(Due Tuesday, 12/14/21, 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 a student was just starting out in MAT 2680 I would tell them to review concepts from Calculus 2 so that they are comfortable with various integration methods. The first couple lessons in this course are about the different types of differential equations and the steps to solving them. You already have enough to learn, don’t make it harder on yourself if you have to reteach yourself integration. There are 10 minute youtube videos you can watch. A 10 minute investment, can have massive returns in the first quarter of this course. Keep the momentum going.
Worry about the
If a student was just starting out in MAT 2680 I would tell them to review concepts from Calculus 2 so that they are comfortable with various integration methods. The first couple lessons in this course are about the different types of differential equations and the steps to solving them. You already have enough to learn, don’t make it harder on yourself if you have to reteach yourself integration. There are 10 minute youtube videos you can watch. A 10 minute investment, can have massive returns in the first quarter of this course. Keep the momentum going.
Worry about the why before the how. Understand why you’re learning something, before you figure out steps to solving a problem. In this class, questions will not always be formulaic but rather conceptual. On an exam, instead of raw calculation, you may be asked for the big idea behind a topic. This alone will make everything easier. Exact Equations are such a topic,where conceptual knowledge is needed.
And finally, just BREATH. Instead of worrying, think about the tools you have. You have youtube, textbooks, instructor email/ office hours, tutoring hours. Approach a problem proactively. And remember, a test does not define you. Have faith in yourself. Good luck!
I completely agree with your statement that exams do not define a person. It should be based on how much material they have gained throughout the topic. There are many resources that we sometimes forgot, but when it comes to this class definitely take advantage of them. Lastly, it is important to review Cal 2 as it will play a big role and studying is a MUST in this class.
From the beginning of the semester i would like been told, to practice and review some topics from calculus 1 and 2, things like derivatives, chain and product rule, and integrals, those topics are the bond for this class, and you will encounter with them in each topic teach in deferential equation.
The topic i found most challenging was Bernoulli Equations where you have to find a solution to the complementary equation then make a guess… I found it difficult because i was still trying to understand First order non homogeneous equations which both have similar steps, and also there were things from calculus 2 that I forgot about over vacation. My advice for you guys that are just coming from vacation and starting this class, is just review from calculus 2, and put your best effort in the first lesson because if you understand it, everything is going to be easier throughout the semester.
i agree with you i wished i studied those topic more which could’ve made this class much easier
I would have to agree on this because from calculus 1 to calculus 2, there is a jump in information that we must learn and understand. But coming into this class I feel like there is a huge jump of information that we must understand, study, and practice to fully understand the class
What do you wish that you had been told at the start of this class, to help you succeed? i wish i was told how hard this class is and then i would’ve taken more serious from the beginning i though it was going to same as calc and did not take it serious which affected my exam grades in the first half of the semester, if i knew how hard this class was i would’ve studied harder and paid more attention in class.
In the start of this class it’s important to know that the skills you learned in Calculus 1 and 2 will be transferred over. In order to have a successful semester you will need to study for the exams, it is also very important to do the HW’s it will help you prepare for the exam. Another few tips are to go to office hours, reach out to your peers, go tutoring, work on the review sheets, and watch youtube videos. There are many different methods of studying so DO NOT FEEL ALONE ! What I learned at the beginning of the semester is that you can not give up, but to try your best. One topic I found challenging during this class was reduction of order which was solving second order linear ordinary differential equations. This topic was hard at the beginning because I struggled a bit with derivatives, which shows how important Cal 2 is in this class. I would say watching youtube videos was very helpful when it came to relearning derivatives. Another way is going to office hours which was very helpful when it came to HW’s and reviewing topics from class. When it comes to math classes it’s not the grade you get in the class, but it’s how much knowledge you have retained. The most important prior knowledge you should know is always be prepared; study beforehand. It will be crucial to studying as that is what will help you throughout the semester.
The advice to look for other resources to understand some of the material is extremely helpful. Sometimes it takes a different approach to understand a problem, and I’ve found myself sometimes looking at YouTube videos regarding certain problem types, seeing a different method and then going BACK to the lecture notes and suddenly things clicked and those notes made sense. Neurology is complicated and brains work in unintuitive ways, and sometimes it takes a few videos of different kinds of material for the neurons to click it all together.
Office hours is also an INVALUABLE resource. If stuck on something, going to office hours gives you some one on one time with the professor where we can both find together, just exactly where you stumble on a problem and how to fix it. Lots of Eureka moments there if you choose to take advantage of it. Definitely don’t disregard the opportunity.
