**(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.

- What do you wish that you had been told at the start of this class, to help you succeed?
- Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.
- 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?

1. The advice I would give to future students is that I wish I knew at the start of class that you should have a a good understanding on derivatives and integrations. The reason why is if you don’t understand how to do integrals it would be difficult to solve certain differential equations, such as, first order homogenous differential equations. So before starting this class, practice how to do derivatives and integrations by going back to your notes, doing practice problems, watching youtube videos, or going to tutoring on those topics.

I totally agree with you in order to understand the differential equations you should have good understanding on derivatives and integrations.

I agree, at the start I had trouble understanding the problems. I consantly question myself – ‘ is this correct?’ or ‘is this the right approach?’ and it takes a while for me to solve a single problem and sometimese still got it wrong. Upon practicing more, everything grew that much easier.

I agree with your advice. YouTube videos on very helpful in that they show step by step examples on nearly every topic in the class. Understanding the topics is very important especially when it comes to Laplace Transforms and Population modeling and Temperature change problems.

2. I would say the hardest topic about this entire course (for me at least) was the beginning, where we start to learn about differential equations. The new concepts where you are able to have variables of x in equations containing y’ or even y” seemed like such a foreign concept I could not wrap my head around it. Learning about identifying new “types” of differential equations such as Bernoulli, Euler, homogeneous, non-homogeneous was such a steep learning curve. I definitely suggest trying get a good understanding in the beginning of the class, so that as you move forward new concepts will become easier to understand as well, since the basics of the class can really boost how fast you can learn new concepts.

I totally agree with you. I never heard about these topics ever before in my life and when they were being taught, I literally had no idea about what was going on.

couldn’t agree more with you, learning so many new materials in such short amount of time is super hard. I spend majority of my time struggling with HW since the lecture only gives us few examples.

1. Before this class started, I wish I knew a little about Bernoulli equations, homogeneous, non-homogeneous, first-order linear equations, because this was such a new concept that I never heard about before. I would like to advice future students that before this class starts make sure you know a little bit about these topics so you can be better at understanding and solving them.

I will recommend people new to this class to start remember back what they learned in calculus I and II, instead get their hands on the non-linear differential equations when they can’t solve first linear equations. It’s essential to know the integration technique to start solve differential equations.

I’d give the students advice is that in order to study the differential equation, students should have basic knowledge differentiation and integration. mainly integration is the most important part to solve the differential equations. Therefore, in order to make this course useful, active participation in the class and interest in studying and regularity in the class are highly necessary.

I totally agree with you because I have struggle on solve differential equation too and later I found out I’m not good at those question is because I’m don’t have the basic knowledge about find any derivatives and doing integration. That’s why after that problem I learn that I need to start to review back the old materials I learn from previous class in order to let me get better knowledge to solve all those differential equations. Therefore, I really think the way that you use to help you learn is really a good idea and can help you become more successful in this class.

I agree with you that new students should prepare themselves on derivatives and integrals before starting the class so then challenging topics, for example, first order differentials equations, such as, Bernoulli, Homogenous, Seperable, etc. wouldn’t be so difficult to them when they enter this course. In addition, by getting a head start in preparing for this class the topics that they will learn throughout this course will become easier to them.

3) The most important prior knowledge that you need to succeed in this class is to learn the chain rule and integration techniques. These two topics are essential because, throughout the course, we been using these two techniques for almost all of the problems. So, I encourage future students to master these two topics.

I definitely agree with this. To add on to this, I’d also suggest to students to take full advantage of the professors office hours to help clear up any confusion regarding these topics.

Before restarting differentials again, I wish someone told me just how much I’d have to prioritize this class over others. The amount of time that must be spent in order to succeed in this class definitely outweighs many other courses out there.

I also feel that if your calculus base is weak, you will suffer dearly in this class. It is because of this that I feel that calculus 1 & 2 are very important to master before taking differential equations. Especially given all of the complex derivatives and integrals that you will encounter, along side applying the rules of differential equations to them.

I cannot agree with the first statement more. Studying for differentials and just being in the class, in general, has taken up the spotlight and time from most of my other classes. If you plan on taking this class please please make sure you got time for it and be sure to do all the homework because they’re a lifesaver for your grades.

You are 100% correct on needing to prioritize this class because it does have a lot of formulas, setups, and answers you need to remember for solving problems and getting the general or particular solution.

The most difficult subject I would say is first order linear equations. It is the first topic when starting the class and it requires knowing things like trig identities, integrals, derivatives and such. I suggest to review these materials the first week of the semester else, it will be very difficult to follow onwards especially for people like me that forget them. There are several branches of first order linear problems and to list a few; homogenous, non-homogeneous, and bernoulli. Getting ahead and learning these materials will be the core of the class as later equations given will come back to these.

