**(Due Monday, 5/22/24, 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. What do you wish that you had been told at the start of this class, to help you succeed?Looking back at the start of this class, I wish I had been told the importance of utilizing resources like the textbook and online tutoring. I underestimated the extent to which these resources may have significantly increased my comprehension of certain lessons and helped me perform significantly better in the class as a whole. Overall, I’ve learned that the professor’s resources are essential for success in the course and shouldn’t be disregarded.

I completely agree acknowledging the importance of utilizing resources like textbooks and online tutoring can indeed make a significant difference in understanding the material and performing well in the class. It’s essential to recognize the value of these resources early on and incorporate them into our study routine to maximize our learning potential.

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?Algebra and the art of simplifying, making sure your work is organized and well written. This course has steps where simplifying plays a major rolling and if done incorrectly can throw you off completely. There’s single problems that fill up a whole page and missing a number or forgetting a sign may not be a big deal when doing the test(professor is very forgiving) but it will keep you up at night doing webwork. All because you forgot the variable was a t not an x, SMH.

I agree with your statement. I also would get tripped up a lot with the variables and would have to pay the consequences, such as losing points on the exam or getting a question wrong on webwork.

yes, being organized is very important. The resulting equations can get really complex and if you are not organized, you can forget that you haven’t added or negated an variable even though you thought you have.

I agree that this helps a lot with organization instead of having it on your mind and instead on paper. I believe not skipping steps also helps so if the solution doesn’t look right then it can be back tracked.

What do you wish that you had been told at the start of this class to help you succeed?I wish that at the start of the class the amount of time that I would need to set aside to understand the fundamental of the class. I wish that I received an equations paper so that I can have as a visual guide for each of the lessons. I wish I was told that this class is very equations based.

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 is algebra. Because I have learned algebra from previous classes, it was kind of easy to get the hang of the class. Another thing was knowing derivatives and anti derivatives. Derivatives and Anti derivatives became a big part of the class getting towards the middle of the semester. Knowing the 2 before hand had a big impact on the class making it easier to understand how and when to derive.

P.S

If you need help, ask the professor. Go to his office hours if you don’t understand a certain question

I agree with your statement because algebra and calculus knowledge is fundamental. As I mentioned, it is also expected that we know how to solve algebra, and calculus problems quickly, so we would be able to work on the differential equation itself. Additionally, some of the problems are lengthy which require not making a slight mistake because of your overall results being thrown off.

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 is challenging in this course might be variation of parameters, (this topic is also similar to the reduction of order) which tests your skills in calculus with antiderivatives to find a particular solution given a set of initial conditions. Its important to mention that bookkeeping in general is important because the steps for this topic relates to topics from early on in the course.

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 you need would be a strong foundation in Algebra and Calculus because it is fundamental in approaching and solving differential equations quickly. By mastering these skills, you will be able to manipulate problems into a format that is easier to understand.

I agree with your statement about having strong fundamentals in both algebra and calculus, as it is essential for understanding and solving differential equation problems. With such strong fundamentals, navigating through problems will become much easier, and solutions will be derived in a much more accurate manner.

I completely agree with your point about the importance of having a solid foundation in both algebra and calculus. These fundamentals are crucial for grasping and solving differential equations. With a strong base in these areas, tackling problems becomes much smoother, and the accuracy of your solutions improves significantly.

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

I would advise incoming students to prioritize developing a strong foundation in algebra and calculus. Understanding fundamental concepts such as functions, derivatives, and integrals will greatly facilitate comprehension of differential equations.

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

Additionally, I wish I had known at the start of this class the importance of consistent practice and seeking clarification on challenging topics. Specifically, mastering the Runge-Kutta method can be daunting due to its computational complexity and reliance on iterative calculations. My advice to students tackling this topic would be to familiarize themselves with the method’s principles through step-by-step practice and seek assistance from professors, tutors, or online resources whenever needed

Hello Dariel, I totally agree with you because if I was following those instructions in the beginning I will be in a better position for my grades.