The biggest piece of advice which I wish someone gave me when I first started this course is to go back to all my previous math classes, especially Calculus 1 and 2 and practice integration. Practice it a lot, with different kinds of problems. The reason is that, throughout this whole class, I found integration to be the skill and tool used the most for almost any kind of problem. In fact, integrating is so abundant in differential equations that when you are lost on the next step, if you just guess that you have to integrate something, you’re often going to hit the math jackpot.
During the course, practice, is the most important tool I believe to grasping the material. Even if you feel like you understand everything in a topic or about a problem, if you aren’t practicing solving it, you are bound to be guaranteed to trip up on the exams. Another skill that I think is very valuable and underlooked in this class is speed. We are conditioned to take our time and “don’t rush” is the usual advice given for all math students in all classes. However, the problems in differential equations can be so long and involved that taking your time can be the difference between surviving and not on an exam. Speed doesn’t mean “rushing” through a problem but rather being comfortable enough with the steps that you can do them quickly, especially the smaller easier steps (your guesses, your basic integrals etc).
The one topic I found to be the most difficult is Bernoulli equations. It’s a topic that comes up fairly early in the course and can really catch you off guard. I had a lot of trouble with finding the integrating factors and performing the necessary substitutions, that it really tripped me up. Since it comes so early in the course, I was really worried that the rest of the material will be this confusing, but the rest did not turn out to be so unintuitive for the most part. For any future studentss trying to master it, my first bit of advice is to just go with the flow, don’t try to dig in too deep and follow the steps. Even if the steps dont seem like they make sense…
The biggest piece of advice which I wish someone gave me when I first started this course is to go back to all my previous math classes, especially Calculus 1 and 2 and practice integration. Practice it a lot, with different kinds of problems. The reason is that, throughout this whole class, I found integration to be the skill and tool used the most for almost any kind of problem. In fact, integrating is so abundant in differential equations that when you are lost on the next step, if you just guess that you have to integrate something, you’re often going to hit the math jackpot.
During the course, practice, is the most important tool I believe to grasping the material. Even if you feel like you understand everything in a topic or about a problem, if you aren’t practicing solving it, you are bound to be guaranteed to trip up on the exams. Another skill that I think is very valuable and underlooked in this class is speed. We are conditioned to take our time and “don’t rush” is the usual advice given for all math students in all classes. However, the problems in differential equations can be so long and involved that taking your time can be the difference between surviving and not on an exam. Speed doesn’t mean “rushing” through a problem but rather being comfortable enough with the steps that you can do them quickly, especially the smaller easier steps (your guesses, your basic integrals etc).
The one topic I found to be the most difficult is Bernoulli equations. It’s a topic that comes up fairly early in the course and can really catch you off guard. I had a lot of trouble with finding the integrating factors and performing the necessary substitutions, that it really tripped me up. Since it comes so early in the course, I was really worried that the rest of the material will be this confusing, but the rest did not turn out to be so unintuitive for the most part. For any future studentss trying to master it, my first bit of advice is to just go with the flow, don’t try to dig in too deep and follow the steps. Even if the steps dont seem like they make sense…
I agree with your point about practice being the most important tool. The more you practice the more you are training your brain to make those quick-“in the moment”- judgements about the next step, which in turn helps cover the speed thing.
I wish someone would have told me to be ready to get pushed out my mathematical comfort zone. By all means there’s going to be a lot of things you recognize and understand, which only makes sense. The thing is there’s so much different mathematical topics and theories you’ll be exposed to with general roots in calculus. So although some things may seem familiar you’ll be hut with something new to work with almost every other class. Definitely, pay attention and be sure to follow the notes and examples they will be your best friend and guide through a lot of your math problems.
If I had to say which topic I found the most difficult would probably be the Taylor/Maclaurin Series. Series is something I’m sure we’ve all dealt with before and isn’t too hard to grasp in any way, but when it come to being a solution to a differential equation there’s a lot of and I mean a lot writing and computations that are easy to get lost in.
Oh! Forgot all about the Taylor series struggles I’ve had. It’s not so much the concept, but for this type of problem, there is a lot of mechanical work which is incredibly time consuming, hence my previous comment about developing speed.
