**(Due Monday, 5/22/23, 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?

If I were to address entering students in MAT 2680, I would offer the following advice:

One thing I wish I had been told at the beginning of this class is the importance of consistent practice and active engagement with the material. Mathematics is not a passive subject that can be memorized; it requires regular problem-solving and critical thinking. By dedicating time each day to practice problems, seeking clarification when needed, and actively participating in class, you can reinforce your understanding and truly excel in this course. Also don’t be afraid to go to the professor’s office hours, because he can really help you clarify and understand what you are getting confused about in class or on the HW.

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

The most important prior knowledge that you need to succeed in MAT 2680 is a strong foundation in algebra, precalculus, and Calculus. Concepts such as functions, equations, inequalities, logarithms, working with fractions and trigonometry are essential for this class. Understanding these topics is important because calculus builds upon these principles and applies them in more advanced and intricate ways. If your algebra and precalculus skills are shaky, try to review and solidify them before diving into differential equations.

// If your algebra and precalculus skills are shaky, try to review and solidify them before diving into differential equations. //

> I agree. If you are struggling with it, it is recommended to re-read your previous math classes notes or google the topics you are in need of help with.

//What is the most important

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?//> You really need to know how to do derivative and anti derivative. Sometimes when the question is not a basic equation, it is quite tricky to do the derivative if you do not know how to do it. When I reach the second order differential equation, derivative is needed much.

I agree the knowledge of derivatives and integrals is the key thing to know before the class. It will be very difficult to be able to do the differential equations without it.

In order to succeed in this class, I wish that I was given the advice of taking good notes. This class covers so many topics and within those topics there will be a lot of theory and classwork. Taking good notes is key to this class because it will be easy to search what you’re looking for, easy to look up the steps when doing homework, and for the finals. I would advise to have a separate list of notes that just lists the name of the topic and the steps. (For example: 1st Order Differential – Bernoulli and underneath that Steps 1 …, 2 …, 3… )

I absolutely agree. I found myself going back in my notes to review many topics and wishing my notes were more organized. I would definitely recommend any new students in this class to space out there notes and write down every step.

I agree taking organized notes is a must. In this class it’s important to observe and recognize what type of equation you’re dealing with because there’s so many methods to solving. Especially when solving second-order equations you have to make an educated guess (y=u*y or y=x) and you’re guess is dependent on your equation

Some prior knowledge that is needed to succeed in this class that I wished I worked on more was first reviewing the derivatives and integrals we learned in calculus 1 and 2 as they are used frequently in this class. You should also make sure to review your algebra skills including grouping and factoring as this will come in handy in the later topics. And by far the most important skill is bookkeeping and organizing your notes, equations and answers as solving these equations gets long and complicated and it’s really beneficial to keep organized.

I agree, calculus 1 and 2 are important for differential equations, without them I can see many students struggle. When we make sure that bookkeeping is neat, it helps us understand all the different topics.

I agree, calculus 1 and 2 are crucial for differential equations. Making sure that we have organized notes gives us an easier time when we do hw and study for tests.

1. What do you wish that you had been told at the start of this class, to help you succeed?

At the beginning of this class, I wish I was told that it is important to take good notes and make sure that you do your homework during the week instead of on the last day. It is important to make sure your notes are concise since you will need to go back to them consistently for homework and review. This class is short, and you need to take time outside of class to study since you won’t remember the material.

2. What is the most important

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?The most important prior knowledge that you need for this class is Calculus 1 and 2. The material that is taught in these classes is necessary for the basic understanding of differential equations. You must understand integrals and partial fractions that are needed for this class. If you aren’t familiar with these topics, it can make the class difficult. You should also brush up on derivatives since

I agree taking good and organized notes is a must. There are many steps to each problem. Also brushing up on skills learned in previous classes. I would like to add utilizing office hours and asking many questions if you are unsure of how to complete a specific problem or step(s) within a problem.

1. What do you wish that you had been told at the start of this class, to help you succeed?

The duration of this class is shorter than the previous math classes. Thus, a sizable amount of information and topics get covered within a short period of time. It is important to take great notes. For example, writing a few words explaining intermediate steps within a problem since referencing back to them occurs frequently. Try to complete the homework within the week since it is a major part of the class grade and doing it at the last minute is not the best idea, some topics take a bit of time. Lastly, it is better to ask questions during class and attend office hours since it’s the fastest way to understand a topic rather than spending a while on youtube looking for a specific step whereas Professor Reitz can help and explain the exact problem right away. You will also need to set aside personal time to review the material.

