# OpenLab #4: Advice for the future

(Due Thursday, 5/22/14, at the start of class). Â Imagine that you are invited to speak on the first day of MAT 2680, to give advice to entering students. Â Write at least three sentences responding toÂ one or twoÂ of the following, describing what you would tell them.

1. What do you wish that you had beenÂ 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 importantÂ prior knowledgeÂ (not taught in the class) that you need in order to succeed? Â Why is it important?

Extra Credit.Â  Respond to someone elseâs comment. Â Do you agree? disagree? Have anything to add?

### 63 responses to “OpenLab #4: Advice for the future”

1. Advice to students that are entering MAT2680 : Differential Equations.

From my knowledge and perspective, having completed the course, Differential Equations is a practical view on calculus (differentiation and integration). It applies derivatives and integrals to real world situations and problems, especially physics.

If you are a student who enjoyed calculus and have a deep interest in mathematics, then Differential Equations is certainly one of the best classes you will study. Taylor Polynomials, Hooke’s Law(from calc. based physics), Method of Partial Fractions, and basically most topics from integration have been applied in solving for y – this is the purpose of differential equations. From my experience, my professor explained that the equation is describing some real world phenomena or even a real world problem which involves derivatives and higher derivatives with respect to time. So be sure to brush up on calculus 1 and most importantly calculus 2. Brush up on the different integration techniques. It is wise to keep calculus notes with you, to study from, and to have it as reference while in class and for studying purposes.

For students who does not have an interest in math, and did badly on calculus (1 & 2) & have to take this class because your degree depends on it, then it would be wise to brush up on your integration and differentiation techniques. Get extra help, extra tutoring or find someone who is willing to help (GO TO PROFESSOR’S OFFICE HOURS!!!!) This class requires time and effort, math is not something you have to only read to understand but actually practice a lot a lot a lot of examples. This is what I do, practice doesn’t make perfect, but practice gets you perfect scores and good grades, dedicate time.

GOOD LUCK ! đ

-Rachel Rackal

• I agree, especially keeping calculus notes are very important since you will be expected to know the general derivatives and integrals of certain trig functions and logarithms.

• I completely agree with you, this class is great. it helps you apply math in the real world. Practice is very important if you want to obtain good grades.

• I agree 100%. the first few days of class i was completely lost because i had forgotten most of my Calc 1 material. Brushing up on how to find derivatives and integration are key to understanding how to work most of these problems. You have to relearn u-substitution and integration by parts to solve some of the DE problems given to you

2. Thanks for leaving the first response, Rachel (you were quick!). Good advice all around.
– Prof. Reitz

3. If it was the first day of the differential equations class. The advise I would give to the students would be to really brush up on your integration techniques and to try and grasp the concept of differential equations instead of just knowing how to solve the question.
Dont be afraid to ask questions im sure more than pne of you will have the same issues.

Webwork is extremely helpful and should not be left until the last second because you dont want to be up at the crack of dawn struggling over why your answers to eulers equation is completely off.

And lastly dont stress yourself out when test time comes around just keep calm or your paranoia will make you forget everything.

• Michael Rivera

I agree with the homeworks as it has helped me extremely since pre calculus. I would also add if you are afraid of asking questions during class time try to meet with the professor during office hours. It helps greatly.

4. In terms of prior knowledge, I would say review the Calculus 2 material! Differential Equations heavily involves derivatives, integrals, and more recently Taylor Series, so by keeping Calculus 2 ready and fresh on the first day of class, it is more likely that Differential Equations will be much easier. If you want to make it even easier, don’t take a break from math for one semester like I did (biggest mistake).
In addition to that, constantly ask questions. If you don’t, there’s a good chance that the answer to that question could’ve helped you solve a problem on Webwork or on an exam. There’s an even higher chance that another student has the same question but doesn’t want to raise their hand up, so in a way you’re doing them a favor too. Finally, don’t save anything till last minute, no matter what class you take, this never works!

• Yevgeniy Babkin

I agree with the “constantly ask questions” part, especially when taking differentials with professor Reitz, take advantage of the 6-7 seconds of silence after the “any questions???” is asked; think about anything you might have had difficulties with and within the 6-7 seconds you’re most probably will come up with a nice question about it.