Agreed. Differential Equations is a class where you will get out of your comfort zone. There is a lot of topics that require tedious steps such as Taylor Series and Euler’s Method. What I have learned in this class is that it’s not about memorizing, but to understand how a question is solved and the approach used.
1: What I had wish was told about this class, was the amount of work is required just to solve one question. The steps that must be followed in order to crack on part of the question, then using that part of the first you must follow up with the second step. And how all of these steps are very important because one mistake you make your whole question can be completely off.
3: One of the most important prior knowledge that is key to succeed in this class would have to be time management, which would seem really obvious at first, but once you get to started in this class and get all the homework and practice exam and start on the exam you will see that time is one of, if not the most important skill to master. I would see that I would run out of time during my exams, so knowing how to time everything is really important in succeeding in this class.
I agree with your first point and time management when it comes to this . It is important to understand each step of a problem because as you said above it may make your question completely off. Like you I have also ran out of time during exams.
The amount of work required to solve the problems can be scary for newcomers I definitely agree with that. I think if students brush up on calculus 2 they will have an easy time keeping up with the work though. Although it is time-consuming it isn’t really difficult per se when you thoroughly understand the concepts. Responding to part 2 of your comment, time management is absolutely crucial to do well in this class. Keeping up with webwork, lecture notes, and studying for exams as well as having to deal with other classes Is quite the task. Definitely have a spreadsheet where you keep track of all your classes and learn to work smarter, not harder.
Some things I wish I was told to further benefit myself in this class was how much Calculus II is required to understand most of the topics in this class. Most of this class’s work relies on a great understanding of integration and its methods. To be ahead of the game when it comes to this class, I would advise looking back at some of your work pertaining to the topics of integration (integration by parts, and u-substitution more specifically). This course also has a heavy usage of exponential (e^x, 1/x, ln(x)) and trigonometric (sin(x), cos(x)) functions in tandem with integration, so there’s another thing to investigate as well. I also would add to review how to solve system of equations, though this isn’t heavily used in this class such as integration, it is needed and it is good to know how to solve the equations (elimination, substitution, Cramer’s Rule, etc.). By nailing down these topics, this class will become much easier in terms of learning the new material in this class.
I would like to say that you are completely right, and I 100% agree. Just like I also mentioned, Cal 2 is very important to understand when trying to learn any aspect in this class. It is also critical to know that some problems may require more than one type of method to be used to solve the problem.
Before I started this class I wish I was informed about reviewing topics such as derivatives and integration from both calculus 1 and calculus 2. The reason for this was I never realized how important these topics would be when trying to solve majority of the problems in this class. Also it would be helpful to go over the trig identities due to the fact we have seen them come up in some problems over the semester.
Something prior I wish I had known before taking this course is how serious this course is. Also I wish I had known to put more time into studying for this course. I thought this would be like every other math course. However after going into topics such as Bernoulli equations and second order nonhomogenous . Due to this I started to spend more time doing the web work assignments along with studying more to fully understand what was going on within the course. My advice is if you are stuck on any topic try to get help as soon as possible from classmates, course notes , or even from online such as youtube videos.
I agree, videos help a lot. I remember rewatching course videos and looking up video explanations on YouTube which helped me a lot in understanding the material.
I agree that students should review over Calculus 2 as a lot of methods which are used there are also used in this course. The problems for this course are definitely more time consuming which is why it is important to study old and new material and can be done as you stated by looking over outside sources such as YouTube videos or other classmates.
I would tell them to do the homework and study, even after class is over review what the professor went over. So that you can solve problems efficiently, these problems take time to solve, time that you do not have, so keep practicing and make it like a second nature to you and you will breeze though exams. Bernoulli equations were the hardest so I’d suggest putting a lot of time into that. Calculus 1 and 2 would actually help you understand this course easier, if you take differential equations before these two it would be as if you are learning all three in the same time.
I find this to be correct because how are you going to retain the information without writing it down. That’s where the homework comes in with it being on Web Work we can do the work on paper and put our answers from said work to see if they are correct (which is really nice because it serves as a check in case you did it wrong). Indeed Bernoulli problems would take forever to complete with all the steps and was pretty hard. The prerequisite to Differential Equations is Calculus 2 so it would be really hard to take it before.
I wish I had been told to be prepared to make mistakes on homework questions with a lot of steps, which will cause you to start them over more than once in order to get them correct on webwork. Many topics in differential equations require patience because when you’re dealing with an equation for the first time you are bound to make mistakes. I wish I had been told that the constant do-overs on specific equations are good,because it will force your mind to remember those steps, which will help you succeed.
