**(Due Monday, 12/19/22, 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?

When the class started, I wish I was told to review over calculus 2 to help with remembering some of the rules needed for differential equations. The topics I had the most trouble with are series solution, and Euler equations. Best advice to get better at Euler and series solution is to ask questions, study, and even look at more examples and YouTube videos for further explanation. For prior knowledge, I’d say having a good understanding of calculus (1 and 2) will be a tremendous help in differential equations since some of the rules (like chain and product rule for example) get used and also derivatives are used all the time.

The most important prior knowledge is a firm understanding of Calculus I and II. Although Professor Reitz does a great job of refreshing your memory, it is understood that you will have taken Calculus I & II prior to taking the course. Spend time throughout the week practicing your integrals and derivatives. WolframAlpha is a great resource for practice problems for both integrals and derivatives. Not only will honing your calculus skills benefit you over all, but it is especially useful in this course because differential equations requires a solid understanding of integration in order to solve the problems at hand.

The most challenging topic that I encountered in the course was the section on Power Series. The reason being that you need to be very focused and maintain a high level of attention to detail and organization of thoughts. My advice is to take a deep breath, be patient, keep your handwriting legible, and keep track of what you are writing. I would consider drawing lines to partition out segments of the problem to help you keep track of what is what.

This semester has not only been interesting but pushed me to study certain topics. Before anything, make sure you brush off your Calc I and II knowledge. It will come up in almost every problem you solve, and although it will not be as complicated as the problems you had in previous courses, the concepts are important to solve a differential equation. Sometimes you have to use different methods of integration to solve a differential equation, so more Calc 2 than anything. I would also recommend keeping up with the webwork, because if you can solve the problems on that then the problems on the test would be easier to understand. I didn’t take studying seriously before, but keeping up with the webwork and asking the professor for help during office hours was a huge advantage for the exams

I completely agree. I would never study for exams and such, but seeing how difficult these classes get, I knew I had to start studying. Consistency with webwork, asking questions, and just studying makes it so much easier to understand topics in this course.

Keeping up with the WebWork assignments helps your grade because it helps you practice at home on your own and improve your skill set for the tests because how much you learn on your own reflects your grade on a test

I was afraid of this class. I was great at calc I, but I started really struggling whenever I took calc II. I never fully understood any topic that was thrown at me, even with practice. I gave up near the end of the semester for calc II due to not finding out ways to understand topics, that’s where my issue is. Once I started this semester and became used to the professors way of teaching, I became way more comfortable. Prof. Reitz is an AMAZING professor. He clearly explains a topic and refreshes previous topics spoken about back in Calc I and II. If someone was having trouble understanding a topic, he would clearly explain it in a different but similar way, which some professors have trouble doing. Do NOT be afraid to ask questions, whether it be in Reitz’s office hours, after class, or even in class! I can’t stress this enough, do the webwork! It helped me get a better understanding of topics. Practice makes perfect!

I agree. ask questions always help. and do not be afraid / shy to ask any question in class.

I forgot to include this but I also agree. Our professor is highly efficient in explaining a topic and you should not be embarrassed to ask a question in his class. When you are lost and ask him to explain, he will take a moment to backtrack to where you got lost and go from there. If you don’t understand a certain step, chances are others in the class are also lost so if you want something explained do not be afraid.

I agree, Professor Reitz ability to explain a topic at varying degrees of difficulty is super beneficial and something that future students shouldn’t shy away from taking advantage of. Asking questions is the number one thing you should do if you aren’t certain about anything, regardless of how you feel about asking questions.

I agree with not being afraid to ask questions. You don’t lost anything and only hurt yourself if you choose to remain clueless about the topic.

make sure to learn or re-learn your fundamental of derivative and anti derivative. that thing will body you if you do not know how to solve them.

one thing that is most challenging is the second order linear. the steps are long and you are one mistake a way during the early parts to waste the next 30 minutes calculating the wrong thing.