5. Yevgeniy Babkin

Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic;

One topic that I believe is important to take into consideration is “book keeping.” Differential equations tend to be fairly lengthy problems and in order for the class notes to make sense I suggest using all the tricks in the book, here are two I had come up with; #1 [Use a multicolored pen/pencil to take notes, which helps immensely when trying to review the notes and differentiate between the intricate steps taken to solve a problem] #2 [Using a smart phone or recorder to record the audio of the lecture while making time stamps on the side of the notes for easy reference later.]

6. I would strongly suggest that students make sure calculus 2 is fresh on their minds. Differential equations touches on a few topics from calculus an calculus 2. Derivatives and antiderivatives are going to become your best friend. Make sure you know how to do integration by parts, this is one topic from calculus 2 that comes up repeatedly.

• Mohammed Ahmed

I am agree with him, everybody should know calculus very well in order to understand Differential Equation. I would love to add one thing that not only differential equation but also try to remember all the math methods you learn and use them when you need it.

• i totally agreed with you Mohammed Ahmed. I will recommend to students to refresh their minds on topics such as integration, derivatives, anti derivatives to avoid unpleasant struggle with the course

• Account Deleted

I agree, because even though I knew my derivatives or anti-derivatives. it gave me trouble. Which made me have little error that i should have notice. It wasn’t bad once you practice or got a hand of it.

• Justin Naing

I agree with making sure that calculus 2 is fresh in your mind because i took it over 2 semesters ago and what i really struggled with this semester is trying to relearn those methods that i needed to reuse from cal 2.

• I am agree with him, everybody should know calculus very well in order to understand Differential Equation and all integration methods for sure.

7. At the beginning I would have liked to have been told that the first lectures would be the hardest and that I should pay attention a lot more.

A challenging topic would be the identification of types of differential equations and how to choose the methods for solving them. My advice would be to well (Pay attention to the methods ) they must be determined to use more than just 1 or 2 hours a week for studying this topic.

Important prior information would be integration techniques from calc II and even some basic math skills like being able to tell if you should put a negative sign or positive sign–Pay attention to the signage of your work XD I have personally messed up on that several times….

8. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.

-Nonhomogenous solution second order differential equations is especially challenging. It will look confusing and difficult but if you group everything up with a common factor, it’ll look neat and orderly and you’ll get an idea of what to do.

What is the most important prior knowledge (not taught in the class) that you need in order to succeed? Why is it important?

-Remember almost everything in calculus 2. From integration, partial fractions, and Taylor series. You will have an easier time understanding and doing the problems in Differentials Equation. Remember how to do derivatives from calculus one also.

9. Mohammed Ahmed

One thing is very important for this class is concentration and revise the previous staff that you have learned from other math class. Taking differential equation class with Prof.Reitz is really amazing, the way he explains the topic is really understandable and always helps to remind previous staff. I would tell everyone to review calculus notes while taking differential equation which helps to solve problems. Paying attention to class is the most important thing which we never learn from class, we have to learn it from ourselves. And paying attention to subject makes all the hard method easy.

• I agree that paying attention in class will greatly ease your journey thorough the course. Revision of prior knowledge will assist as well. The professor does also do a good job explaining most topics.

• Account Deleted

I agree, that you need to pay a lot of attention in the class. As well have the previous knowledge of previous math courses. Professor Reitz is really amazing at explaining the topics so you can understand and always helpful.

10. I would say doing all of the homework question and redo all cal 2 homework so everything would in your mind ready to use.

• I agree know cal 2 is very important also you need to have good algebra skills.

11. Account Deleted

One topic that gave me the most problem this semester was the first linear order. It requires you to have the basic knowledge of calculus 2. If calculus 2 wasn’t your strong area then finding the derivative or even integration by parts. It would make it harder for you to understand a problem let alone solve it on your own. I would say review your notes for the first few topics so one can have a better understanding of the class. Doing the webwork homework also gives youâre a better understanding because youâre doing the problem over and over.

• Sabeeya’s comment has been the most useful so far because it cover what we have done so far throughout the semester, first linear order equation. Therefore, I can relate to this comment. To the other comments not so much because they are too advance, the speak about things I have never seen like ( partial fraction, euler’s and yada yada yada), but I get it I have to get ready for those topics because I’ve seen everybody is getting stomp.

Based on this advice I want to go back to calculus II and learn integration by parts again since my notes are not useful. Right now i’m struggling so hard on webwork doing separable and first linear order equation. 17 tries and counting all I can say is GG.

PD omw to Prof. Reitz’s office hours.