I completely agree with you. Consistency and a good background of calc and algebra is key to doing well in this course. staying consistent in reviewing the material and practicing. I went to office hours, but I definitely should have gone more.

I totally agree, consistent practice is key and seeking help is important,. the Runge Kutta method is tough but practicing regularly and staying ahead of the material are helpful for understanding it.

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

Any advice that I would give any student that signed up for this class would be to have a strong understanding of integrals, derivative and algebra. And to do their best to keep up with their assignments on webwork in a weekly basis.

I agree with keeping up with the webwork as it’s not only good practice but you can get extra credit if completed, boosting your final grade.

I agree with this, with solid calculus skills this class could be a nightmare. Keeping up with the webwork assignments is essential as well.

If I could go back to the start of the course, I wish someone would have told me how much Calc 2 was going to come back to bite me. It’s important that you have a good foundation in calc2, derivatives and integrals pop up but also partial fractions. If the foundation is weak the whole structure will crumble along with your grade in differential equations. Take the first week of class to review and refresh your memory. in this class you get out what you put in so study. Another keep tip is write down your steps when doing practice problems or working on homework it may seem tedious, but it is really useful when helping you remember what to do on an exam. You will work on using A LOT of different types of methods to solve differential equations and you need to memorize and know the different steps of each method to perform well in the course.

One topic in this course that was difficult for me was Variation of Parameters. This topic was difficult because I had trouble with integration so if I were to start over and try to master this topic I would revisit and master working on various integration techniques then that would make working on variation of parameter problems way easier.

I agree with writing the steps when doing practice problem because yes it may be tedious, but in the long run it helps miles. Considering that most processes that we learn in this class have multiple steps and it’s easy to get lost in them. Especially with numerical methods, it gets not only ugly but brutal if you mess up the first step. The professor also, like you mentioned provides various methods to solve a problem which have their drawbacks so I would also suggest as a tip to write the drawbacks for the method. Some methods only work in specific cases, but when they do, they make a problem leagues easier.

To this day I will continue to struggle with the derivatives of sin and cos because I’ll mix it up for the integral of sin and cos. And those are just easy points to be losing, so I would definitely say to brush up on derivatives and integrals. As for cos, sin, tan, etc we do go over them in this class so escaping them is futile. I’d say brush up on those as well!

What do you wish that you had been told at the start of this class, to help you succeed?Not only was I not prepared for how much this class comes back to Calc 2 fundamentals, I was not prepared for the alphabet soup this class was. At a certain point I started to question if we were still in math class because there was more letters than numbers. I would’ve told my past self to be organized. I hate organization because it’s too rigid and I like to be able to move around things freely, but as we go into a topic like inverse Laplace Transforms (partial) with the variables (S,t,A,B) it’s so easy to mix up the letters and which values belong to A or B. I found myself inputting the answer for B in A more times than I could count and my S looks like 5 so while I’m computing this I have to question if it’s an S or 5. In short, I would say to be organized and write clearly so when looking back and going through the process of learning, you spend less time questioning what was written and if the steps were in order.

What is the most important prior knowledge (not taught in the class) that you need in order to succeed? Why is it important?As many of the students stated the fundamentals of Calc 2 and Calc 1 are important! I would argue that in the beginning of this class we focus more on Calculus 2 with integration, but then we are stuck in derivatives for a good while which is Calc1 based. So I would say brush up on your integrals and derivatives! Often we use a combination of both, because we don’t spend any class time reviewing derivatives or integrals and a lot of the procedures we learn in this class assume we know derivatives and integrals. Basically, you’ll struggle immensely if you don’t brush up on derivatives or integrals. I would recommend printing out a table of rules, equations/formulas for derivatives and integrals to keep on the side.