One thing to know that is not learnt in this class is the basic algebra. make sure to know how to reorder algebraic function so you can find what the questions asked. sometimes just reordering the function can make you makes mistakes so be careful on that

I agree. Reordering algebraic functions are fundamentals and crucial even though we are expected to remember them. It’s sounds very sad but I needed to review some algebraic methods in order for to help me solve some of the questions. Some of the second order could also get very long so it can also lead to very simple careless mistakes that gets you a different answer so you should also be wary of it as well.

First of all, this semester opened up my eyes to a whole different concept of math solving problems, it was hard keeping track of all the steps and equations we had to solve throughout the semester. I wish I knew earlier that the professor posts all the lecture topics on openlab and you just need to search through openlab to find them. Also, the professor is awesome when it comes to learning from him so feel free to ask questions when you feel lost or don’t have any clue on what to do.

Second there were several topics that were challenging personally, but one specific challenging topic was Euler’s equations, especially Runge-Kunta method of solving. However, the best way for me to tackle this method is to become more familiar with the topic and the particular pattern this method was using.

Lastly, one of the most thoughtful skills you can have prior to this class may be to refresh your memory on specific topics from calc I and II for example inverse operation rules, your sine and cosine rules and the differential equations knowledge you were taught because of topics you will encounter in this course will challenge you.

If I were invited to speak on the first day of MAT 2680 class, I would tell the students that the key to success in this course is to start working on the material early and seek help from professor Reitz, Professor Reitz explains topics well by breaking down the problem in steps and make sure his students understand the material. also, advise them to make use of online resources to supplement their learning.

One topic in this class that was especially challenging for me was series solutions. This can be a difficult concept to grasp, but it is essential for understanding many real-world problems. My advice to students trying to master this topic would be to approach it systematically, breaking it down into smaller steps and practicing with a variety of examples such as doing the Webwork Assignments and watching YouTube videos about it. It may also be helpful to work through the material using in-class notes and online resources.

The most important prior knowledge that students need to succeed in this course is a strong foundation in calculus I and 2. The MAT 2680 class is built upon the principles of calculus, so without a good understanding of calculus, students may struggle to keep up with the material. It is important to review and master the concepts of calculus, for example, the product rule before starting this course.

When I first entered into differential equations, I wish I had been told that it would be very algebra intensive and require me to memorize a lot of concepts and formulas in a short span of time. One topic in the course that was very difficult for me was Series Solution Trench because it requires me to fill out a lot of numbers and do a lot of algebra. I would recommend getting very good algebra and being able to do arithmetic in your head very quickly. The most important prior knowledge not taught in the class, that you need in order to succeed is to master all the prerequisites of the course otherwise you will have no idea what you are doing.

Hello irbahimmuhammad, I agree with you that Differential equations can be a challenging subject, particularly because it requires a strong foundation in algebra and the ability to quickly perform arithmetic calculations in your head. Additionally, mastering the prerequisites of the course is essential for understanding the material and being able to successfully complete the course. Series Solution Trench can be especially difficult because it involves a lot of algebraic calculations and requires careful attention to detail. It is important to make sure you have a strong foundation in algebra and are able to perform calculations quickly and accurately in order to succeed in this topic.

If there was anything i wish i was told prior to this class is to take this class immediately after Calculus. The lessons learned in that class is extermely important in the beginning of this class. Create a large gap in-between classes and you will most likely forget everything. As 1st order differential equations primalrily uses intergrals and derivatives; if it is forgotten, then you will spend a lot of time catching up and may not get to understand the new content as you would have otherwise.

In terms of prior knowledge, you really need to know common integrals and integration by parts, and be able to do them relatively quickly. Towards the end, while doing Laplace transformations, you need to remember fraction decomposition. Knowing Linear algebra to solve system of equations is helpful and almost mandatory to solve systems of 3 equations or more that will infrequently pop up during second order differential equations and Laplace transformations.I recommend that while you’re learning numerical methods, look up how to solve system of equations with a matrix and a calculator(Google “Guassian elimination” and “reduced row echelon form”). There is a section on Taylor series and power series, though you can probably get by if you just remember the basics.