• Hi Gabriel,
Thanks for your reply! But it looks like you left it on the OpenLab site for the 2014 class. Could you copy/paste it to the current site (so I make sure to include it in my grading)?
Thanks,
Prof. Reitz

12. One thing i wish i have been told at the beginning of the class is yo review calculus 2 notes because this course uses alot of those concepts and techniques
The most difficult top in this course is finding approximation of a point using the numerical methods.
To succeed in this course a person has to practice, practic, and practic and do all the problems required.
Also if you taking this course with prof Reitz then your in the right place because Are actually going to learn the material

13. At the onset of the Differential Equations class, I believe it is important to know that the first part of the class [ Solving First Order D.E’s] is the trickiest part of the class, at least for me, once you get past this, the remainder of the class is relatively easy. Try not to miss any days, and always do the homework problems.
One thing that would be essential to review before hand would be your algebra skills, the integration isn’t necessarily the hardest part of solving the problem, but it is the messiness of the algebra that can be confusing. If you review your algebra, you make the class easier for yourself. Of course don’t forget to review derivatives and integration as well.

• I think the hardest topic in general was when Euler’s Method Approximation first appeared.

14. 1)What You Need to Do:
Focus, commit to this class, it’s not easy but will be if you give it time, don’t be afraid to ask questions and don’t be upset when you’ve done the problem six times and still don’t understand why it’s wrong (you probably forgot to distribute, or its a minor error). If you follow the work and pay attention in class you should have no problem in this class, yes you do need to brush up on Calc 2 (Taylors/Partial Fractions) but don’t think your at less of an advantage if you did not do well in Calc 2.

2) What Could Be Challenging:
Euler’s/Backwards Euler Method, personally I had problems with Euler’s as it’s method is well a bit ambiguous. You won’t like practicing it, but if you do, you will master it. I personally spent about 4 hours collectively studying solely Euler’s/ Backward’s Euler Method, if you have any questions don’t hesitate to ask Pr. Reitz he is extraordinarily good the little mistakes that make all the difference.

3) What You Need to Know:
Partial Fractions, you will need to know how to do partial fractions well, it will sneak up on you at the end of the semester. Integration IS A MUST for basically half the class. Lastly, be good at keeping your work organized on paper, (trust me, your work will get messy and there will be a lot of it), be wary of your sign/coefficient distributions.

• ” …Pr. Reitz he is extraordinarily *good at finding* the little mistakes that make all the difference.”

• I have to agree with you Alexis. Euler’s method was painstaking, especially before we had those nice formulas. And the only way to understand it is through practice. I also have to agree that Pr. Reitz is amazing when it comes to teaching and explaining the material.

15. One important thing to remember is to study!! If math is something that comes easy to you, then that’s great, but don’t forget to study still. Always refresh yourself by reviewing your previous courses. In Differentials you’ll need to know calculus and a lot of calculus 2. Don’t forget to ask for help and to do all of your assignments. Assignments give you the opportunity to work on more examples on your own, and it gives you the chance to test what you learned in class.

• I strongly agree with you Karen. Students must do all homework and if possible extra homework will be a plus. Previous knowledge of calculus is very important.

16. I would advise students to focus a lot on the first topics taught in Differential Equations, especially in integrating factor. Students must know how to take derivative and integrals for this class. There are many problems in this class where integration and derivatives of trigonometry functions need to be performed, so I advise all students to know trigonometry integrals and derivatives before taking differential equations. Finally, itâs very important to do all the homework on time since falling behind with homework will affect your capability to learn the following topics.

17. 1. What do you wish that you had been told at the start of this class, to help you succeed?
from my experiences, i think the course works were well organized with the webwork homework. The professor style of teaching was very great from the beginning to the end of the semester. From my perspectives , everything that needed to known to succeed was properly instructed.
the only issue was the room were the course was lectured., the room need to be changed because most students couldn’t properly read on the board.

2. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.
i think the first part of the course that focus on solving partial, homogeneous , integrating by factor, exact equation,was challenging. i would advice students not to slack on homework to properly understand that part of the course.

3. What is the most important prior knowledge (not taught in the class) that you need in order to succeed?
to succeed in this class or any other class, you need to come on time, and try not to miss a course to be able to get the full experience of the course and to miss homework. As a student you should be always on you good behavior to pass a course and if you having trouble doing well , seek help , because there is always people willing to help you to succeed

18. Account Deleted

Would of been helpful to have taken Differential Equations right after Calculus II, as with any math course they tend to follow. Meaning that you will most likely need to have knowledge of previous course. It is not to say you just need just knowledge on Calculus II, previous math classes play a part as well.

