2019 Spring - MAT 2680 - Reitz

"...how it differs from the rocks"

Final Grades are posted

May 24, 2019 / / 0 Comments

Hi everyone,

Your final exam grades as well as your overall average for the course are posted under Dashboard/OpenLab Gradebook.  To convert a course average to a letter grade, you can use the table on the  Syllabus page.  Your letter grades have also been submitted to CUNYFirst.

Best of luck to you all in your future studies,
Prof. Reitz

OpenLab #3: Advice for the future

May 9, 2019 / / 53 Comments

(Due Tuesday, 5/21/19, at the start of class).  Imagine that you are invited to speak on the first day of MAT 2680, to give advice to entering students.  Write at least three sentences responding to one or two of the following, describing what you would tell them.

  1. What do you wish that you had been told at the start of this class, to help you succeed?
  2. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.
  3. What is the most important prior knowledge (not taught in the class) that you need in order to succeed?  Why is it important?

Extra Credit.  Respond to someone else’s comment.  Do you agree? disagree? Have anything to add?

Assignments Week 14

May 7, 2019 / / 0 Comments

WeBWorK:  Assignments 14-InverseLaplaceTransforms, and 16-LaplaceIVP  are due Tuesday, 5/24, at midnight.
OpenLab:  OpenLab #3, Advice for the Future, is due on Tuesday, 5/21 (the day of the final exam).

OpenLab #2: Numerical methods PROJECT – Scoring Guide

April 28, 2019 / / 0 Comments

Hi everyone,

Your overall grade (out of 20 possible) for the numerical methods project has been posted under Dashboard/OpenLab Gradebook.  The scoring guide that I used to assess your work is given below.  If you’d like more details about your score, please send me an email or ask me after class.

Regards,
Prof. Reitz

 

NUMERICAL METHODS PROJECT

SCORING GUIDE

20 points total (Written Assignment + Implementation)

WRITTEN ASSIGNMENT – OpenLab (5 points total):

  • 1 point – 300 words minimum
  • 2 points – Describe project & how it works, Describe process of building it (what tech did you use/why? Unexpected challenges?)
  • 1 point – Why do we need numerical methods?  Why is this assignment included in the class?
  • 1 point – include link or state you will send by email

IMPLEMENTATION (15 points total):

3 points: General setup
  • 2 points – Correct differential equation: dy/dx = x^2/(y-1)
  • 1 point – Correct initial condition y(-1)= -0.5
4 points: Euler’s Method
  • 2 points – functioning solution, displays x,y,f(x,y) at each stage
  • 1 point – correct x-target value
  • 1 point – four digits of accuracy after decimal:  y(2)=-1.87228… (will accept -1.8722 or -1.8723), optimum # of steps 11795
4 points: Improved Euler’s Method
  • 2 points – functioning solution, displays x,y,k1,k2 at each stage
  • 1 point – correct x-target value
  • 1 point – four digits of accuracy after decimal:  y(2)=-1.87228… (will accept -1.8722 or -1.8723), optimum # of steps 291
4 points: Runge-Kutta Method
  • 2 points – functioning solution, displays x,y,k1,k2,k3,k4 at each stage
  • 1 point – correct x-target value
  • 1 point – four digits of accuracy after decimal:  y(2)=-1.87228… (will accept -1.8722 or -1.8723), optimum # of steps 12

Assignments Week 12 & WeBWorK NEW FEATURE ‘MathQuill’

April 14, 2019 / / 0 Comments

Assignments Week 12

WeBWorK: Assignments 12-Trench-EulerEquations  and 13-Trench-VariationOfParameters**  are due Tuesday, 4/30, at midnight.
** WeBWorK problem set 13 will be assigned no later than Tuesday, April 22, and will be due on 4/30.

OpenLab: None

 

 

New Feature in WeBWorK

WeBWorK now has “MathQuill” enabled by default, which allows more natural “pretty print” input for your answers.  You don’t have to do anything special to use it – once you click in an answer box, it will start working.  It will detect the mathematical symbols you type and display the answer correctly onscreen – (for example, when you type a fraction “/”, it automatically becomes a vertical fraction).  There is also a popup menu with common expressions such as radicals.

WHAT IF I WANT TO TURN THIS FEATURE OFF?  You can control this in WeBWorK under User Settings/Use live equation rendering.