Not only should you freshen up on Calculus, but you should also take some time to relearn concepts of advanced algebra. In this class you will need to deploy just about every strategy you have been taught over previous math classes, so the key to success is to refresh on secondary concepts by writing them down in a document and studying them for as long as you need. It may help to look at some examples of different differentials problems, and start to identify the different mathematical options used in order to get a better understanding of the methods for arriving to a solution.

I would say that Modeling – Cooling and Spring problems are likely the most challenging topic to tackle by yourself because they require you to have a fundamentally good understanding of the reasons behind deploying differential equations, and test you on understanding how variables interact with changes and the resulting algebra and differential strategies which must be deployed to solve the problem. With these problems, I think what I had mentioned earlier can help with understanding these problems – look at some examples and work to identify and write down the strategies used to reach the solution. Next, try it for yourself!

I think some important advice would be to create a shorter set of notes alongside the usual longer set of notes which has every topic in one place; explaining basic forms of problems with general steps, theory, and common characteristics of the topics at hand. This way, it will be easier to readdress previous topics when you may need to during the class, and while reviewing.

Some prior knowledge I’d suggest knowing is reviewing back to how to integrate and also algebra. For the most part, a lot of these methods that you’ll learn in order to solve a differential equation has a possible algebraic solution. That means it can be tedious to do rough calculations but also know how to work around functions. What had me struggle the most is actually the algebraic solving. For example, what got me puzzled and if I hadn’t reviewed my notes, it would be homogeneous y/x where you would try to make denominators the same in order to get a single solution u. Same goes with Bernoulli’s equation. That’s just the beginning. In this course, you are taught a vast amounts of methods to solve first order and second order differentials so it’s also a hassle having to memorize or learn a strategy onto what to use and how to use them.

At the beginning of this class, I wish someone told me to take the homework more seriously. The homework given out usually goes step by step through the problems and is a very good way to learn how to do the problems with the methods taught in class. Even though the repetition of the problems can get annoying I learned the most from doing them and going through the methods step by step.

Walking into this class in the beginning of the semester, just the name alone came off intimidating. I didn’t really know what to expect and how I’d fare. What I wish I was told was to go over and review the particular rules of calculus 1&2. They played a major part in understanding differential equations. Over time, as the material came back to me it sort of lightened the load when learning new information. The topics I felt troubled me the most was the Euler methods/runge kunta, along with the series solutions. The advice I have is to really looking and understand while studying. Practice questions over and over, ask for help from the professor or watch other instructors tackle similar questions online. The most important prior knowledge I believe would be a saving grace would just be rules such as the power, chain and product rules, as they go hand in hand with the derivatives we deal with throughout questions. Most of the time, these rules are the only thing we need to put us on track to the right answer.

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?In the beginning of this semester i thought i had it all figured out. Now i didn’t do bad but i could’ve done better. I wish someone would have told me to pay attention to my webworks. HW is worth a good amount and its so easy to lose track of your grade because of not doing your webworks. If it wasn’t for the professor being so friendly HW would’ve definitely dropped my grade at least a letter!

If I had to pick one topic from the class that was challenging, id have to pick modeling cooling. Now my advice will be very slim since I in fact still struggle with this topic. But what I will say is, take good notes so you can review at home, and dont be afraid to go to office hours. Anything I didn’t understand I went to office hours and learned it all over again. Theres office hours for a reason, use them! I promise in the long run it will help you so much.

The most important thing I think to take from prior classes is understanding basic integrals and derivatives. A lot of the mistakes I made in this class were from stupid simple derivatives and integrals or simply messing up the number. Keep a strong basic knowledge because you dont wanna lose points on something so small. And trust me it happens! Its so important to not mess up these small things because they can change the entirety of the problem and then you feel like you dont know what you’re doing. Just take the advice trust me.

Before you enroll in this course you should make sure that you properly understand certain methods of derivatives such as the product rule and the power rule. This topic is not going to be taught but is one of the main elements of DE. Personally, the topic I struggled with most was the second-order nonhomogeneous. This topic can get messy and complicated if the solution turns out to be zero.