Topics I found challenging are Euler Methods and Taylor Series just because they are long, and you have to keep track of everything. Best to practice it, till you get used to it. Slight mistakes can throw everything off, similar to how Calculus is you have to be good at book keeping. Take good notes and understand your notes, helps to take side notes as well.

Partial fractions as they sneak up towards the end, as well Taylor Series as it’s covered in Calculus II towards the end of the semester and usually is just breezed over. MUST KNOW INTEGRALS AND DERIVATIVES, as it’s a major factor of the course. Review Calculus material; Professor Reitz does take the time to explain previous course material but the class time is short so he can’t spend as much time on it. Professor Reitz is great on helping, and he gives you the 5 seconds to think if you have additional questions.

19. Yusuf

I would say differential equation may not be hard subject if you pay attention in class and finish all of your assigned home works (important). Come into class without practicing is useless. So, Pay attention + Practice will make learning much easier.
âNon-homogeneousâ problems are challenging because you have to find the coefficient by doing many steps. So, you have to track what part of the problem you are working.
You need ââPartial Decompositionââ knowledge, Although this topic has been taught in Cal-2 but thatâs not enough for understanding. So I recommend to watch YouTube video (Patric) before you come to the class.
Lastly, if you donât lose confidence, then you may succeed.

20. William Zagare

I would tell people that this class really isn’t very difficult; but that the topics covered are incredibly important, and their are quite a few of them. I would also recommend brushing up on their calc2 materials (especially the partial fractions stuff, which I still struggle with). and to occasionally work on hold homework and class problems. It’s very easy to learn a topic, move on and forget it after the test. Don’t do that! You’ll save yourself a lot of time and trouble in the long run.

• Vitaliy Panov

I agree with everything you said, especially how important it is to remember everything taught throughout the semester and not to forget the information after each exam since it will all be on the final again.

• Aslan Gousseinov

One hundred percent! I agree, it’s incredibly easy to finish the final exam for a class and then completely forget all the material learned. It’s best to hold on to old notes and homeworks so you can refresh your mind in preparation for 2680!

21. Yamba Subba

One topic which gave me trouble is all the Euler’s method. If I have to say something about all the Euler’s method is one have to give really importance in Euler’s method which is easy compared to other but this is the base for all the Euler’s method like Backward, Improved, Runge-kutta which is coming in your way. If you cannot get grasp of Basic Euler’s method, you will probably struggle in other method which contains a large chunk of differential equations class.

22. Vitaliy Panov

I wish I had been told to pay extra close attention in the beginning of the semester. It was definitely the hardest part of the class and took me by surprise. If I had to give advice to students taking this class it would be to do every single homework on time and to try your best to understand the problems. I feel like without doing homework it’s next to impossible to pass this class. You can’t understand math without doing practice outside of class, so I would have to say doing homework is an absolute must.
The most important prior knowledge that one might need in order to succeed in this class would have to definitely be Calc I and II, because without knowing how to take derivatives and how to integrate you simply won’t be able to do these problems. All in all I’d say this class is tough but is very doable if you put some time and effort into it; and having a great instructor like professor Reitz, definitely helps a lot!

• I have been paying close attention since the beginning, it is still pretty difficult to stay on track. Even though some of the homeworks took my by surprise, I ended up doing it with a group of friends learning as we solve the problems. Most of the homework problems we had to learn as we go, it was pretty time consuming and frustrating. But the moment we understood it and correctly solved it for it, it felt like an accomplishment.

• Hi William,
Thanks for the comment – but it looks like you left it in my previous class’ OpenLab site (from Spring 2014) by mistake. If you could post it in the current semester’s OpenLab site that would be great.
Regards,
Prof. Reitz

23. Justin Naing

I wish I had been told remember everything in calculus 2 because a lot of it came back in differential equations
One of the topic i found challenging was intergrating factors and to master you just have to remember the formula for get mu by heart.
I think the most important prior knowledge was knowing taylor series because it branched out to a lot of important topics such as euler’s method and laplace transform

• I agree with you on that.i thought I be done with Taylor series after cal 2 but came back again in differential equation.Was able to be better at doing Taylor series problems b/c of cal 2.