« Older posts

RSS Differential Equations on Math.Stackexchange

  • Multiplying both sides by $dx$
    I have some questions about a proof I've seen that shows why we're allowed to "multiply both sides by $dx$" in separable ODEs. The proof goes like this: let $y=y(t)$ and $x=x(t)$ for some independent parameter $t$. Then, by the chain rule, we have $$\frac{dy}{dx}=\dfrac{dy/dt}{dx/dt}$$ which means that, in a separable ODE like $$\dfrac{dy}{dx}=y,$$ we […]
  • Solving differential equatiom via complex numbers [closed]
    Solve $(D^3+D)y=\csc x$. Can it be done via $(D^3+D)z=e^{-ix}$? If yes/not,how/why?
  • Finding the general solution to the given differential equation
    I want to find the solution to the following differential equation: $$y'=-\frac{4x+3y-1}{3x+4y+1}$$ I use the substitutions $x=s+1$ and $y=u-1$ to obtain $$\frac{dy}{dx}=\frac{du}{ds}=\frac{-4(s+1)-3(u-1)+1}{3(s+1)+4(u-1)+1}=\frac{-4s-3u}{3s+4u}.$$ If I now further substitute $z=\frac{u}{s}$ this yields $$\frac{du}{ds}=s\frac{dz}{ds}+z=\frac{-4s-3zs}{3s+4zs}$$ $$\frac{dz}{ds}=\frac{1}{s}\frac{-4s-3zs-3zs-4sz^2}{3s+4zs}=\frac{-4-6z-4z^2}{s(3+4z)}$$ This is now a seperable equation so I can integrate both sides $$-\int \frac{3+4z}{4+6z+4z^2}dz = \int \frac{1}{s}ds.$$ By substituting $w=4z^2+6z+4$ I can solve […]
  • Finding the value of $k$ if the differential function is an identity?
    Question $$\frac{\mathrm d^3x}{\mathrm dy^3} + {\left(\frac{\mathrm dy}{\mathrm dx}\right)}^{-4}\frac{\mathrm d^3y}{\mathrm dx^3} - k {\left(\frac{\mathrm dy}{\mathrm dx}\right)}^{-5}{\left(\frac{\mathrm d^2y}{\mathrm dx^2}\right)}^{2}=0$$ is an identity, find the value of $k$. My approach I know identity means this equation should be satisfied for any function. One easy way to do it is assume $y=x$ or any other simple function. But I […]
  • Analyse the behaviour of Van der Pol oscillator using Finite Difference Method with Newton iteration method in MATLAB.
    I'm trying to analyze the behavior of van der Pol oscillator using Finite Difference Method with Newton iteration method in MATLAB. I have try to solve the problem but getting singular Jacobian matrix. Can any one suggest how to proceed to get it's true behavior (oscillation). Here is MATLAB code that I have used for. […]
  • Can we find a neighbourhood around a singular point such that the given expression is undefined in the neighbourhood too?
    I was solving the following differential equation: $$x^2y''+(1+x)y'+3y = 0$$ I tried to express the equation in the form: $$y''+p(x)y'+q(x)y = 0$$ where $p(x) = \frac{1+x}{x^2}$ and $q(x) = \frac{3}{x^2}$. The exclusion of the point $x=0$ for the second equation is understood but my question is that does there exist a $\delta$-neighborhood of $0$, such […]
  • How to solve $\frac{dy}{dx}=\frac{x+y+4}{x-y-6}$? [duplicate]
    I have started learning ODE and I couldn't solve this exercise: $$\frac{dy}{dx}=\frac{x+y+4}{x-y-6}$$ I am a beginner and only learned separation of variables and how to solve homogeneous equations by using $y=ux$ but I don't think this problem can be solved by any of these. I tried to use sub $x-y=u$ but I didn't get anything […]
  • How can I adjust the modified Bessel functions for a scalar co-efficient of y'? [closed]
    I have a 2nd order ODE of the form: $$ t^2y'' + 3ty' -t^2y =0$$ The modified Bessel functions $I_{\nu}$ and $K_{\nu}$ are defined as the solutions to the modified Bessel equation: $$t^2y'' + ty' - (t^2 + \nu^2)y =0$$These equations are clearly very similar. Is there a way to modify the Bessel equations to […]
  • On extensions of solutions to ODEs.
    I'm struggling to understand extensions of solutions for ODEs. Consider the following initial value problem: $$x'(t) = f(t, x), \quad x(t_0) = x_0.$$ Assume that $f$ is continuous and bounded on its domain $\Omega$. Typically, maximal solutions are constructed by defining a function that agrees on intersections, which is possible when we have uniqueness. However, […]
  • How to solve an heat kernel-type equation [closed]
    I was wondering if there is an elegant way to solve the following heat kernel equation, $$\left[2 \omega p-a i p^{2}-a i p \frac{\partial}{\partial p}\right] K(p,k,\omega,s)+i \frac{\partial}{\partial s} K(p,k,\omega,s)=i \delta(s) \delta\left(p-k\right).$$

© 2024 2019 Spring – MAT 2680 – Reitz

Theme by Anders Noren — Up ↑

The OpenLab at City Tech:A place to learn, work, and share

The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.

Support

Help | Contact Us | Privacy Policy | Terms of Use | Credits

Accessibility

Our goal is to make the OpenLab accessible for all users.

Learn more about accessibility on the OpenLab

Copyright

Creative Commons

  • - Attribution
  • - NonCommercial
  • - ShareAlike
Creative Commons

top