaching an introductory differential equations course. In my experience, this course tends to be a laundry list of methods that apply to specific forms of differential equations ...
3k views

### Why do we study ordinary differential equations?

What is a good answer to the question: Why should one study ordinary differential equations? I would give the answer: ODEs are used in many models to determine how the state of this model is changing ...
211 views

### A more natural motivation for the appearance of generalized eigenvectors in linear system with repeated eigenvalue

When I teach constant coefficient linear differential equations, the usual guess of an exponential can be motivated because it is "approximately" a fixed point for the differentiation operator. The ...
1k views

### Commonly taught method divides by zero

I just saw this question and the two answers. Now I am very sure that if many teachers see these answers they would accept them. Unfortunately they are deeply flawed. The second one is clearly invalid ...
158 views

### How much prior math should I review in teaching a graduate-level course?

I am scheduled to teach a graduate-level course in engineering whose basis is in the solution of ODE’s and PDE’s, and thus is about halfway between a math course and an engineering course. We ...
181 views

### Differential equations - definitions

I am having a great deal of trouble with the definitions used throughout the book so far - i.e. linear, homogenous, non-homogenous, etc. I am not sure why exactly they are useful to know. I am having ...
281 views

### Why aren't integral equations often taught “back to back” with differential equations?

In single variable calculus, integral calculus is taught "back to back" with differential calculus. This is generally true, although to a lesser extent, with multivariable calculus. Yet I don't see ...
315 views

### A Plan for a Treatise Study of the Classical Theory of PDEs

The Plan In the study of any special issue in mathematics, two things may be of importance, namely, subjects and order of them. I just wrote down a plan to study the theory of partial differential ...
163 views

### Second Order Differential Equation Example Request

I am looking for some non-complicated second order differential equations to illustrate certain techniques for control engineering. It doesn’t matter if the differential equations are linear or non-...
272 views

### Differential equations book

I am looking for a book on differential equations (ordinary/partial) of a particular kind. I figure out I am terrible at solving differential equations. This a vast field and unfortunately I don't ...
124 views

### How to explain linear approximation to an equation to calculus students?

I am, at the moment, teaching calculus to students whose majors are, for example, biology, biochemistry, chemistry and geology. The course book is Claudia Neuhauser's "Calculus for biology and ...
75 views

### Split differential equations into two video courses; theory and calculation?

I'm creating a course on differential equations, and I'm painfully aware that there is a LOT to teach. As of right now, I'm considering splitting the course into two, in the following manner: theory ...
164 views

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

I'm teaching at high school level and the next topic will be differential equations. I would like my students to be able to solve some simple linear and non-linear ODEs using the ansatz \$x(t) = e^{\...
98 views

I'm looking to put together a 1 hour talk about monodromy aimed at undergraduate math and physics majors. In terms of prerequisites, I only want to assume the students have seen multivariable calculus,...
137 views

### Easy tool to draw stencils

I'm looking for a simple tool (preferably online or at least that works on Linux) to draw stencils. When teaching and creating notes for students, I often feel that it would make understanding in some ...
112 views

### What is the preferred method of teaching “linear” differential equations today?

For the purposes of this question, there are two kinds of differential equations: linear, and non-linear, which is to say that there could be two ways to teach the subject. One way is to separate ...