I agree, at times I found some of the homework questions to be long, tedious, and other times down right confusing. However, once I had figured out the steps, the question became so much easier that I could then answer the next questions with a proper approach. The approach is what’s really important when it comes to the homework because you can use that approach on the test.
I totally agree Rashan! Mistakes are going to be made, but that isn’t the end of your semester! Patience is definitely key in this course along with a disciplined study schedule and repetition.
For a student now entering MAT 2680, I would tell them to understand the different types of differential equations and to grasp the concept of doing them in different steps. Different integration methods require different steps and some may be longer than the other so it would be best to understand what’s being thought from the starting because it progresses into the next chapter sometimes using similar steps.
Also for someone who doesn’t really understand the concepts there is always office hours you can attend to try to better your knowledge of the topic. Try your best to do the homework as well, because they help you to practice and understand more.
The most important prior knowledge that you will need in order to succeed is the ability to talk to people. It is important because that how you make friends, go to tutoring, and/or go to the office hours. By talking to people you can make friends and have a second opinion on homework and class work. By talking to people you can tell the tutors where you are struggling. By going to office hours and talking to the professor they can get a better idea of what you understand and where you need help. If you don’t talk to people then it is very hard for anyone around you to help all they would have would be your number grade and that’s it.
I must agree, studying alone takes time especially when you’re struck on problem. But tutoring and study group everyone can share their thoughts together and make it much easier to study.
I agree with you Anthony about talking to people because it will help to make new friend and also will improve our communication skills which would help in future in our field as well as our daily life. I also agree that going office hours because not every class we have that option and when we have in this class than we should grab the opportunity because this would help us to understand the topic more in depth. I guess before we go to office hours we should review the lecture reading first and then go to office hours because reviewing it before will give us idea where we are struggling or we don’t understand.
I would tell them to do the homework and study the past exam, tutoring helps a lot in the early stages of the class. Most problems in this class take a lot of time to solve but I find that with a clam mind any question can be solve and even if you cannot finish in time submit it anyway to earn some credits, those one points adds up. Lastly, you can get a lot done if you study together make sure to make a study group of some kind at the beginning of the semester, it’ll save you a lot of time.
Homework is the key to passing, especially with this class and I wish I knew that earlier. Studying helps too but not as much as actually practicing the material like with homework. Also like in my post, this class isn’t for the weak, many of problems we faced required additional steps and configurations which can be overwhelming at first glance but with the proper mindset and guidance, anyone can persevere no matter how complex the problem.
Some things I wish I had been informed to help me succeed in this class are that Calculus II is the precursor to Differential Equations and that you should set aside time to do assignments. This is more for personal reasons, but doing homework for this class took too much time to fit in with job, other classes, family, and relaxation. Anyone else in my situation should make a balanced schedule and have a strong will since this class is not for the faint of heart. The majority of the content assumes a thorough familiarity of integration and its approaches. When it comes to this lesson, I recommend going over some of your previous work on the themes of parts integration and u-substitution review. Though not as commonly employed in this subject as integration, the ability to solve systems of equations is required to solve the equations.
What is the most important 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 that upcoming students need is to review calculus 2 and in specific derivatives as they play a role in the topics you will learn throughout the semester, many of the rules which were introduced in calculus 2 transfer over to MAT2680 which is why you should keep previous notes organized even if you think you won’t need them it’s always better to have them ready just in case.
What do you wish that you had been told at the start of this class, to help you succeed?
Be prepared to spend quality time to solve a problem as one problem can have numerous steps before coming to a final answer, I find this can be discouraging to students as it may be possible to get lost in the middle of a problem and if this happens to be the case don’t be afraid to ask classmates or professor for assistance as it will only benefit you as the semester advances. Also do not underestimate the power of note taking, it is important to organize your notes in a way where you can look back at a topic whenever you need to such as studying or for homework, the problems which are shown in class are similar to those in the homework and exams so always write down the in-class examples.
Differential Equations is definitely a course in which you need to spend the appropriate amount of time studying for. What i wish that i had been told at the start of the class is to make better use of the college’s online tutoring seminars as well as utilizing professor office hours. One of the more challenging topics in this course can be the Taylor/Maclaurin Series problems. It’s not necessarily all too difficult, but it is time consuming and I do remember running out of time during one of my exams due to a Taylor Series question. The most important prior knowledge that is needed to succeed in this course would be the methods of integration that you learn in Calculus 2.
