There are several reasons. Importance of Differential Equations. They tell you the underlying rule for the interactions, not the result of them. I am an EE student. Thanks, that is really a new view on ODEs I haven't considered before... Perhaps a good idea to expand BCH to Baker-Campbell-Hausdorff. Forward domain to a specific port and IP while using the forwarded domain in the URL. What is the significance of learning ''cadences" in music composition? Differential equations have a remarkable ability to predict the world around us. One way that I've seen it explained by non-mathematicians (electrochemists, in this case) is with equivalent impedances in the frequency domain. People won't understand what you mean, but then you remind them that acceleration is just the derivative of velocity, which is just the derivative of position. Any videos or demonstrations I can show are a plus. I am a differential geometer, so I need them: to construct diffeomorphisms from vector fields. And then, once we understand ordinary differential equations, we can then start look for ordinary differential equations — like the old adage goes, if you have a hammer, everything looks like a nail. Linear algebra, or perhaps matrix theory, when combined with calculus provides abstractions of ordinary functions which behave in ways similar yet fantastically different than ordinary functions. Baby proofing the space between fridge and wall.

Looking for a function that approximates a parabola.

The language of analogue circuits, signal processing and control is differential equations, there is simply no way to understand them without it. I've always disagreed with trying to find "applications" in math classes. In addition, math courses tend to teach more with x's and y's, which is just a less complicated fashion than learning math with a bunch of constants and variables signifying particular quantities (energy, force, etc.) Quick link too easy to remove after installation, is this a problem? Mention the field of dynamical systems, large parts of which are about understanding and classifying the solutions to ODEs. introductory article what differential equations are and why they are studied, very nice and short book by Alcock and Simpson, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, “Question closed” notifications experiment results and graduation. Models, as you mention, are a huge source of applications. A Differential equation is an equation that expresses a relationship between a function and its derivatives. You Do the Gallbladder, I'll Take the Appendix, Can I run my 40 Amp Range Stove partially on a 30 Amp generator, Convey 'is raised' in mathematical context. In mechanics, E&M, circuits, heat transfer, and many, many more. I don't know who said it first but I've always liked the quote "The laws of nature are expressed as differential equations". We should study Ordinary Differential Equations because it is beautiful mathematics which clearly illustrates the wondrous connection between analysis and algebra. It's a pain, and if they are first or second year EE's it will probably go over their heads, but it's a good start. It's a cute five-minute office trick that seems to work pretty well. I often point out to them that understanding even simple circuits (eg RL-circuits, RLC-circuits) require differential equations in an essential way, but I don't feel like this totally drives the point home to them. If they don't get the RL and RLC circuits require diff equations, they are going to have a bad time. For that matter, even more immediately, and maybe not known to absolutely everyone, Liouville's and others' results about (non-) integrability in elementary terms show that even the trivial differential question $u'=f$ with $f$ elementary leads outside the usual. The beauty of the subject, tying together several branches of maths that student tend to consider separate, is of course also a strong motivation. Of course, the actual algebra of solving the harmonic oscillator differential equation isn't so straight forward (that's why a lot of authors do it the lazy way and say "verify that this sum of a sine and cosine that I took magically out of a hat are a solution"). The theory of differential equations is closely related to the theory of difference equations, in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Therefore, F = m d²y/dt². In Picketty's Capital in the XXIth century (where I read it) is stated as the second law of capitalism the relation As the quadratic equation is to "ICE" chemical equilibrium problems, so is the harmonic oscillator for basic engineering and physics. Manifestly, this is the case for many of the classical special functions. While some problems might naturally take the form of an ordinary differential equation, we solve other problems by finding ordinary differential equations that give us information about them. After all, constant gravity is just an approximation, as it actually changes with height as well. They are a very natural way to describe many things in the universe. It can become tough to learn a new topic, and new math (and perhaps new notation) all at the same time.

The book "Chases and Escapes" by Paul Nahin contains many applications of ODE that would convince the student of the utility of studying ODE. Maybe run through one of the RC or RL circuits to show them how they relate.

However, in EE in RLC circuits they are later taught to use phasers instead of diff. Why did MacOS Classic choose the colon as a path separator?

Which is to say that much modern number theory relies... That is, "description (of an important thing)" is quite often "by a differential equation". ginghin Uncategorized June 27, 2018 2 Minutes.

But g depends on something that also depends on time: the height. So I solved the problem entirely by myself and it felt damn good.

across to the kids in terms of x and y, so they have a better time of surviving their engineering courses (which can be tough on the kids). I have added the (differential-equations) tag; I also wondered about removing the (calculus) and/or (mathematical-analysis) tags, but hesitated to do so, as differential equations are often introduced in calculus and do fall under mathematical analysis, even if not necessarily taught in a course with that name. Take-Home Examination on Ordinary Differential Equations? After some struggling I realized the ''difficulty'' of trying to solve this problems with the tools I had.

