2019 Spring - MAT 2680 - Reitz

"...how it differs from the rocks"

Category: Resources (Page 1 of 2)

Getting Started, How-Tos, and so on

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

How to enter ‘ (prime) in WeBWorK on your iPhone

April 11, 2019 / / 0 Comments

By default, the iPhone automatically converts straight quotes like this:  ‘
into smart quotes, like this ` .  You need to turn this functionality off in order to enter the prime (straight quote) symbol in WeBWorK.  The short version is:

To turn smart punctuation off, all you have to do is go to Settings > General > Keyboard, and then turn off the “Smart Punctuation” toggle.

More detailed instructions can be found here:

https://www.howtogeek.com/344310/how-to-turn-off-smart-punctuation-on-your-iphone-and-ipad/

 

WeBWorK 9: Tips for guessing solutions to nonhomogeneous equations

April 1, 2019 / / 0 Comments

Hi everyone,

As you work through WeBWorK #9, you may run into a few instances where it is not obvious what guess to make for the particular solution to the nonhomogeneous equation.  Here are two tips that might help:

 

What if the right side has both an exponential and a trig function?

If the right side of your differential equation has form similar to:  e^{ax} \cos(bx)

then your guess should have the form:  Ae^{ax} \sin(bx) + Be^{ax} \cos(bx)

 

What if the right side is a solution to the complementary equation (where the complementary equation has a repeated root)?

If your initial guess:  Ae^{ax} is a solution to the complementary equation, we adjust it by multiplying by x: Axe^{ax}.

If Axe^{ax} is *also* a solution to the complementary equation (due to a repeated root), adjust it by multiplying by x again:  Ax^2e^{ax}.

 

Let me know if you run into other weird things.  Questions are natural, and welcome!

Prof. Reitz

Exam 1 SPECIAL OFFER Scoring Guide

March 16, 2019 / / 0 Comments

For your reference, here is the scoring guide I will be using for the EXAM 1 Special Offer

-Prof. Reitz

 

Name: ____________________

 

____ Includes Name, Date, Problem #s, original scores (up to 6 points deduction)

____ Presentation is neat, well-organized, readable (up to 4 points deduction)

____ Includes Original Exam

____ Max bonus (30 points for <50%, 20 points 50%-59%, 15 points 60%-69%, 10 points 70%-79%, 5 points 80%-89%)

 

First problem #:  ____

____ Original Score (out of 25)

____ Revised Score

____ (up to 5 points deduction if incomplete) Written explanation,  2 sentences,  what you did wrong OR how to solve the problem.

____ Bonus points earned for problem 1

 

Second problem #: ____

____ Original Score (out of 25)

____ Revised Score

____ (up to 5 points deduction if incomplete) Written explanation,  2 sentences,  what you did wrong OR how to solve the problem.

____ Bonus points earned for problem 2

 

EXAM 1 SPECIAL OFFER BONUS POINTS:   _______

(Bonus points for problems 1 and 2, with maximum bonus based on original exam score, minus any deductions, ).

EXAM 1 REVISED SCORE: ______

Exam 1 Grades are posted, and SPECIAL OFFER

March 4, 2019 / / 0 Comments

Hi everyone,

The grades for Exam 1 are posted (under Dashboard/OpenLab GradeBook).

With some exceptions, you will notice that the scores are not as high as you might have liked!  This exam covered a lot of material, and relied on a great deal of prior knowledge and skills (especially Calculus and Algebra).  With that in mind, I am giving you the option to improve your score through the ONE-TIME SPECIAL OFFER below (note: this offer will almost certainly *not* be repeated on future exams), due in two weeks on Tuesday 3/19.

Let me know if you have any questions,
Prof. Reitz

Exam 1 Special Offer – earn bonus points.  You can improve your grade on the exam, by doing the following:

  1. Choose ONE OR TWO problems in which you did NOT earn full points.  You are working to earn back (some of ) the points you missed on this problem.  For each problem you chose:
  2. Do the problem over, neatly and completely, start to finish, on a separate sheet of paper.
  3. Include the following information on the sheet:
    1. Your name
    2. The date
    3. The problem number
    4. Your original score on the problem (out of 25)
  4. On the same sheet, write a short paragraph (at least two complete sentences) explaining why you lost points.
    1. If you lost points due to a mistake or mistakes, explain what you did wrong (this is to let me know that you understand your error).
    2. If you lost points due to not completing the problem, then explain how to solve it (this is to let me know that you have learned how to solve it).
  5. Hand in your original exam and your corrected problem(s) and explanation(s), stapled together, in class on Tuesday, 3/19.
  6. Bonus points will be added to your Exam score based on the number of points you missed on the chosen problem(s),  the accuracy of your corrections and explanation, and your overall grade on the exam.  Bonus points are limited as follows:
    1. If you received less than 50% on the exam, you can earn a maximum of 30 bonus points.
    2. If you received between 50% – 59% on the exam, you can earn a maximum of 20 bonus points.
    3. If you received between 60% – 69% on the exam, you can earn a maximum of 15 bonus points.
    4. If you received between 70% – 79% on the exam, you can earn a maximum of 10 bonus points.
    5. If you received between 80% – 89% on the exam, you can earn a maximum of 5 bonus points.
    6. If you received 90% or more on the exam, you may not earn any bonus points.

 

Calculus Review – some helpful hints

January 29, 2019 / / 0 Comments

Having trouble with the WeBWorK?  First, don’t panic – it’s a lot to remember!!  But do be prepared to put in some time re-learning stuff from Calculus I and II.  I’ve picked out a few video resources for you that hit some of the most important techniques  (I tried to find videos that were focussed on examples, rather than theory, since this is meant to be review).

Comments are welcome (just click the “leave a comment” button above).

  • Like a video? Leave comment and let me know.
  • Dislike a video (it wasn’t helpful/ it was confusing)? Let me know.
  • Need help with another topic (like the product rule, or equations of tangent lines, or something else)?  Let me know.
  • Have a video or other resource to suggest? Let me know!

Derivatives: The Chain Rule (similar to Problem 4):  This video is short and sweet, a single example using the chain rule with a logarithmic function.

 

Integrals: U-Substitution (similar to Problems 5 & 6):

This video has three examples – the first two are most similar to what you will see in WeBWorK (the last one is a little trickier – but could be useful in the future):

 

Integration by Parts (similar to Problems 7 & 8)

This video also has a few examples – the first two will be most useful for the WeBWorK:

Getting Started with WeBWorK

January 29, 2019 / / 0 Comments

WeBWorK is accessible from on and off campus, anywhere you have access to the internet.  Your first two WeBWorK assignments are due next Tuesday, February 5th, at midnight.

To get started, you must complete the following three steps.

Step 1.  Log in to WeBWorK here:  http://mathww.citytech.cuny.edu/webwork2/MAT2680-S19-Reitz/.  I have created Usernames and Passwords for each student registered for my class.

Username.  Your username for WeBWorK consists of your first initial plus your last name, all lowercase (for example, John Smith would have username ‘jsmith’).

Password.  Your password is your Student ID (EmplID in CUNYFirst)

Step 2.  Update your email address if you wish.  To do this, select “Password/Email” from the main menu on the left.  Use whatever email address you like (I suggest using one that you check often).

Step 3.  Complete the first two assignments, by clicking on them on the main screen.

If you have any trouble – either with logging in, or with completing the assignment, post a comment here or send me an email and I will get back to you.

WeBWorK Tips:

  1. Click on a problem to see the details (the list of problems appears in the menu on the left).  Enter an answer and hit “Submit Answers”.  Don’t worry, if you get it wrong you can try it again.
  2. You can work on the problems in any order you wish.  You can do some problems now, and come back and do the rest another day (your work will be saved, as long as you submit your answers).
  3. If you want to print out a copy of the assignment, click on the assignment name in the main menu on the left, and then click the link in the main screen area that reads “Download a hardcopy of this homework set.”
« Older posts

