Images, posts & videos related to "Differential Equation"

I'm 3 days into Differential Equations and my brain is already mush lol. How do you all remember these endless substitutions? They never end...

Given equation... substitute x with this and y with that, somehow an h appears out of know where. Then you find out its homogeneous, and z's start popping up. Integrate and you discover constant C. Before you know it you're back to x and y, but added in exponentials and a few trig identities.

For those of you taking Diff EQs next semester, hereβs a flow chart to determine which technique to use on a given Differential Equation.

I PASSED DIFFERENTIAL EQUATIONS

Back story: So I finished my business degree in 2016 and started as an engineering major in 2012 then switched to business because I was partying a lot and not taking the course load seriously.

Fast forward to 2020 and I decided to do what I am meant to do and go back to engineering. I finished calc 1 and calc 2 in 2012 and was told I need linear algebra, calc 3 and differential equations to get caught up this semester. My advisor said I shouldnβt take them all at once because itβs practically not possible considering I hadnβt taken calc in years.

I have never struggled so much and taking three math courses at once was a nightmare. I was literally dreaming of matrices and Laplace. Half of the differential equations class dropped out in the beginning because my teacher was very tough. I had a 63% the entire semester and got up to a 73%.

I needed a 50% or so to pass on the final and the fact that I had a 34% on my first exam made me VERY nervous. I studied my ass of and finished with a 74. Iβm usually an A/B math student and this class really got to me BUT I PASSED. IM SO EXCITED AND HAD TO GET IT OFF MY CHEST. Iβm so excited to be back in engineering and actually take real engineering courses next semester.

I know a lot of people think diffeq is easy but my prof made it painful. Iβve never felt so much relief in passing a class IN MY LIFE.

[Keim] Earlier this month, Taylor Heinicke was taking his ODU finals. Took two; will take other two after the season. his classes this semester: Numbers theory; Partial differential equations; applied numerical methods; Math and nature mobile.twitter.com/john_kβ¦

How to learn Stochastic Differential equations to be applied in finance

Hello, for the start of 2021 I promised myself to learn something out of my grasp or field but would undoubtably peak my interest. I have always wanted to learn various mathematical concepts used in finance and I know it's a tall order to want to learn Stochastic Differential Equations even tho I have no background in math/calculus, heck, except for your basic addition, subtraction, division and multiplication I am completely illiterate at math. I was wondering if there were any material (books, yt videos or websites) that would allow a complete novice like me to learn this kind of subject matter. I'm really sorry if this seems like such a dumb question. Thank you in advance :)

"Differential Equations: A Historical Refresher", by V. N. Krishnachandran. "This paper presents a brief account of the important milestones in the historical development of the theory of differential equations." [abstract + PDF, 24p] arxiv.org/abs/2012.06938

[20] Spring semester just started and I have differential equations this term, wish me luck! ; ^ ;

Can a non-trivial continuous dynamic system be expressed without differential equations?

I'm really interested in continuous dynamic systems that produce complex behavior: reaction-diffusion systems, KuramotoβSivashinsky equation, etc.

So far, all of the continuous nonlinear systems I stumbled upon online have been described in terms of nonlinear PDEs. I'm an amateur mathematician with little training and I (unsurprisingly) find PDEs challenging to work with: while there are relatively simple numerical methods (I played with explicit time-stepping and finite-differences for spatial derivatives), they tend to come with a lot of caveats and complications like instability, oscillations, numerical artifacts.

Its further complicated by the fact that I'm mostly interested in coming up with arbitrary equations, tweaking them and looking at how various starting conditions evolve under them.

I tried looking into more refined approaches within finite-difference methods (stencils designed to have less anisotropy, operator splitting, stabilization of explicit methods) and while my simulations had better results, there are still problems. Implicit methods look like a common choice, but the need for solving large nonlinear algebraic systems at every time step makes them impractical for me.

I also looked into finite element and finite volume methods, but they seem to be mostly focused on physical systems. They also involve calculus of variations and other topics that are a bit too advanced for me right now.

I know that there's no "black box" algorithm that can numerically solve an arbitrary PDE without need for careful design and specialized approaches depending on the type of the problem.

So I was wondering if there's a way to construct an explicit time evolution rule that doesn't require the handling of differential equations? Something like a function, designed in such way that makes it easy to discretize without distorting its behavior too much.

I get that the dynamical systems designed that way probably won't have relevance in modeling real world, but since I'm just exploring these simulations out of curiosity, that isn't particularly important.

