Assignment, due Monday, 12/16/24 (300 words minimum): Imagine that you are invited to speak on the first day of MATH 1575, to give advice to entering students.  Write at least 300 words responding to one or more of the following questions, describing what you would say to the class.
- 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 elseâs comment. Do you agree? disagree? Have anything to add?
I wish I would have been told to not miss a class without good reason. The reason is because the lectures from one class helps with doing the topic of the next class. If you need to miss a class to just take a break for your mental health, then at least look at what topic you are going to miss and try to watch a video or two to get an idea of what you are missing. If the videos donât help you fully understand the topic, then ask questions in class or go to office hours, if your schedule allows it, and ask questions then. Furthermore, you need to carve out time to do the review sheet for the test. If you are one of the students who arrive to class before class starts, I suggest doing problems from the review sheet then. For the discussion assignments, I would say to just do it as soon as possible to get it over with. Just share what comes to mind and not think too hard, even if you think why do you need to do a small writing assignment for a math class. By not doing the discussion assignments, you lose easy points and it is not even by doing a math problem. The last thing is to find the best way to study personally. If you have or find a method that works, then you would be less stressed when test day arrives.
The first thing I would say is important prior knowledge is the different rules. It is used a lot when doing integration and is useful when you canât automatically do it in your head. The second piece of knowledge is how to change a square root into an exponent to make it easier to apply other rules or just make integration easier to do. It also helps with the third piece of knowledge which is to know how to flip a fraction that has an exponent. All this prior knowledge will help with what will be taught in Calculus 2, and makes the class a bit easier because that is a couple of less things to worry about.
To start this off, this was probably the best Calculus class I have taken because of how all the materials were taught and even though I get really nervous when working in groups, those group works helped me a lot to understand the topics. One thing that I wished someone told me before the start of the class is that, getting practice outside of class is super important in order to understand and maintain that understanding of a topic. Making sure to do all the homework assignments and don’t start cramming last minute for exams, as well as showing up for class helps a lot with succeeding in this class. Additionally, in this class that thing that was the most challenging was trying to memorize formulas, especially Trig Functions and rules, because there are so many and it got really confusing. So I recommend to find little tricks and patterns that can help you memorize those functions and rules and make it a habit of whenever you have to use those trig functions or rules, refer back to the trick and patterns to help you remember what it is.
I agree, your advice about practicing regularly and using tricks to memorize formulas is practical and relatable great insights for future students.
I agree I definitely missed a few assignments. I would’ve told myself to do the assignments earlier and not procrastinate.
I agree on the topic of trig fun being more of the challenging topic in this class, due to the sheer steps and rules that needs to be memorized
Seeking practice on this course is definitely important! This course is specially challenging not only because there are a lot of formulas to memorize, but also because you also need to develop a skill to anticipate when and where to apply each formula.
Starting a new math class can feel overwhelming, but with the right mindset and effort, youâll do great. One thing you should know right away is how lucky you are to have a teacher who truly cares about students. Our professor doesnât just teach, they take the time to explain each concept step by step, ensuring that everyone can follow along. If you ever feel confused, donât hesitate to ask questions. Your professor is not only knowledgeable but also active and approachable, always willing to work with students individually to address their specific needs.
As a student, Iâve found that success in this course depends on two main things: staying consistent and asking for help when needed. The material builds on itself, so itâs important to keep up with the work. Set aside time every day to review your notes and do practice problems, even if itâs just a little. Youâll thank yourself later when youâre able to tackle more complex problems with confidence.
One topic that students often find challenging is derivatives, especially when applying rules like the chain rule or combining multiple rules in a single problem. My advice is to pay close attention during lectures because the professor does an amazing job breaking these down into manageable steps. Donât be afraid to ask for clarification if youâre stuckâyour teacher genuinely wants to help you succeed.
Lastly, make sure your algebra skills are solid. While this isnât an algebra course, youâll use those skills constantly to simplify expressions, solve equations, and work through calculus problems. If you feel rusty, spend some time reviewing.