RSS Differential Equations on Math.Stackexchange

  • How do I determine the stability of an equilibrium solution to a differential equation?
    According to the notes issued out by my class, "an equilibrium solution $N (t) ≡ c$ to a differential equation (DE) is stable if $N(t)$ stays close to $c$ whenever $N(t)$ is a solution to the same DE such that $N(0)$ is sufficiently close to $c$." What does this mean? I'm unsure as to how […]
  • Do we have to set boundary at $0$?
    Hi all I have a fundamental question about heat equation, so far all the heat equation set up I have experienced asasume boundary at a boundary at $x=0$, (assuming it's one-dimensional). I'm wondering what may happen if I say boundary is $x=1$ for example (the domain is $x>1, t>0$). Will that change the solution? I […]
  • How to convert a set of first order DEs to a single higher order DE
    I'm wondering how to convert a set of first order DEs into just a single DE. I've been looking at this for a while and I can't figure it out. I understand the opposite direction, a single DE into a system of first order but I just can't figure this out. Specifically I'm looking at […]
  • Determining values of a parameter for which an initial value problem has a polynomial solution
    Given the following IVP: \begin{cases} \ddot{y}-3t\dot{y}-ky=0\\ y(0)=1; \; \dot{y}(0)=0 \end{cases} I want to determine the possible values of $k$ in order to obtain a polynomial solution; if $p(t)=a_0+a_1t+ \dots + t^n$ would be a solution; then $a_0=1; a_1=0$; so I'd get $p(t)=1+ a_2t^2+ \dots + t^n$ and I also have that: $$(-3n-k)t^n=0 \iff k=-3n$$ But […]
  • I am struggling to connect the general transfer function formula for a second-order system with this specific question. [closed]
    Struggling with this transfer function question
  • Polynomial solution of second-order differential equation
    $\ddot{y}-2t\dot{y}+3y=0 \quad(\ast)$ I want to investigate if there is any polynomial solution for the given differential equation Considering $y(t)=\sum_{n=0}^{\infty} a_nt^n$ and substituting above in $(\ast)$: \begin{align*} \sum_{n=2}^{\infty} n(n-1)a_nt^{n-2}-2\sum_{n=1}^{\infty}na_nt^{n}+3\sum_{n=0}^{\infty}a_nt^n=0 \\[10pt] \implies \sum_{n=0}^{\infty} (n+2)(n+1)a_{n+2}t^{n}-2\sum_{n=1}^{\infty}na_nt^{n}+3\sum_{n=0}^{\infty}a_nt^n=0 \\[10pt] \implies 2a_2+3a_0+ \sum_{n=1}^{\infty} \bigr[ (n+2)(n+1)a_{n+2}-2na_n+3a_n\bigr]t^{n}=0 \end{align*} If I assume that $a_0=0$, then $a_{2n}=0; n \in \mathbb{N}$, because $a_{n+2}=\frac{(2n-3)a_n}{(n+2)(n+1)}$. And if I let […]
  • How to solve this difficult differential equation with Runge-Kutta methods?
    Given the following differential equation (it can be seen as a matrix differential equation): $$\begin{cases} x'=\dfrac{dx}{d\phi}=\dfrac{ \cos(\phi) }{ 2+\beta z-(1/x) \sin(\phi) } \\ z'=\dfrac{dz}{d\phi}=\dfrac{ \sin(\phi) }{ 2+\beta z-(1/x) \sin(\phi) } \\ x(\phi=0)=0; \\ z(\phi=0)=0 \end{cases} $$ How can I solve this using a Runge-Kutta method? $\phi$ exists in $[0,\pi/2]$. Thank you for the attention! I've […]
  • Hypoteses about the stable manifold Theorem
    In Perko's book, he proves the stable manifold theorem when the equilibrium point of the dynamical system is the origem. Can I use the same theorem for an equilibrium point that isn't the origem? Why?
  • How to normalize the general solution of a Sturm Liouville problem?
    Say for instance we have a solution to a differential equation which is a Sturm-Liouville problem $$y(x)=\sum_{n\geq 1}a_n\Phi_n(x)+\sum_{n\geq 1}b_n\varphi_n(x)$$ with $\{\Phi_n\}_{n\geq 1}$ and $\{\varphi_n\}_{n\geq 1}$ being orthogonal autofunctions bases and they're orthogonal to each other too. In order to normalize $y(x)$ what should I do?: Should I do $$\begin{aligned}\hat y(x)=\dfrac{y(x)}{||y||}=\dfrac{y(x)}{\sqrt{\!\langle\, y\,|y\,\rangle}\, }&=\dfrac{y(x)}{\sqrt{\displaystyle\sum_{n,m\geq 1}a_na_m\langle\Phi_m(x)|\Phi_n(x)\rangle+\sum_{n,m\geq 1}b_nb_m\langle\varphi_n(x)|\varphi_m(x)\rangle} }\\ […]
  • Am I seeing only half of the whole picture in linear differential systems?
    When one studies systems of linear differential equations with constant coefficients, for example systems of the form $$\begin{cases} \dot x = ax + by \\ \dot y = cx + dy \end{cases} $$ or, equivalently, $$ \dot v = Av $$ where $A$ is some square matrix, one immediately is confronted with a classification of […]

© 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