Sorry for the wall of text, I'm really excited about this topic but after spending weeks upon weeks trying to find a "method that works" I feel like I'm out of my depth and need help.

[A math] solving first order differential equations by separating variables. How do I differentiate z to get d2y dx2?

No wonder Heinicke played so hard. He has to take his Differential Equations final now that weβre eliminated nbcsports.com/washington/β¦

[R] Bayesian Neural Ordinary Differential Equations

Bayesian Neural Ordinary Differential Equations

There's a full set of tutorials in the DiffEqFlux.jl and Turing.jl documentations that accompanies this:

- Bayesian Neural ODEs with NUTS
- Bayesian Neural ODEs with Stochastic Langevin Gradient Descent
- General usage of the differential equation solvers (ODEs, SDEs, DDEs) in the Turing probabilistic programming language

Our focus is more on the model discovery and scientific machine learning aspects. The cool thing about the model discovery portion is that it gave us a way to verify that the structural equations we were receiving were robust to noise. While the exact parameters could change, the universal differential equation way of doing symbolic regression with the embedded neural networks gives a nice way to get probabilistic statements about the percentage of neural networks that would give certain structures, and we could show from there that it was certain (in this case at least) that you'd get the same symbolic outputs even with the variations of the posterior. We're working with Sandia on testing this all out on a larger scale COVID-19 model of the US and doing a full validation of the estimates, but since we cannot share that model this gives us a way to share the method and the code associated with it so other people looking at UQ in equation discovery can pick it up and run with it.

But we did throw an MNIST portion in there for good measure. The results are still early but everything is usable today and you can pick up our code and play with it. I think some hyperparameters can probably still be optimized more. The

If you're interested in more on this topic, you might want to check out the LAFI 2021 conference or join the JuliaLang chat channel (julialang.org/chat).

Hi there all I have a question. Is taking calculus 3(Multivariable Calculus) and differential equations at the same time ok?

This is my first time posting on this subreddit and I just need some advice or wondering if anyone else has been in the same situation. From what I understand many of the topics learned in Calculus 3 don't overlap with Diff Eq. Since its most vector functions and 3-D.

I want to make sense of Differential Equations

I've already passed my DE class with an A. I've solved a dozen differential equation using a dozen different methods and I dare say at some point I was actually good at solving my class' problems. I never made sense of it though, I can't *feel* those DE and I can't intuitively apply them to practical problems, nor can I understand why they are presented the way they are in any given real world application. I believe I do have some sense for calculus, but differential equations still feel like an enigma when applying them.

Are there any resources you would recommend that help with this intuition?

How are analytic techniques for solving differential equations used in applied math research?

Applied math undergrad here and I'm curious how techniques from upper-division differential equations classes are utilized in applied math research at the PhD level. I know that techniques from numerical analysis are incredibly useful since most solutions to differential equations have to be approximated in applications, but I'm curious if Laplace Transforms, series solutions, and other methods learned in an ODE class are used extensively in applied math research? I would really appreciate your help!

how to use the ODE45 method to solve a 3rd-degree differential equation

This is the equation

and the conditions are also included

The problem is I don't understand the ODE45 method

I don't need you to give the answer to this problem, what I need is for someone to give me a good explanation about the ODE45

I didn't get what Matlab help had written

and please upvote this so more people can see it and help me understand this method

https://preview.redd.it/89hdbrm6e1b61.png?width=535&format=png&auto=webp&s=dff2447537d376802308a82a597305c104ba3fb8

I'm having trouble with this differential equation

[Research] Fourier Neural Operator for Parametric Partial Differential Equations

View the full paper presentation here which includes a time-stamped outline:

Numerical solvers for Partial Differential Equations are notoriously slow. They need to evolve their state by tiny steps in order to stay accurate, and they need to repeat this for each new problem. Neural Fourier Operators, the architecture proposed in this paper, can evolve a PDE in time by a single forward pass, and do so for an entire family of PDEs, as long as the training set covers them well. By performing crucial operations only in Fourier Space, this new architecture is also independent of the discretization or sampling of the underlying signal and has the potential to speed up many scientific applications.

**Abstract:**

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime). Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers.

Authors: Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar

Anyone take differential equations?

I wanna know how it went and if itβs extremely difficult or not. Also, has anyone taken it with Andrea Welsh. Iβm currently a freshman about to take this class, wanna know what Iβm in for.