Remember, this course is a journey, and youâre not alone. Lean on your teacher and classmates, stay proactive, and trust the process.
Hello Min, I definitely agree with you about professor’s teachings and how he is lean towards us students. Professor Reitz is always eager to help us, even if it’s about math concepts from previous math courses. His office hours were very helpful to me. because I would be stuck on a topic and professor would go over each problem step-by-step which really helps with grasping math concepts.
Hey Min, I can 100% agree with you on staying on top of the workload and setting time aside to review your notes. In this course, there are a lot of formulas and key concepts, such as the trig identities and their derivatives, that are helpful to memorize because they save you a lot of time and also help you see the connection between them when tackling a difficult problem. Also as you said is also helpful to reinforce your review of notes with practice problems through WebWork cause they give you that first-hand experience of tackling problems at all levels of complexity.
In the beginning of the class, I was nervous because I did not know what to expect in the class. I was able to understand the teaching from the professor really well. The groupwork and the classwork discussion was very helpful in the class. The most enjoyable thing for me in the class was definitely the group work because it allowed the students to work on problems on our own but also help each other out. Though, not related, I did have at home/out of school issues which did affect how much time I could put in math. However, the class organization is really good. The professor teaches with enthusiasm and explains things very detailed. Thus, I have nothing that would’ve told myself in the beginning, except use the little free time I had to study.
One topic in the class that was the most challenging was the limits. I think that there were a lot of rules to remember which caused me to overthink sometimes. Sometimes I did not know what rules were used for which problems, which is really frustrating.
I think the most important prior knowledge taught in school was definitely trigonometry. There were many calculus problems involving sin, cosin, and tangent. I am very very happy I know the values of some of the trigonometry problems.
One thing I believe I should’ve done was watch more videos on the math problems to be able to answer the problems with confidence. There were some personal regrets I had during the class, however I hope do improve on my lacking’s. I appreciate the professor for being really easy to get to and the enthusiasm he has to teach the class even though sometimes I am very tired in the morning haha. Overall the class is a 10/10.
I agree with you on the value of group workâitâs a great way to collaborate and understand problems better. I also understand your struggle with limits; there are a lot of rules to remember, and it can be tricky knowing which one to apply. Practicing with simpler problems can help approach it. Trigonometry is definitely crucial for calculus, especially knowing the basic trig functions. I agree that it made a huge difference in solving problems more easily. Your idea to watch more videos is great! It is helpful to reinforce it with what youâve learned, especially when youâre struggling with confidence. The professorâs enthusiasm and support is definitely very good and helpful.
I wish someone had told me about practicing problems from each topic, having different examples for us to practice, or watching a video about the topic since they provide more examples and explain it further if you didnât understand the topic clearly or taking a peek at the textbook, especially if they carry example that you didnât cover in class, Example with steps and explanations would have a big impact on understanding the material. Another tip is to try to use the textbook and read it beforehand, learning about the material can allow you to ask questions or request a problem in the textbook that you donât understand.
I think the topic that is challenging for me is the trig function due to there being so many rules and steps that if you did the calculation one bit wrong, the whole answer is going to be wrong, I think to master it, is identifying the different problems and understanding which rules that you need to apply, or doing a lot of practical problems, where when you see something similar, you can immediately know which rules to apply.Another tip is to not rush the learning process as pressuring yourself make you forget it easier, but with practice and longer, spaced out time, would allow you to absorb the knowledge easier.
I think the most important prior knowledge is to not procrastinate either on studying or homework assignments, as studying beforehand using those given problems to find something similar, and trying to solve them ( maybe one and a half to two weeks in advance). For Homework Assignment, I think we could’ve copied the homework problem down, and while the professor is done with the lecture, try to solve it after class immediately, or asking for assistance/ help if you donât understand.