I agree with you that the first topic we encountered is the most challenging since we’re jumping head first into a challenging topic right at the beginning of the semester. But on the bright side, almost all the techniques and methodologies we encounter later in the semester are very similar to the topic we studied on the first day.

By far the most difficult subject is probably second order differential equations. It seems to demand the most knowledge as well as the most steps than other things that would be taught in the class. Yes, you need to have a grasp on First ODE but even then it doesn’t really prepare you for what’s about to come with Second ODE. I wish that I would have been told just how different the tests were going to be. Honestly as much as learning the material matters what matters the most in college is just how the tests are going to be distributed and what would be on the test. If I had known that most tests would be just 4 questions of long arithmetic then I would prepare myself mentally and focus on things in the review that had to do with such things. The most important knowledge necessary to have before class just has a good grasp on derivatives, because as much as u may need some knowledge of integration it is nowhere near as important as derivatives.

The most important prior knowledge that you need in order to succeed in this class is a good understanding of derivatives and integrals. Almost all of the topics that we have covered include steps where integration is needed or taking the derivative is part of the problem. If you are a master at derivatives and integration, then you will have no problems in this course, as the professor does a very good job in explaining each topic with detailed steps.

Prior knowledge that would have been useful to review at the start of class would have been integration by parts, U-substitution, and integrals and derivatives of exponential functions. This is important because differential equations tend to have multiple steps that need to be kept track of many of which use integrals and derivatives, and if this part is familiar to you, than you can focus on the techniques to solve the differential equations instead of being hung up on these. The most difficult part of this course is keeping track of all the pieces. My advice is find a way to stay organized and neat so it’s easier to follow. The one thing I found extremely helpful were office hours Prof. Reitz is able to walk you through the areas you’re struggling so you know what you need to work on.

The hardest topic in the course that is especially challenging is the beginning of the course which first order differential equations were introduced . Specifically, for non-liner differential equations. Unfortunately, there are no single way to solve all the non-linear differential equation, but more practices on both homogeneous and Bernoulli will help you identify what type differential equation you are dealing and sometime they can be easily converted to separable differential equation which will help you solve the problem easier.

I agree. I also struggled with Bernoulli equation problems. Learning how to deal with the different types is really key.

1. I wish I had been told in the beginning how delicate differential equations is. Remember guys, failure to plan is a plan for failure. Make sure you really take the time to understand the material. Don’t keep pushing it till the last minute before an exam and cram everything. Not knowing how to do the first couple of techniques can and WILL come back to haunt you. Also don’t be afraid to ask questions. If you never ask questions, how could you pass or know what the problem is.

2. A challenging topic for me was first order exact equations. The best advice I would give is to ask the professor to try one in class. More advice would be to Youtube the type of problem or try Khan Academy. Believe it or not, lots of learning is done outside the classroom, maybe even more.

3. Prior knowledge would be Calc 2 and a little bit of calc 1. Make sure you brush up on your integration techniques, as this is a big concept in differentials. You actually can’t solve without integrating, so make sure that’s up to par.

I wish I had been told how important many of the fundamentals of calculus I/II were to this course. Having a good grasp of finding the derivative and integral of various functions will make it earlier to focus on the new information and techniques being thought in Differential Equations. Spending that first week on review and keeping up with the homework problems will make a significant difference on your understanding of the topics.

What I wish someone had told me before starting the class is that while Differential Equations looks intimidating, it isn’t much harder than calculus 2. The class itself does require a lot of study time but its methods and concepts are easy to follow if you put in an effort to learn them. The most important prior knowledge needed for the class is knowing how to derive and integrate. This is important because a lot of the differential equations require you to differentiate or integrate in order to solve the problem.

The advice that I wish to give to the future student in the start of the class in order to let them succeed in the MAT 2680 differential equation class are before this class begin you should start to review what you learn before in calculus one and two because this two class have the most main material you need to learn, know and understand it before you can start to solve differential equation. For example like limit formula or equation , all the formula to find derivatives, integration by parts, partial fraction and series so if you can know and understand all this topic then I can definitely sure you will be very comfortable and easy for you to solve those differential equation. Moreover, you need to review your notes from previous math class too because you still need to know how to use algebra to solve any math problem and mainly we need algebraic equation to solve Laplace Transform problem. Also, of course if is hard for you to study by yourself and you can’t focus by doing independent work, then you can always go to tutoring and find a tutor to help you study in anytime. I think the one topic in this class that I have most challenge is first order differential equation because they don’t always have the same format to get the general solution as the second order and first order equation have too many step to remember and cannot skip any step. Also, there have different type of first order differential equation to remember and they don’t have any specific or straight forward formula to use that’s why I think this topic will be my most challenge from this class. In order to master this topic in this class the only thing you can do is pay a really good attention in class, review the notes everyday after you finish that topic or lesson, stay after class, ask the professor any question you have from the topic that he teach and go to tutoring session if you have time. The most important prior knowledge that I need in order for me to succeed in the future is Third order or even higher order differential equation and I think is important for me to learn is because I am an engineering major and I know the materials I need to know in that last class before I graduated is all about differential equation so maybe at that time I will need to know how to solve higher order differential equation and I going to have a chance to need that knowledge to help me learn and get a good grade in the test and that class. Therefore, that is the reason why I need this topic and is very important for me to learn from now on.