I wish I would have told that I have practice some of the important things from my previous math courses. Such as integration as well as Taylor/ MacLourin series from calculus II which I think would help me a lot in this course. I also there is a lot of thing that differential equation has similar to calculus II such taking partial derivatives, integration with u-substitution, integration by parts and power series and we have done all this in course to solve a problem. Also even through I have don’t remember a lot of this but knew some of them which helped me but if I would had know all of them which would have helped me a lot to succeed in this course.
One of the topic that I think was challenging was doing the Second Order Nonhomogeneous because it was kind of challenging to find the non-homogeneous solution to the differential equation. After finding the non-homogeneous solution it become more easier to find the general solution but some time it was harder to find the particular solution because when I add the initial value to the problem some missed the calculation or the sign which can easily lead us to get the wrong answer. So I guess we should have check twice our calculation before submit our answer. Also I think it would be helpful for us watch the lecture video as well as the lecture because we have this opportunity to watch the video which we might don’t have it for other class so when we have that chance we should grab it with both hand. I also personally think the lecture note will help you a lot when you are stuck or you also have an option to go office hours and professor will help you every angle he can help you a lot because when I had difficulty with any problem I will go to his office hours and it helped me a lot.
I guess other than the work in class we should have focus on time management which would help every students because I personally think time management will be key of success. Also we should focus in class when professor give an lecture and ask question if you don’t undestand anything or you can ask the question in office hours which would be very helpful for you because not every professor has an office hours to help you. As I said in second paragraph that we should watch the lecture video and read the lecture reading. Also we practice more and more because practice will make us perfect and will help us to succeed to the course.
At the beginning of this class, like other I’m sure said, I wish I was told to review material from cal 1 and cal 2. A lot of the material is very still relevant and key building blocks when learning new material in this class. I also wish I had reached out for help earlier in the semester. I realize that I’m not alone and there are many ways that I could’ve been helped.
The webwork homework is also not the best way to practice, if you get the answer wrong, that’s it, no credit, no partial credit, and no other way to try and understand the problem. Our class was also all online learning, which I personally didn’t find to be very good when taking a class.
One thing I wish I would have been told before starting this course is that it’ll need the most dedication you’ll probably ever need for a course. My other courses you have to study/practice of course, but with this one you REALLY need to. If you’re able to get an A in this course that very commendable in my opinion. One of the most important knowledge to have prior to entering this course is good study habits. You could wing it in some other classes, but this one you definitely have to.
I agree that it’s really important to practice solving problems. I had the most trouble with the third test which didn’t have as much homework problems and I didn’t get a chance to do the practice problems before the exam.
Coming into differential equations for the first time honestly, I didn’t know what to expect. I quickly learned that my calculus 1 and 2 foundation was not strong enough to sustain the work that was given to me so if there’s anything I can recommend before you walk into this class is to review calculus 2 concepts and brush up on things such as integrals, derivatives, etc. Youtube has some great content to brush up on and review, promise it would only take you a couple of days. The most challenging topic in the class for me personally has to be hands down Bernoulli equations. You need to be patient and really buckle down on these to understand them properly and even more to be able to solve them. Finally, some advice I can give you anon, always be on track with your work, you miss even one-two lectures and it’s like you are on a whole different planet. Trust me, make a spreadsheet or to-do list if you have to. Most importantly, just trust your abilities and intelligence and you’ll make it out fine, breathe.
The most used skills for Differential equations are algebra, differentiation and integration. If you have trouble with any of these then it’s a good idea to practice them before learning differential equations. In particular, logarithms and polynomials are used a lot so you should learn how to differentiate and integrate them. Integration by parts is also used often so you should know how to do that as well. If you have these basic skills then you shouldn’t have trouble with the class as long as you do each problem step by step.
If a student were to begin Math 2680, I would advise them to practice and review what they learned in Calculus 1 and 2, since some of the ideas taught in those classes transfer into Math 2680, which will greatly benefit them. However, take the given assignments seriously because they will serve as a great review for the tests. The most difficult topic in this course for me was “Modeling Population.” I was concerned about how the other topic would be after this one because it was so tough to understand. Yet, all the exercises that were provided as a practice were quite helpful. Because of the number of explanations, you had to make for only one question, the equations required a long time to complete in class and on tests. So, I’ll suggest that time management is crucial if you want to succeed in this class.