# Questions tagged [differential-equations]

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23 questions
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 ...
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 ...
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 ...
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 ...
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 ...
106 views

### A robot to simulate differential equations for undergraduate students. [closed]

I was recently at EPFL drone days and enjoyed a demo of a robot that could follow a black line like in the sketch (I can improve the sketch on demand): Then I remembered my good all times at the ...
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 ...
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 ...
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 ...
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 ...
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-...
104 views

### Workshop about ODEs and connected rates of change (A-levels)

I'm preparing a workshop about ODEs and connected rates of change for pre-college students (smart and interested in mathematics). I'd like to include some fun parts as well - even if these are ...
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 ...
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,...
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 ...
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 ...
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. ...
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 ...
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^{\...
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 ...