Struggling with Linear Algebra component of Differential Equations ππ reddit.com/gallery/jxn9d9

ONLINE MATH CLASS TUTOR: I am a Mathematics writer. Feel free to contact me at any time for your Calculus, Statistics, Linear Algebra, Trigonometry, Permutations, Combinations, Probability, Geometry, Differential Equations, and any other related field. Email: [email protected]

Discord: Andywriters#7925

Looking for a good method for refreshing topics from calculus 1-3, differential equations

Hi everyone! I am currently in the process of applying for graduate school for a PhD in meteorology. I dealt heavily in 3-D calculus during my upper division undergrad coursework, but I decided to take a year between undergrad and grad school to work. I don't want my foundational math skills to get too rusty, but I'm having trouble pinning down a good method for refreshing topics. Should I go through my calculus textbooks again? Do practice problems? Are there any resources that someone can provide that can overview topics without having to go through them from the ground up? I would appreciate any help with this.

Can anyone suggest a website that generates Differential Equations, and Vector Calculus practice problems?

I'm looking for a website that generates Differential Equations and Vector Calculus problems, so I can get more practice. I'm subscribed to Wolfram Alpha, but their problem generator only goes up to Calculus 2.

I dont know how to solve a differential equation with a certain substitution.

My problem is this, I have to solve this differential equation: 2tyy' +(t-1)y^2 = t^2 e^t and I have to substitute y^2 = tz (y and z are functions, t is a variable). When I tried to fill this in i became an equation that seems even harder to solve. Anyone an idea what I am overseeing? Thank you!!

Is there a model using Convolutions, RNNs, and Neural Ordinary Differential Equations at the same time?

Hi there,

I finishing a semester project where I used an architecture consisting of Convs, RNN, and NODE. As far as my internet researches go, there is no record of sucssesfully using all of the 3 concepts in one model, so i want to write something like: "To the best of our knowlege, we are the first to propose ...".

Does anybody know of such a model?

tl;dr: the title says it.

How to solve 2nd order differential equation with variable coefficients?

So i have this expression

u''(r) + f(r) u(r) =0

with

f(r) = C(E+5 e^{-r^2/2}), (C is a constant)

And I'm not sure how to solve for the values of E (are supposed to be discrete). Any ideas where to start?

Thanks in advance!

Question about the importance of topology, real analysis and differential equations in financial mathematics

Hi, I'm a last year undergrad student looking to pursue math at a graduate level focusing more on financial mathematics.

Having that in mind, will there be any issues with me now knowing any topology or higher level analysis (such as Fourier and Laplace transformations, gamma function properties, differential equations)?

We unfortunately haven't covered any of these topics during the three years of study here (at least during the courses that were mandatory).

As far as I know, topology and higher level analysis could be useful in measure theory which is a useful thing to understand if you work with stochastic processes used for option pricing. Besides that, I've heard that differential equations can be very useful but I'm not sure where as I'm not that informed on the topic. Do you have some book recommendations i should read about the topics in hand? Should i worry about my lack of knowledge in these topics?

I want to learn the importance of symmetry groups in solving differential equations. How should I go about it?

I am currently in graduate differential equations for engineers, and we have been running through the whole gamut of standard diff eq solving techniques: Green's functions, separation of variables, combination of variables, similarity transforms, and so on.

I am a little awestruck with how powerful similarity transforms and separation of variables is. It baffles me that boundary conditions are actually at the core of solving DEs, and that boundary conditions really dictate how your solution should look like. After diving into it a little bit, I realized I was reading quite some heavy abstract algebra and Lie groups kept popping up.

I have only done a small bit of abstract and group theory. But if it means understanding why these techniques work, I definitely want to go deeper.

How do you recommend I start learning this?

How did people solve systems of linear differential equations before eigenvalues?

It seems as though every text book I pick up talks about solving systems of linear differential equations by matrix diagonalisation. How did they do it before eigenvalues and eigenvectors were discovered? Seems it's not obvious how to do it, even numerically as an IVP.

I'm struggling to understand & visualize differential equation. Using Newton's Law: Acceleration = Force/Mass is a diff. eq. since A is 2nd derivative, but I'm not sure about force and mass. I'm guessing these are just another two different function, right?

https://i.imgur.com/I2ZuhLb.jpg

Force as a function w.r.t. time is just a constant:

"f(t) = 10" since force doesn't change at all as time goes by.

Same with Mass as a function w.r.t. time:

"m(t) = 5" since mass doesn't change as time goes by.