I agree with you. Reviewing your notes from calculus one and two as well as refreshing yourself with algebra makes this class a lot easier. So of course it is best to do this before the class starts because once it foes the material can be overwhelming, nevertheless still do-able.

1) An advice that I wish I knew to help me succeed in the beginning of the class is to always ask questions when you are not sure of something. In differentials, not understanding a single part of the problem can change the entire problem because each part relies on the previous one being correct. Its also important to ask questions because it can not only help you but others with the same problem.

3) The most important prior knowledge needed in this course is remembering the rules of integrals and derivatives. Having a good knowledge of these will make differentials much easier because every problem requires you to use some form of it. Such as product rule which is used in certain problems.

The best prior knowledge to have for differentials equations would be a strong understanding and confidence with derivatives and integration techniques. You would possibly need a small understanding of partial derivatives from Calc 3 but that will be covered in class so it’s no that much to worry about. As long as you have a strong foundation in those three areas, the rest of the class will just be applying that knowledge to actually solving differential equations.

3) The knowledge that I believe is the most crucial for me before taking this class was the mastery of taking derivatives and integrals. These two concepts learned in previous calculus classes should be a second nature if you want to be comfortable in this class from the beginning of the semester. If you weren’t able to master those concepts in the previous courses, try your best to review it before the beginning of the semester. However don’t be discourage if you didn’t fully grasp derivative and integral, this class is also a way to learn them again. So take advantage of the different resources you have access to and the office hours of your professor.

Def having basic understanding on integration and derivatives is important. As long as you have the basic idea on how to attack these concepts, you should be on the right track to attack the class.

Having a basic understanding on derivatives and integrals is super important when coming into the class. Without this, you will have a hard time though not impossible to get through it. YouTube videos are very helpful in that there are videos on nearly every topic covered in the class but don’t rely completely on the videos.

3) The knowledge that I believe is the most crucial for me before taking this class was the mastery of taking derivatives and integrals. These two concepts learned in previous calculus classes should be a second nature if you want to be comfortable in this class from the beginning of the semester. If you weren’t able to master those concepts in the previous courses, try your best to review it before the beginning of the semester. However don’t be discourage if you didn’t fully grasp derivative and integral, this class is also a way to learn them again. So take advantage of the different resources you have access to and the office hours of your professor.

The most challenging part of the course was the material covered in the first exam. Trying to figure out how to solve first-degree equations was a lot harder than trying to solve second-degree equations. The best way to get better at it is to practice as much as you can. This leads to the most important prior knowledge to remember is derivatives and integration. As knowing them, makes the rest of the material simply and all a matter of remembering the steps that follow. I struggled with that in the beginning, but after the first exam, i definitely focused on revising derivatives and integration.

The most important (at least in my opinion) tips you’ll need to know in order to be successful in this course is to be proactive and plan ahead. That means you should be prepared to set aside time every week to go over the material and to complete the homeworks, which can be quite time-consuming. You should also clarify any confusion you have as soon as possible, so that when it comes to the exam you can focus solely on studying the material, and not “learning” it for the first time. It’s also important to not get discouraged at the beginning of the semester when we first start to learn how to solve first order equations, particularly first order linear homogenous differential equations.. The procedures for solving the differential equation is very similar in almost all topics that you will learn, including some second order equations. So although it’ll seem like it’s a lengthy process at first, we repeat the same steps (with a few minor deviations) for the rest of the semester for most topics, so you’ll definitely get a lot of practice at it. What I would suggest future students to do in order to master these topics would be to look at the big picture and try to understand that before delving in deeper. For example, you should know the whole outline of all the steps you’ll need to do in order to solve the problem, and how they are related to each other.

And as many of the other comments said, it’ll do you well to go back and review some topics from Calculus 1 and 2. Specifically, you should know the basic derivatives and integrals, chain rule, product rule, u-substitution, integration by parts, and some algebraic manipulation.