24. I think the most important prior knowledge that’s need for this course is calculus 1 and 2. I say calc 1 and 2 because almost all of the methods we studied involved integrating of taking derivatives. A good understanding of basic algebra and trigonometry is also essential because most of the problems are arguably 30% differential equations related and 70% algebra related.

• I totally agree with you. This course entails a lot of integration. Without knowledge of derivatives and integration it will definitely be a challenge to succeed.

25. Michael Rivera

1. What do you wish that you had beenÂ told at the start of this class, to help you succeed?
I wish that before leaving Cal 2 I was told to go over everything learned in class before entering differential equations

4. What is the most importantÂ prior knowledgeÂ (not taught in the class) that you need in order to succeed? Â Why is it important?

One of the biggest prior knowledge you must master is calculus 1 and calculus 2. Many different techniques taught here in Differentials involve almost everything you learn in Cal 1 & 2. From the very basic derivatives all the way to Taylor series.

26. 1)I wish I reviewed by calculus 1-2 topics that I learned before at the beginning of the semester .
2)Had problems with exact and separable problems But doing more practice problems and tutoring helped big time.
3)Need to be good at integration and differentiation or will struggle in the class.Actually found differential equation easier than cal 1-2.

• anass baroudi

I agree sometimes I would procrastinate and have too much to study.

27. The most important prior knowledge (not taught in the class) that you need in order to succeed are partial fraction decomposition, different methods of integration and algebra. You need to know these topics in order to apply it to topics taught in Differential Equations. Make sure to review previous notes from Calculus 2. Knowledge of these topics make it easier to understand what is taught. Although Prof. Reitz gives a brief review of the topics, it will be more beneficial to be verse in these topics prior to this course.

28. Aslan Gousseinov

What is the most important prior knowledge (not taught in the class) that you need in order to succeed? Why is it important?

Cant stress it enough, review your cal1&2 basics. Derivatives and Integrals! Simple as that, most of the material you learn in 2680, you will need to have a good understanding of prior knowledge from other mathematics classes. Studying Taylor Series wouldn’t hurt either, a really important chunk in 2680 is Taylor Series so reviewing that wouldn’t negatively affect you.

• 100% agree, better to go over old stuff 15-30 minutes a day it will have a lasting affect of how the course can go, and it will definitely be for the better.

29. Most important thing that I founded I needed to do was make sure I made time to study the class work after class. Also make sure you do the Webworks problems, as you sometime tend to not do the HW and only focus on webwork problems, so not doing them will hurt you in long run.

The most helpful thing I found was watching videos to supplement the class lectures, with another voice explain the same topics. Finding someone you like on youtube will make learning a lot easier for learning concepts not solving actual problems.

30. anass baroudi

What I found helpful was doing a ton of problems. It made me more able to solve the problems. Also you should take notes and never commit anything to memory.

31. From all the responses the advice that is most relevant to me personally is that itâs very important to review or become familiar with material from calculus 1 and calculus 2. For example, integrals, derivatives, anti-derivatives, and trig identities. I also agree with Gin Pena from your previous differential equations class when he states âIf you want to make it even easier, donât take a break from math for one semester like I did (biggest mistake)â. The reason why I agree is because since I took calculus 1 and calculus 2 two semesters ago I do not fully remember the material very well. This makes it very difficult to solve problem that require prior knowledge.

Based on this advice the changes I can make right now to help me with this course is to review/brush up on calculus 1 and calculus 2. In addition, I can do practice problems to make sure Iâm refreshed and fully understand. Lastly, if I have any difficulties I can just ask questions in class, email the professor, go to his office hours, or even ask a classmate for help.

• Whoops – thanks for your comment, Carolina, but it looks like you left it on the OpenLab site for last year’s class. Could you copy/paste it to the current site (so I make sure to include it in my grading)?
Thanks,
Prof. Reitz

32. Based on reading these comments from people that took the course i picked up a few things. One that really stayed on my mind was study up and review calculus and some topics like derivatives and integrals. One of the Previous students stated don’t be afraid to ask questions. I am a person who always asks questions and tries to understand the material to the best of my ability. Another advice i will take from the students that took this course is that i will spend more time on studying and reviewing the topics and materials discussed in class. I will study and keep studying calculus even though i took calculus 2 last semester.

• Hi John,
Thanks for the comment â but it looks like you left it in my previous classâ OpenLab site (from Spring 2014) by mistake. If you could post it in the current semesterâs OpenLab site that would be great.
Regards,
Prof. Reitz