Lastly, x(t) is yet another function. So I'm actually dealing with three different function w.r.t. time in this diff. equaton A = F/M, right?

Differential Equations and Linear Algebra

My DiffEq class (and probably Linear Algebra) are using this awful online-only textbook that is pure garbage. Can anyone recommend a decent book or books (physical, hold it in my hand, smell the pages, lick the cover book) that cover Differential Equations and Linear Algebra

Bayesian Neural Ordinary Differential Equations arxiv.org/abs/2012.07244

Has anyone taken Differential Equations with Yulong Li?

Hi!

I'm debating if I should take MATH 285 this semester, the only professor that fit my schedule is Yulong Li. Couldn't find anything on rate my professor, how is he as a professor? Thanks!

Differential Equations (MA226) is completely full

I need to take MA226 but all three sections are full. I emailed one of the professors and he said that I would have to wait until Jan 19th then get put on a wait list.

Is there a chance that I actually won't be able to get into this class?! Also does anyone know what else I could try, or who else to contact for help?

Thanks!

Applications of Differential Equations

https://imgur.com/S9OO1fO

Linear Algebra, Differential Equations, and Calculus Videos

With most classes online this quarter, Iβve made a number of math videos on topics such as linear algebra, calculus and differential equations and plan to post videos throughout the school year. I hope this serves as a helpful resource to other educators and students.

Link to my Youtube channel:

https://www.youtube.com/c/mathwithjanine/videos

Playlists:

At what time does the model predict 10,000 bacteria? (differential equations)

Q: http://prntscr.com/wksb4b

w/o: http://prntscr.com/wksc8n

What did I do wrong? The ans in the textbook is 11:02 am.

Why don't Cornell girls like my elliptic partial differential equations?

I introduced myself to a girl in Goldieβs the other day. I saw her sitting alone and I walked up to her. It felt like love at first sight.

I said my name and we started talking about our majors and that typical stuff. but I couldn't think of how to keep the conversation going at one point. I pulled out my phone and asked if she wanted to see my elliptic partial differential equation from my Cauchy problem. She nodded and I started going through boundary conditions. I started it a few characteristic timescales ago and was really proud of my canonical form and analyticity within the domain especially. I think she was really interested and I thought she really liked me and she was pretty too so i asked her "Do you want to couple our PDEs?" and she said "ummm no im sorry." I felt really awkward so I just apologized and said bye.

This has kinda shattered my confidence and I can't stop thinking about it.

Has anyone else had their existence and uniqueness shattered at Cornell in a similar manner?

What is some good book for a review on ordinary differential equation

I'm looking for a book like Baby Rudin's principle of mathematical analysis or Paul Halmos's Finite dimensional vector spaces, having contents that would be covered in typical undergrad level ODE classes with concise proofs and few good exercises, but not too long one, and that is geared toward advanced pure math students who've already taken ODE. Thanks!

I don't know if this is the right sub but there is a problem in my textbook that i just cant seem to solve. Its a differential equation where you have to substitute y^2 (a function) with a variable multiplied by another function z. Thank you!!

Is the Coulomb potential really a solution for this differential equation?

I'm stuck with a problem that's stating the following Coulomb potential for a negative point charge

Ξ¦(r) = -(1/4ΟΞ΅0)(q/r) in spherical coordinates

is the solution to this partial differential equation β^2 Ξ¦ = -(q/Ξ΅0) Ξ΄^3 this delta being Dirac delta in three dimensions.

I can find the electrical field through the negative gradient of Ξ¦(r) and with this do a surface integral to obtain the flow through the surface (a sphere centered in the origin). According to Gauss' theorem, this should be equal to the volume integral of the divergence of the electrical field (implicitly this means that the divergence of the electrical field is equal to the negative laplacian of Ξ¦(r), so the volume integral of this is also equal to the surface integral of the electrical field), to do this volume integral the Dirac delta is necessary (because both the divergence of the electrical field and the laplacian of the potential are 0 for all values of r different from 0 and infinity in r=0), so -β^2 Ξ¦ should be equal to -(q/Ξ΅0) Ξ΄^3, or β^2 Ξ¦ = (q/Ξ΅0) Ξ΄^3, which is different from what was given above. Which of these laplacians is the right one to have the Coulomb potential as its solution?

[REQUEST] Differential Equations and Linear Algebra, Penney, Edwards, 3rd Edition, 2010, Prentice Hall, 978-0138141028.

would love some help here :)

differential equation

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