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

The most important prior knowledge that you’ll need in order to succeed in MAT 2680 is good skills in Algebra, Calculus 1 & 2. The skills learned in these classes are fundamental to solving and understanding differential equations. Brush up on topics covered in Calculus 1 & 2 such as factoring, product rule, quotient rule, integration by parts, integration by substitution, system of equations, etc. They are used for almost every problem.

I agree with you, it is crucial to go over calculus 1 and 2. And to also attend office hours. Specially since class is shorter than other math classes.

In order to succeed in this class, I would say to review calculus 1 and 2 and to also take good notes in class to review later on. It is also important to complete do the webwork assignments early rather than the day of, so if you are having trouble with a question you can ask the professor for help, so you don’t have to be stressing on the last day to complete that question. But most importantly take advantage of office hours and always ask questions.

3.What is the most important

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?The most important prior knowledge that you need in order to succeed is that you must have an understanding of integrals, derivatives, and partial fractions and it would be very difficult if you are not familiar with these topics. Some other topics that should be reviewed for this course is factoring, product rule, and quotient rule. But overall, go over calculus 1 and 2, it is very important.

I agree– reviewing key skills like product rule and quotient rule as well as all the integration methods like u-substitution and integration by parts could’ve been really helpful as they are essential in solving many problems. Starting the homework earlier is also a must as the course does go by quick

I agree that it is definitely important to review topics and concepts from Calculus 1 and 2. Every topic in this class requires some sort of knowledge from those classes. I also really agree with taking advantage of office hours. Going to office hours really helped me understand more about the topics taught in class. Also going over WebWork with Professor Reitz really helps.

1.What do you wish that you had been told at the start of this class, to help you succeed?

At the start of this class, I wish I would have been told to try to focus more on understanding the reasoning and explanations behind certain methods that we use in class. I feel like understanding how to do each method and the reason why we do it is more important and beneficial than just getting the correct answer. It also helps you to understand the steps taken in these methods which helps with solving them too.

3.What is the most important

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?I think that the most important prior knowledge not taught in the class that you need to know in order to succeed is how to do derivatives and integrals. Almost all topics covered in class require you to either take the derivative of a function, integrate it, or both. At the beginning of the semester, I remembered basically nothing about either. Over time your memory comes back to you and you start to remember the rules and concepts taught in Calculus 1 and 2.

I agree with you that trying to understand the concepts taught and the explanations rather than trying to get the right answers is beneficial to succeeding in this class. I also agree that derivatives and integrals is the most important prior knowledge needed to do good in this class.

1.At the start of class, I went into it knowing that the Webworks would be the best practice for mastering the different topics we had went through. Webwork was especially helpful for practicing how to solve first order differential equation problems as I was able to practice with the topics and types I struggled with the most. If I could pick one thing I wish I would have known, it would be to review lecture notes the same day as the lecture and rewrite them step by step. The lectures were extremely helpful, but our class time is short so it goes by quick. I wish I had reviewed my notes the evening after lectures so that I would be able to follow the steps without confusion. I noticed that waiting too long to review my notes would leave me confused at certain steps which required me to need to refer to the textbook.

2. One topic that I found challenging was Bernoulli as it required the most steps to solve. It often left me having to go back and double check whether each computation was right. For this topic and its corresponding homework, the first answer I attempted was usually incorrect in Webworks. The method to solve these problems is straight forward and has a fixed series of steps which Professor Reitz makes clear and understandable. Executing better organizational skills when practicing these problems would have benefitted my efficiency in solving them as I found myself scribbling all over the paper to eventually get a final answer.

I definitely agree with both points clean notes and consistent review can remedy most questions on a topic. Organization also plays a large role in the resistance for learning you as a student may have, I know that I’d be more willing to review notes if I could read them and can avoid confusion with steps If they’re labeled or have annotations.

What do you wish that you had been told at the start of this class, to help you succeed?

I wish it was stressed more to work on our WebWork assignments. Not only does the webwork assignments reinforce the concepts taught in class, they also familiarize us with the procedure to solve the problems. After spring break, I stopped working on the webworks and it affected my performance in test significantly. Once I started working on the webworks again, I felt more confident in my ability to solve the problems on the test.

What is the most important

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?The most important prior knowledge needed to succeed in this class is Calc I and Calc II. It helps a lot when you already know concepts like chain rule, product rule, and integration by parts. There will also be some algebra as well. These are important because they are used throughout the class.

