Assignments Week 4

February 19, 2019 / Jonas Reitz / 0 Comments

Exam #1 will take place on Tuesday, 2/26, covering material through Sec 4.1. A review sheet will be distributed on Tuesday, 2/19, and posted to the OpenLab.

WeBWorK: Assignment 6a-Modeling-Population will be due on Tuesday, 2/26, at midnight.
NOTE: Assignment 6b-Modeling-Cooling will be due one week after the exam, on Tuesday, 3/5, at midnight.

OpenLab: none

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assignments week 4

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Finding the Steady-State Solution of the Burgers' Equation
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Second order differential equation with ln
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Solutions of an ode with Wronskian zero?
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Solving the coupled Nonlinear System in Stability analysis using Lyapunov function [closed]
I'd like to ask about the stability of system using Lyapunov function. How to find an appropriate Lyapunov function to show the stability of a system: $$ \begin{align*} \dot{S}(t) &= k - \frac{\mu_{\text{max}} S(t) b(t)}{\delta \left(K_m + S(t)\right)} + \frac{d \beta b(t)}{\delta} + \frac{\alpha \beta b(t)}{\delta}, \\ \dot{b}(t) &= \frac{\mu_{\text{max}} S(t) b(t)}{K_m + S(t)} - […]
Which of the solution curve of the differential equation is correct? [closed]
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Strange ODE system
As I was solving a physics problem I came across this very strange ODE. My goal is to get the differential equation for the temperature T. The problem is that I can't get rid of the current I in any ways. Thanks $$\begin{cases} I=\dfrac{\alpha}{R_0}(T-T_0)-\dfrac{L}{R_0}\dfrac{dI}{dt}\\ C\dfrac{dT}{dt}=-\alpha TI-k(T-T_0) \end{cases}$$ I tried differentiating the equations with respect to […]
Can we interpret indefinite integrals as limit of sums like definite integrals? If not, how does solving separable differential equations make sense?
To illustrate my point, let's consider an example: the amount of a radioactive substance is a function of time, $Q(t)$. At the beginning, $t = 0$, and the initial amount of the radioactive substance is $Q(0) = Q_0$. The substance decays at a rate \begin{equation} \frac{dQ}{dt} = -kQ \end{equation}, where $k$ is a positive constant […]
Best Textbook for Applied Ordinary Differential Equations
I'm looking for suggestions for a textbook that covers Ordinary Differential Equations and their applications, I understand this is a commonly asked question, but I'm looking for a text that would best supplement the course I'm taking, which covers: First Ordinary Linear Differential Equations Dimensional Analysis and Buckingham Pi Theorem Second Order Linear Differential Equations […]
Application of Picard-Lindelof Theorem to enumerate all solutions of y'=y^2.
How to use Picard-Lindelof Theorem to show that all solutions of $y'=y^2$ on some open interval $I$ bounded in one-side are either of the form $y=\frac{1}{-x+C}$ (where $C$ is any constant that is not in $I$) or $y=0$? And if the interval is the whole real line then the only solution is $y=0$? What I […]

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Assignments Week 4

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