2
votes
0answers
9 views

Academic Prerequisite of Dynamical system and applied PDE

With a very strong intention on future research closely related to Dynamical Systems and applied PDE. What are the materials as a prerequisites which are strongly recommended to study hard during ...
0
votes
1answer
92 views

numerical update rule for discretized hawkes excitation process

So I think I am just misunderstanding some simple notation or something and would appreciate some help. I am trying to replicate this model in an agent based model, but I cannot seem to figure out the ...
1
vote
1answer
56 views

Analyzing the stability of equilibria

There's a model with a condition $r>\mu$: $$\begin{align} S'&=r(S+I)-\beta SI-\mu S \\ I'&=\beta SI-(\mu +\alpha)I \end{align}$$ I can easily see that the equilibria of the second ...
0
votes
1answer
29 views

Finding the basic reproduction number of a particular model

I have been reading a paper about a host-parasites models and for the model: $$\begin{array}{rll} \displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\ ...
2
votes
0answers
61 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
1
vote
0answers
146 views

Modeling bacterial growth with differential equations

I hope this is the right place for this question. I am working on building a growth model for bacteria for a risk assessment, and would like to move the growth model past static temperature ...
2
votes
5answers
390 views

Why - not how - do you solve Differential Equations? [closed]

I know HOW to mechanically solve basic diff. equations. To recap, you start out with the derivative $\frac{dy}{dx}=...$ and you aim to find out y=... To do this, you separate the variables, and ...
1
vote
1answer
126 views

Background for studying and understanding Stochastic differential equations

Assume I have back ground of the following knowledge based on the textbook as : ODE : ODE by Tenenbaum Baby probability : Ross 's baby probability Baby real anlysis : Bartle's introduction to real ...
1
vote
1answer
429 views

Optimisation of a rectangles area under a function curve

I have a questions asking for the dimensions of the rectangle with the largest area that has two bottom corners on the x axis and two top corners on the curve $y=12-x^2$. I have plotted the curve and ...
1
vote
3answers
136 views

Differentiation problem solving

I have a question which I'm unable to provide much working for as I'm not sure how to start it. A metal sphere is placed in seawater to study the corrosive effect of seawater. If the surface area ...
2
votes
3answers
408 views

Modelling with exact differential equations?

I'm teaching some very elementary differential equations to engineering students, and their constant question to me is "What's the use of this?" or alternatively "Where would we use this?" Now, I'm ...
2
votes
0answers
107 views

Calculate half life of esters

I'm trying to calculate the level of testosterone released from different testosterone esters. Here are some graphs of testosterone levels after single injections of 250mg of each ester. Testo U ...
1
vote
4answers
75 views

Find the equation of the tangent to the curve

Find the equation of the tangent to the curve $\sqrt X + \sqrt Y = a\;$ at the point $\left(\dfrac {a^2}{4},\dfrac {a^2}{4}\right)$ I don't know how to find $\dfrac {\mathrm dy}{\mathrm dx}$ in ...
5
votes
1answer
169 views

What is the physical meaning of fractional calculus?

What is the physical meaning of the fractional integral and fractional derivative? And many researchers deal with the fractional boundary value problems, and what is the physical background? What ...
2
votes
0answers
106 views

Positive eigenvalues in differential-algebraic equations not appearing in time-domain simulation

I am solving a system of equations derived from power system applications. It consists of index-1 differential and algebraic equations in the form: $$\dot{x}=f(x,y) \\ 0=g(x,y)$$ To get the ...
2
votes
2answers
83 views

Need to explain an application of $y' = ky$

I have to write application of the ODE $y' = ky$. i want application or any that explain little bit. Thanks!
3
votes
1answer
118 views

Geometric reason for 3/4-power growth rate?

It seems pretty well established that organisms grow according to a 3/4-power law. For example, Niklas and Enquist, in their paper "Invariant scaling relationships for interspecific plant biomass ...
0
votes
1answer
224 views

how to find the application of ordinary differential equation

This question may be out of the scope of this website, if so let me know and i will delete it. so I am right now taking an ODE class, which i find to be mildly interesting, though it seems to be more ...