I one hundred percent agree with your advice about organization. There are a lot of steps to solve different differential equations. Having clear notes that go through how to solve a differential equation step by step is crucial in doing better in this class. Also reviewing derivatives and methods of integration never hurt!

3) The most important prior knowledge

Very important prior knowledge to have before beginning this class is a solid understanding of algebra and calculus. Another skill to have is time management, with this skill the hours it takes to complete the homework and study for exams are properly delegated. Trying to cram this type of study doesn’t work because high level math isn’t intuitive. These knowledge and skills are important in order to achieve a good grade because the work can pile up on you if you don’t have a solid foundation in calculus and/or time management skill.

I suggested that students should work on webwork assignments as soon as they become available and review past webwork assignments to better understand the steps to solve each type of differential equation because as you said, you cannot just learn these steps without a lot of practice.

Reflecting on my experience, if I could turn back time to the beginning of the course, I would have appreciated a heads-up about how crucial Calc 2 would be. A solid grasp of Calc 2 is essential, especially derivatives, integrals, and partial fractions. Without a strong foundation, everything else crumbles, including your grades in differential equations. It’s wise to spend the first week of class reviewing and refreshing your memory. The effort you put in directly correlates to your success, so hit the books hard.

Another valuable tip: write down every step when tackling practice problems or homework. It might feel tedious, but it’s a lifesaver come exam time, helping you recall the necessary steps. You’ll encounter a variety of methods to solve differential equations, and knowing each method inside out is key to doing well.

One particularly challenging topic for me was Variation of Parameters. My struggle stemmed from difficulties with integration. If I could start over, I’d focus on mastering various integration techniques first. This foundation would have made tackling Variation of Parameters much more manageable.

I agree on how important it is to write down every step when doing a problem. I would like to add the importance of also organizing the steps when writing. It would make reviewing the notes and homework easier to understand.

One thing I wish i was told at the start of this class is to go the office hours after class more often! The professor is really chill and will try his best to help in any way he can. I can say with certainty that going during his office hours always helped me. Even if its just for a small clarification I strongly recommend going. I was able to get a better understanding on a topic I couldn’t really understand.

I agree with your statement. Office hours could help you in so many ways. It could help you understand a topic that you are having a hard time with.

I wish I had been told to review my calculus basics throughly especially derivatives and integrals as these are essential for the course. differential equation can be very challenging my advice is to practice every day to become familiar with various methods. one challenging topic is the method of variation of parameters for solving differential equation, make sure you understand the method of undetermined coefficients first as it forms a good foundation, practice as much as you can to get comfortable with the process. the most important prior knowledge is a good understanding of calculus (derivatives and integrals )this is important cz the course is builds on these concepts if you’re strong in calculus you will find it easier to understand and solve problems in this class.

As a student that took a 2 year break from school, the best advice i can give that helped pass the class were the following; do not skip homework. the value of homework could help your chances of passing the class by a letter grade. Do all the small side projects. participate in class. Be that perfect student for this class. that student that goes the extra mile and gets an extra hour of tutoring.

speaking from experiencing, this is what i did to pass this class.

One thing that I wish I was told at the start of the semester was how the tests were going to be set up. When the first test came up, I was prepared to solve a bunch of math questions, but there weren’t that many questions and half of them were explanation questions, like explain what type of equation this is or based on the following equation, what should the next step be. After the first test, I started to study how to not only solve a question, but the theory part of it, so I would advise that future students do the same thing because some questions could be free points if you know how to answer and explain it.

I agree, it make it so that you not only need to know how to solve a problem which can be seen as following a list of memorized steps but how it works in theory which made it challenging in a different way.

One of the things I wished someone told me at the beginning of this class was how important the smallest details in the lectures are. Adding certain symbols, and certain numbers can change the entire question and the answer to that question. There were times when I could’ve gotten full credit for work in the exam but since I didn’t read it correctly, I wasn’t able to answer the question correctly. That is why I strongly urge that, whoever is about to take this course, please understand how important it is to pay attention in class.