Um, maybe that differential equations are the sole mathematical method we have for robustly representing and manipulating systems that have changing differences in quantities interacting and that if they want to ever work on any kind of dynamical system, they'll need it? Eventually with some help I managed to set up the differential equation, which isn't a big deal since I knew basic calc back then. Why is there some obligation for this? Most people have a physical intuition of what a spring will do, and what friction will do, but not what a RLC circuit will do. See my answer at. Or just explain how important Maxwell's equations are. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Biology has some systems to it, but is much more descriptive. All of the students in the class are electrical engineering majors, but still tend to struggle with a lot of math concepts, and have poor math intuition in general. Many of these are even covered to an extent in standard ODE books, but some are additional. They're exactly the same thing mathematically, which shows the beauty and power of differential equations. +1 I always point out the "slope equals value" property of $e^x$ but have never thought to use that as a way to talk about ODEs. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. to construct the exponential map of a Riemannian manifold, Mention Newton's Second Law.

Looking for a function that approximates a parabola.

The language of analogue circuits, signal processing and control is differential equations, there is simply no way to understand them without it. I've always disagreed with trying to find "applications" in math classes. In addition, math courses tend to teach more with x's and y's, which is just a less complicated fashion than learning math with a bunch of constants and variables signifying particular quantities (energy, force, etc.) Quick link too easy to remove after installation, is this a problem? Mention the field of dynamical systems, large parts of which are about understanding and classifying the solutions to ODEs. introductory article what differential equations are and why they are studied, very nice and short book by Alcock and Simpson, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, “Question closed” notifications experiment results and graduation. Models, as you mention, are a huge source of applications. A Differential equation is an equation that expresses a relationship between a function and its derivatives. You Do the Gallbladder, I'll Take the Appendix, Can I run my 40 Amp Range Stove partially on a 30 Amp generator, Convey 'is raised' in mathematical context. In mechanics, E&M, circuits, heat transfer, and many, many more. I don't know who said it first but I've always liked the quote "The laws of nature are expressed as differential equations". We should study Ordinary Differential Equations because it is beautiful mathematics which clearly illustrates the wondrous connection between analysis and algebra. It's a pain, and if they are first or second year EE's it will probably go over their heads, but it's a good start. It's a cute five-minute office trick that seems to work pretty well. I often point out to them that understanding even simple circuits (eg RL-circuits, RLC-circuits) require differential equations in an essential way, but I don't feel like this totally drives the point home to them. If they don't get the RL and RLC circuits require diff equations, they are going to have a bad time. For that matter, even more immediately, and maybe not known to absolutely everyone, Liouville's and others' results about (non-) integrability in elementary terms show that even the trivial differential question $u'=f$ with $f$ elementary leads outside the usual. The beauty of the subject, tying together several branches of maths that student tend to consider separate, is of course also a strong motivation. Of course, the actual algebra of solving the harmonic oscillator differential equation isn't so straight forward (that's why a lot of authors do it the lazy way and say "verify that this sum of a sine and cosine that I took magically out of a hat are a solution"). The theory of differential equations is closely related to the theory of difference equations, in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Therefore, F = m d²y/dt². In Picketty's Capital in the XXIth century (where I read it) is stated as the second law of capitalism the relation As the quadratic equation is to "ICE" chemical equilibrium problems, so is the harmonic oscillator for basic engineering and physics. Manifestly, this is the case for many of the classical special functions. While some problems might naturally take the form of an ordinary differential equation, we solve other problems by finding ordinary differential equations that give us information about them. After all, constant gravity is just an approximation, as it actually changes with height as well. They are a very natural way to describe many things in the universe. It can become tough to learn a new topic, and new math (and perhaps new notation) all at the same time.

The book "Chases and Escapes" by Paul Nahin contains many applications of ODE that would convince the student of the utility of studying ODE. Maybe run through one of the RC or RL circuits to show them how they relate.

However, in EE in RLC circuits they are later taught to use phasers instead of diff. Why did MacOS Classic choose the colon as a path separator?

Which is to say that much modern number theory relies... That is, "description (of an important thing)" is quite often "by a differential equation". ginghin Uncategorized June 27, 2018 2 Minutes.

But g depends on something that also depends on time: the height. So I solved the problem entirely by myself and it felt damn good.

across to the kids in terms of x and y, so they have a better time of surviving their engineering courses (which can be tough on the kids). I have added the (differential-equations) tag; I also wondered about removing the (calculus) and/or (mathematical-analysis) tags, but hesitated to do so, as differential equations are often introduced in calculus and do fall under mathematical analysis, even if not necessarily taught in a course with that name. Take-Home Examination on Ordinary Differential Equations? After some struggling I realized the ''difficulty'' of trying to solve this problems with the tools I had.

Um, maybe that differential equations are the sole mathematical method we have for robustly representing and manipulating systems that have changing differences in quantities interacting and that if they want to ever work on any kind of dynamical system, they'll need it? Eventually with some help I managed to set up the differential equation, which isn't a big deal since I knew basic calc back then. Why is there some obligation for this? Most people have a physical intuition of what a spring will do, and what friction will do, but not what a RLC circuit will do. See my answer at. Or just explain how important Maxwell's equations are. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Biology has some systems to it, but is much more descriptive. All of the students in the class are electrical engineering majors, but still tend to struggle with a lot of math concepts, and have poor math intuition in general. Many of these are even covered to an extent in standard ODE books, but some are additional. They're exactly the same thing mathematically, which shows the beauty and power of differential equations. +1 I always point out the "slope equals value" property of $e^x$ but have never thought to use that as a way to talk about ODEs. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. to construct the exponential map of a Riemannian manifold, Mention Newton's Second Law.