I agree, especially since many students who take differential equations must get a C and above in order to move on to other courses, it’s key to practice integration tactics from Calculus 2 and basic differentiation skills. The other thing i would say is extend the course hours to help alleviate students from rushing to finish exams due to the limited time that we have at the moment. But again, we should understand that in differential equations, its mostly integrating and differentiating first and second order ODE’s so it’s key to do well in Calc 2.

1)For the student of future Differential equation students, I’d recommend them to spend as much time as possible on different types of method to solve a differential equation. I wish that i had been told that the review sheet is the key to becoming the A student in this course.The reason being the actual exam is pretty much the same as the review sheet but with some number tweak. Thus, if you can do all the review questions with little to no issue, you can ace the exam.

Contextually I could say “This class won’t be difficult if you follow the simple rules, attend to class, pay attention, and practice a lot. Unless you are one of the mediocre students who will only come to class to be distracted by your phone, so just please do yourself a favor and drop the class, this is not for you. Now, I hope you guys remember material from Cal I and II, because you are gonna use need it. Those are like the baby steps, so if you are kind of rusty on cal material, my recommendation is to practice derivatives, and integration techniques. U-substitution, integration by parts, very important stuff, and of course algebra. From my experience of the class you need to pay close attention to two particular topics, Bernoulli’s equations, and Reduction of order. Bernoulli’s equations are not really challenging, but those problems have a couple of steps that you might get confuse or something. Now, problems involving “Reduction of order” were difficult, or maybe it was just difficult for me. I could’ve 100 for all three exams we took, but the only -2 points I got in one exam it was because of the problem involving reduction of order. There is no trick under the sleeve, you must practice and practice, you won’t understand how to solve the problems by just spending one hour and fifteen minutes in the class, you need to invest more time into solving and understanding each topic. Good luck”

Something I wish I knew at the start of the class was to keep all my tables of derivatives and integrals. The reason why is that differential equations relies a lot on knowing your derivatives and integrals. One of the hardest topics in differentials arguably is the beginning of the course. Differential equations is such a new concept to learn and if you don’t pay attention in the beginning you’ll be completely lost in the long run. In order to succeed in this class, best bet is to study, there is no loop hole no easy pass. All it takes is some studying and practice, and never be afraid to ask a question. Asking a question will always be the best solution

Although this was a math class and prior math knowledge on basic algebra, derivatives and integrals is needed there is one important thing that I would tell the incoming class. I would advise them to have patience and perseverance when taking this class. At first the topics might seem intimidating and complicated, but it is important to keep trying and never give up when learning the topics. Taking everything step by step and carefully is the most important.

1) Honestly, one of the things that i should’ve been told at the start of class to help myself succeed is practicing integration and differentiation, in other words practice Calculus. In differential equations, there’s plenty of problems that involve integration mostly, and it’s pivotal that you must ace this area of mathematics in order to do well. Another thing to note is that practicing problems from the textbook is also a good way to further improve your understanding in certain concepts. Studying is also key to passing differential equations since in exams mostly there are problems that require almost a page to complete, it’s always good to practice consistently because missing a step in a long problem can cost you alot. Since this class focused on webwork, it’s also crucial to do all the problems there to not only gain credit… but to further understand the topic because as you move on to second order ODE’s it’s important to know how to solve first order ODE’s the best way possible.

2) The hardest topic in the class by far is varation of parameters, hence it was a topic that wasn’t introduced as clear as possible due to time conflict. Before i go on, i also believe NYCCT should consider increasing the class hours of 2680 to at least an hour and 45 minutes because sometimes there are certain topics that have one long example and sometimes there isn’t enough time to cover the whole thing. The second reason is due to exams, mostly towards the end of the course… it takes a while to solve 1-2 problems and if you only have 1 hour and 15 minutes to do everything, it’s not gonna work out. Coming back to what i said, varation of parameters is the hardest and i suggest that in future courses there should be a better way to bring more attention to this topic. I would suggest for future students that take this course should watch youtube videos on the topic and also practice problems from the textbook to further understand the topic. Lastly, i hope i pass this class with a good grade.

Although this was a math class and prior math knowledge on basic algebra, derivatives and integrals is needed there is one important thing that I would tell the incoming class. I would advise them to have patience and perseverance when taking this class. At first the topics might seem intimidating and complicated, but it is important to keep trying and never give up when learning the topics. Taking everything step by step and carefully is the most important.

2.a) I think the most important advice I got is that I need to brush up on my Cal 1 and Cal 2 knowledge. Sometimes I get stuck if the prof. takes a short cut. If he explains it later, it gets really easy. Otherwise, I go back to the problem later on and understand it. I will go back to my notes to refresh my knowledge. Also, I will watch youtube videos in the future to supliment my lessons. Solving similar problems gives a better understanding of the material.