I agree, paying attention in class and otherwise can prove to be a simple and useful skill

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important? The most important knowledge is note taking. Textbooks are always different and the class may use different symbols so understanding the actual work being done and writing it down as notes helps as a reference.i totally agree with you going to office hours and ask questions when you are stuck rather than sit back. notes taking is one of the most important things anytime you are stuck you can just go behind and have a look.

At the start of this class, I wish I was told that this class requires a good grasp of Algebra, Calculus I and II. The class is like a cookbook, you learn why and how to solve different types of differential equations step by step. But to do these steps you need to use Algebra and Calculus.

One of the challenging topics for me was Reduction of Order. This topic is challenging for the fact that the procedure is long because you will have to substitute variables with other variables. When it comes to solving differential equations with Reduction of Order, it is best to solve it slowly and be organized as it’s easy to get confused.

Important prior knowledge from Algebra are Natural log and Exponential rules with base e. You will have to know these rules to solve a majority of the topics. You’ll need Partial Fraction and Complete the Square for the last topics. Differential Equation is Calculus heavy, so knowing the derivatives/integrals of standard functions is a must. Also, practice the Product Rule and Integral by Parts.

prior knowledge(not taught in the class) that you need in order to succeed? Why is it important?I believe that the most important prior knowledge for this class is is a solid understanding of algebra. I say this as it allows you to manipulate and solve a lot of the equations we see. You need algebra to rearrange equations, isolate variables, and simplify expressions, which are common tasks in in this class. Additionally, I would also say that another good thing to be knowledgeable about prior to this class is linear algebra as you can use matrices to solve partial fractions with are seen in the later half of this class.

I thought the semester would be really difficult at first, and when semester started and i started to understand it was not that hard as i thought, do not need to overthink questions and solve it as it stated. Here, practice is the most important thing. You would realize algebra is simple once you started doing it and worked out the problems. Things don’t need to be overthought; just try to understand them and then find a solution. In my opinion, the Runge-Kutta and Eulers methods were difficult since it was so simple to make mistakes using them.

Doing the webwork problems as soon as you can really help you succeed in this class. You have the material fresh in your head right after the lecture on the topic and if you do have any questions or trouble with the problems, you can bring them up at the next class session or office hour.

Understanding the differences in each type of differential equation can be challenging. To get better at understanding the differences, go back to previous webwork assignments and do the problems over again to get the steps down. Practice is really going to help you remember the steps for each type of differential equation.

Understanding how to find the integrals is key to finding the solutions to some of the differential equations. Review the integrals that are the most challenging to you (i.e. integral of sin(x) = -cos(x)) as they will be primarily how to solve some of the differential equations in this class.

1) On the first day of class I wish to have been told that the tests are easier than they appear and that there won’t be departmental finals anymore. (yay). I also wish I’ve been told that Professor Reitz, in particular is a trickster, and a skilled one at that. He likes to mess with students when they ask about tests, but over all is very merciful. When I say mess, I mean he’s usually very vague about what will be on the upcoming test, except for the total number of questions. Also that the tests are like a flashbang: they’re unpredictable, but are usually easier than the study material or the homework. Also, use study materials efficiently, since most of the time it’s either a waste of time to do what you’re sure you know; OR it’s been a while since the material you’re being tested on. PS: Beware of homework. There’s a LOT of it and the deadlines are tighter than tolerances on a rocket

2)Numerical methods are boring, stupid, and overall useless. That’s why they should be studied extensively, so that when they’re asked on any of the exams, you can actually remember what they’re about.

3)Y’all will have to do a project sometime early half – mid semester, spend some time figuring out what mathematical software or regular programming language you will use. Save a bit of time for yourself, since right about then is when you have your first or second exam, and the project along with the homework will be a BIG problem. One thing not to leave for last is the project.