I can agree with both of the really good points you’ve made, as the lessons taught in Calculus I and II are come up again in this course and it is essential to retain them. Along with having that prior knowledge the webwork also really helps with the understanding of the material, both really helping out in getting better at solving the problems.

I wish it was more stressed to me at the beginning of this class the importance of keeping up with the webwork. Webwork is probably the best tool to help you reinforce the knowledge gained in class. The WW questions are always purposely harder than the ones given on the tests, so by taking the time to work through them, you’re guaranteed a good understanding of the material and good scores on the tests.

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?Obviously the most important prior knowledge is of Calculus I & II. These earlier classes have the most important basis information for the material in this class. You need to have a good understanding of derivatives, integrals, series, and most importantly, solving said problems quickly and efficiently, to be able to succeed in this class.

I agree that Calculus I & II are very important prior knowledge, because this knowledge is often used when solving differential equations. Also, know how to solve quadratic equations and system of equation is important too because we need to use that to solve some of second order differential equations.

i agree with being more stressed about webwork because it is the easiest to overlook but by doing them you get a better understanding of how to solve harder problems and makes test questions simpler. also i would like to add an example to some calculus things we would need to know like sometimes in the process of solving a problem you might need to use substitution, using partial fraction decomposition etc. so these are some small things we need to use in the process of solving differential equations and would make it a loit harder to learn if we did not know this in calc 1&2.

What do you wish that you had been told at the start of this class, to help you succeed?

I think it is to take class notes and try not to be absent, because each class would has new content and is interlocking. If you miss one class, you may not be able to understand the next class. The notes are the same , because before each exam, the class notes will help you the most. The process of solving differential equations is not short, notes can help you quickly understand the solution to each question.

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

You must be familiar with Calculus 1 and Calculus 2, because if you don’t know Derivative or don’t know integral, your differential equations will be very difficult to learn because solving differential equations is inseparable from these.

Agreed, a good foundation/knowledge of derivatives and integrals is vital to succeed in this class.

Totally agree with you. Note keeping and have a good knowledge on cal 1 and 2 ayer the keys to succeed in this class

1: Even though this isn’t the same kind of advice for everyone, because of how people have different schedules, but the one thing I wish someone had told me at the start of this class is to make sure to not overwhelm yourself with taking something like 6 classes, as it can really mess with how much time you would dedicate studying for exams and doing homework for this class, which can help a long way in keeping your grades high.

2: One topic I did find challenging is the power series that I had struggled with is remembering the equations correctly, and the best advice I can give to master that is to just write down the steps you need to successful solve the problem, with calculations as an afterthought to try not mixing up the steps for other problems solutions. Though, this can be said for any topic that has a difficult method to remember and it is just a good way to try making sure you have any method committed to memory when you have done it repeatedly.

Totally agree about 6 classes. Starting from Junior year, the classes get only harder, and require several hours to complete one assignment. Do not overwhelm yourselves with 6 classes, it will only lead you to dropping the class or doing worse than you actually could.

yea 100% agree I made the mistake of taking 6 classes this semester was a horrible idea

I wish i was told to connect with my peers more. I don’t think study groups are necessary even though they can be helpful. At Least having a line of communication to other people can help you increase your understanding by receiving help and helping each other. It will also be helpful when you miss a class because each class would have new content and your peers will be a good resource for help. It will also help to keep organized notes with key concepts and tips to help you later.

Before this class you should have your calculus skills prepared. It’s important to know how to take derivatives and integrate but some of the key principles to the theorem of calculus show themselves many times in this class. It’s also good to review some algebra tricks because they will help you simplify your equation.

If I was told to have consistent communication with the professor my experience would’ve been much better. Passively hoping that your example will be picked before class for review or giving up on something that confuses you will bite you in the end (webwork will creep on you). Your prof is pretty straight forward and has office hours; or you can neglect the person willing to help with a Ph.D (and years of experience) and struggle on your own.

It’s been mentioned many times that a strong foundation in algebra, trig and calculus is needed as a background for this class (and I’m sure they’re also required to enroll) but I’d say it’s more so the knowledge of what you don’t know from the classes as you’ve already taken them but what do you need to know? In relation to my first paragraph you can reach out to your professor for a guideline or resources and strengthen what you don’t know. It may be daunting otherwise to try to review several months of work in an effort to be prepared.

if i were to give some advice to students entering this class i would tell them the following:

1) first i would say that do not think that online homework is easier. webwork is used for this class and at first you would think it will be fine but it is an easy forget so set alarms and be very attentive to due dates because once the due time passes its gone. I fell into this trap getting confident i will remember all of the due dates in webwork and getting occupied with other classes and work that i forget and once i remember its too late and only if i had set some sort of reminder it could have helped boost up my grade. so be very careful and do webwork assignments.

