Category: Resources (Page 1 of 2)

Getting Started, How-Tos, and so on

Help with Partial Fraction Decomposition

May 15, 2017 / Jonas Reitz / 0 Comments

Hi everyone,

As we launch into our next topic, you will see that one of the (forgotten?) skills you will need is that of re-writing a complicated fraction as a sum of simpler fractions (“partial fraction decomposition”). For those that need some extra help/reminder of this process, here are a couple of videos:

Partial Fraction Decomposition – a basic example. This is a good basic example.

https://www.youtube.com/watch?v=HZTv4zCgEnA

Partial Fraction Decomposition – another example. This is a slightly longer example, and it includes a good explanation of how to set up your partial fractions for different kinds of factors in the denominator.

https://www.youtube.com/watch?v=pZ9FfGy3Cfw

Final Exam Review Sheet is posted

May 13, 2017 / Jonas Reitz / 0 Comments

The review sheet for the final exam is posted under Classroom Resources / Exam Reviews.

Regards,
Prof. Reitz

Exam #3 Review Sheet is posted

April 30, 2017 / Jonas Reitz / 0 Comments

Hi everyone,

The exam #3 review sheet is posted under “Classroom Resources/Exam Reviews”. Let me know if you have any questions or corrections.

Regards,
Prof. Reitz

Exam 2 Review is posted

March 26, 2017 / Jonas Reitz / 0 Comments

Hi everyone,

The review sheet for Exam #2 (which will take place on Thursday, April 6th) is posted on the Exam Reviews page. Let me know if you have any questions.

Best regards,
Prof. Reitz

Exam 1 SPECIAL OFFER Scoring Guide

March 25, 2017 / Jonas Reitz / 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: ______

Resources on repeated roots and complex roots (second order linear homogeneous differential equations with constant coefficients)

March 23, 2017 / Jonas Reitz / 0 Comments

Hi everyone,

My apologies for missing class today (my daughter is sick). I missed you! Your substitute Prof. Singh gave me an update – it sounds like he was able to cover repeated roots and complex roots, and you will get a chance to work on them in your WeBWorK assignments (due Tuesday). I encourage you to post questions here, and I’ll do my best to respond.

In the meantime, if you are looking for additional help, I wanted to leave you with a few resources on these two topics (repeated roots / complex roots).

Paul’s Notes

These are very complete notes – they include an explanation of each rule, and several examples worked out. Here are links for his notes on repeated roots, and complex roots.

Videos

If you learn better by watching, you can check out these videos from PatrickJMT: an overview, with two examples (one with two real roots, one with repeated roots), and an example with complex roots.

Best of luck,
Prof. Reitz

Exam 1 Grades are posted, and SPECIAL OFFER

March 5, 2017 / Jonas Reitz / 0 Comments

Hi everyone,

The grades for Exam 1 are posted on the Grades page (email me if you have forgotten the password).

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 3/21.

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:

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:
Do the problem over, neatly and completely, start to finish, on a separate sheet of paper.
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)
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).
Hand in your original exam and your corrected problem(s) and explanation(s), stapled together, in class on Tuesday, 3/21.
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.

Exam 1 Review is posted

February 19, 2017 / Jonas Reitz / 0 Comments

Hi everyone,

Exam #1 will take place on Tuesday, February 28th, during class. The review sheet for Exam #1 (along with the answer key) has been posted under Classroom Resources/Exam Reviews. Let me know if you have any questions.

Regards,
Prof. Reitz

Spring 2017 Tutoring available

February 13, 2017 / Jonas Reitz / 0 Comments

Here is a flyer for math-specific tutoring this Spring, funded by a Perkins Grant. The tutors are City Tech students who excel in mathematics, and I have heard great things about them. Although the flyer says it covers only through MAT 1575, in fact they will help with more advanced courses as well – including Differential Equations (priority is given to classes through 1575, however).

HOMEWORK HINTS: Interval of validity

February 9, 2017 / Jonas Reitz / 0 Comments

Hi everyone,

I wanted to post a quick followup to our work from Tuesday, regarding intervals of validity – this may be of use as you work on WeBWorK #3.

Let’s look at an example – this is my version of Problem 6:

Separate the following differential equation and integrate to find the general solution:
$y'=(5-2x)y^2$

Then give the particular solution that satisfies the initial condition $y(0)=\frac{1}{-6}$ and state the interval on $x$ for which this solution is valid.

Let’s look at the particular solution satisfying the initial condition – it is: $y=\frac{1}{x^2-5x-6}$ .

What is the interval of validity? It is the largest interval of the x-axis which a) contains the initial condition, and b) on which the solution is defined and continuous.

By setting the denominator equal to zero, we find that the solution is undefined at $x=6$ and $x=-1$ . These two values break the entire x-axis up into three intervals on which the solution is defined (and continuous): $(-\infty,-1) \cup (-1,6) \cup (6,\infty)$ . We now simply have to choose the correct interval – here, we use the fact that the initial condition $y(0)=\frac{1}{-6}$ refers to the point $(0,\frac{1}{-6})$ , so we must choose the interval containing $x=0$ .