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 and classifying Hénon map bifurcations and periodic points
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Second Order Differential Equation Help! - Underdamped Spring-Mass System
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ODE with non-negative initial value has a non-negative solution?
Consider the coupled system of ordinary differential equations given by $$ \dot{x}_i (t) = g_i(t) \cdot f_i( x_{i+1}(t) ), \ i = 1, \ldots, n. (x_{n+1} = x_1)$$ $$ x_i(t_0) = x_{0,i}>0.$$ If each $g_i, \,f_i$ are non-decreasing and $g_i (t), \, f_i(x)>0$ if $t, \,x>0$, is true that the condition $x_{0,i}>0$ implies that the […]
Fixed-point iteration and backwards Euler's method
I have just started with numeric methods for differential equations and have come across this exercise: We have $f$ which is Lipschitz-continuous in the second argument with constant $L$ and we are looking at the backwards Euler's method: $y_{k+1} = y_k + h_k f(x_{k+1}, y_{k+1})$. Now define the fixed point iteration $v_{k+1} = y_k + […]
When solving a third-order ODE using reduction of order, what happens when the v’ term drops out
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Why this discrepancy is occuring in finding the order and degree of differential equation.
Yesterday while studying the chapter Differential Equations I found that in the book it was written that 'The degree of differential equations involving one or more terms of the form of $\cos(\frac{dy}{dx})$, $\sin(\frac{dy}{dx})$, $e^{({\frac{dy}{dx}})}$, $\ln(\frac{dy}{dx})$ are undefined.' In the book some examples were also given like: The degree of the differential equation $\frac{d^{2}y}{dx^{2}}+e^{\frac{dy}{dx}}+y=0$ is undefined. […]
Solving 4th order differential equation
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First order ode with tricky IC. How to obtain same solution as computer?
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Suppose $f:[a,b]\rightarrow\mathbb{R}$ is a piecewise linear continuous function and I want to solve the differential equation $dx/dt=f(x)$ with initial condition $x(0)=x_{0}$. My thought is: Suppose $f(x)=ax+b$ on some interval $(p,q)$ containing $x_{0}$. By using separation of variables, we can do $$\int \frac{dx}{ax+b}=t,$$ assuming that $x\in(p,q)$. If it moves outside of the interval, then we do […]
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Assignments Week 4

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