3) also some things you would need to know to be successful in this class is a very good background in calculus. specifically using partial fraction decomposition, taking integrals, there are more small things you learn in calculus 1&2 that are implemented so just to have a good understanding in calculus.

The due dates are my weak spot too. As a professional procrastinator, I missed way too many due dates on Webwork assignments. I totally agree about the difficulty of webwork assignments. In prior Calculus classes, the webwork assignments were 3 times easier than the problems solved in class or retrieved from other textbooks. In case of Differential Equations this quiet opposite, with the Spring Problems being the most difficult.

I wish that I had been told before the start of this class to review my notes on derivatives and integrals and calculus. This class expects you to have a strong foundation on these concepts so knowing to review them before the class would’ve been helpful. Also, I wish somebody would’ve told me to always keep track of the WebWork assignments as it can be easy to forget to do them in time.

The topic I personally had the most trouble with was Numerical Methods. It was hard to understand the concept and each method had increasingly more steps which made them tedious and easy to mess up. My advice to future students is to ask your professor lots of questions about Numerical Methods and make sure to focus on understanding the concept itself rather than just simply memorizing the formulas and steps necessary for each method, this will make it less likely for you to forget.

The most important knowledge needed prior to the class is a solid foundation in derivatives and anti-derivatives (integrals). It is important because this class assumes that you already know how concepts like integration by parts and power rule, etc. So knowing these concepts very well beforehand will make the class easier.

I agree with numerical methods being troubling, the book-keeping was definitely atrocious. You had to really be careful each step & double-check, triple-check just so you wouldn’t come out with the wrong answer. When you feel like you’re doing right by your calculations, its easy to mess up and forget. So yes, for the future I hope others really crackdown on this topic and not give in to the tedium.

One thing that I wish I was told before taking this class was to have a deep knowledge of derivatives and integrals before. By the time you are taking this class you need to review everything you did in previous classes. It is also important to give yourself time to study for the class. There is a lot of material covered and you will not pass if you don’t study. The webwork helps a lot so make sure to do them. Lastly try to take as many notes in class as possible as it will help you for ur tests.

This class can honestly scare anybody off. Initially, retaining mathematical knowledge from prior class, you’d notice the similarities, certain formulas and rules still apply while also taking on new approach. It honestly only gets difficult when you remain unorganized with your work or slack off on it. To catch up from behind when we’re steam rolling ahead on new topics is a tall task, so you want to save yourself the extra work as much as possible. Playing a big role in differential equations, what I wish I was told was to go over and review the particular rules of calculus 1&2. What I thought I would have trouble with definitely didn’t trouble me as much as certain ones in the second half of the class. The topic I felt troubled by would have to be the reduction order/variation of parameters. The only other thing I could call out is exact solutions, those are horrible. The advice I have is to really derive your thoughts and common knowledge from the class sessions and homework and understand while studying. It does wonders just knowing the main idea of a topic and how to solve it, just applying it when practicing or on a test. The most important prior knowledge I believe would be locking in just rules such as the fraction, 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.

I completely agree with you on the matter of Reduction of Order. Even though, the way of solving these problems is straight-forward, it is extremely easy to make a mistake along the way. Had to start the problems over numerous times.

prior knowledge(not taught in the class) that you need in order to succeed? review your math foundation such as derivatives and integration because you would need them to succeed in this class.Even for someone who is good at Calculus, this course is indeed intense and demands a significant amount of your time. Make sure to stay ahead with your studies and assignments. The more proactive you are, the less overwhelmed you will be. This is not a subject you can cram in at the last minute. Regular practice, which includes solving numerous problems and consistently completing your homework assignments, will help you along the way.

The most important prior knowledge you need in order to succeed in this class is a good understanding of calculus 2. The concepts of integration, differentiation, and limit are the backbone of many topics in differential equations. They are used in defining, solving, and analyzing differential equations. Therefore, it’s important to review these topics if you’re not already comfortable with them.

Stay on top of your work, be confident to ask for help from Professor Reitz, and do not procrastinate.