An important thing to keep in mind during this course is that it can and will be more challenging than you imagine. My advice would be to always get some practice on each of the topics the same day that it is taught to you. This way, you would be able to retain information much better and you could pick up on some things that you might have missed during the lecture. If you donât understand something, always ask your questions, and if you need help, there is always a tutoring center. Do not hold your questions, they will come back only to haunt you.
The hardest topic to master in this course, for me at least, was using trigonometric function to solve an integral. Since the beginning of my academic carrier, math was but a topic full of specific formulas where all we had to do was plugin numbers and hope that the final calculation is correct. This was not the case here. As the professor said, the trigonometric identities used in this topic are merely tools which you can use to solve a problem, but they will not guide you to a solution immediately. It is up to you to master these tools. My advice? Practice. Or watch videos, do whatever you need.
Do not abandon any skills you learned suffering through your Calculus I course; they are not ready to say goodbye just yet. Trust me, you will need them if you plan on succeeding here. One particularly useful skill that you will see pop up often is to take the derivative of a function. The professor will most likely not have any time to go through all the process of reexplaining derivatives, so if you donât know how, you will get lost, so if you are not clear on your derivatives, this is your sign to start practicing.
This class was pretty challenging. I am personally not a big math person but this class has taught me and also helped me accept math more as a whole. At the start of this class, one thing that I would have suggested myself is to really hammer into your head all of those different topics but also study a lot more, even more than you think you should, because trust me, you will need it. To help yourself succeed in this class, I believe that learning and practicing by yourself is probably just as or possibly more important than listening to lectures. It may sound cliche but practice makes perfect, and if you don’t practice anything here, it just is not going to work out for you well.
Some of the most important prior knowledge that you need when it comes to Calc 2, is most definitely having a good understanding of calculus 1. Much of calculus 1 carries over onto this class but not all of it, personally I found calc 2 to be much more vague with its material, where you really just have to solve problems in your own way. A good understanding of prior topics even when it comes to stuff like algebra is much needed as most if not all carries over to much more advanced math courses. One topic in this class that I found challenging but also interesting is this whole area of sequences and series. At first, I was a bit familiar with sequences since it is a topic somewhat related to my other classes like data structures and algorithms, but when going deeper into the topic, I realized that it is a much tougher topic compared to what I already know, especially the whole series side of things. To wrap it up, this class was really challenging but also taught me a lot, it requires a lot of effort and practice but once you get a grasp onto things, it may just get a tiny little bit easier, even if its just a little, its still progress.
The best advice I could give to anyone is that you don’t know what you don’t know. This lesson I learned when I was in calculus 1. I was feeling overconfident because I basically glided my way through pre-calc. The 68 I got on the first exam was enough to wake me up. Thankfully our lowest grades were dropped. But the most useful part of learning, in my opinion, is being able to correct your mistakes. The notes I take are often messy, sometimes illegible if I’m moving too fast. But what I noticed helped me the most, was when I wrote down every single thought and misunderstand. If you have a question, write it down. If it doesn’t get answered through the demonstration, thatâs when you ask to clear things up. Whenever Iâm at home doing the work, I make sure to go back to those notes. Everytime I get stuck on a particular problem, thereâs some chicken scratch in the margins that tells me exactly what to do in that scenario.
Additionally, you can’t expect your professor to do all the thinking for you. Mindlessly writing whatever comes up on the board will do more harm than good. I love math because it has a purpose(most of the time). Derivatives made absolutely no sense to me, until I watched some videos on what it was actually used for. Because of this, I was better able to visualize the numbers in my head; as well as have an idea of what the answer would look like. The point is, when you actively seek out where you have blind spots on a certain topic, the payout is always worth it. That conceptual learning will give you a newfound appreciation for the process. Unless itâs rational integrals with trig functions. For that you’ll just have to practice problems until you wake up reciting formulas.
One piece of advice for this class is to try to get to class a few minutes early. Professor Reitz usually arrives ahead of time and is available to answer any questions, whether it’s about a homework problem or something from the previous class. I didnât have time to attend office hours, but those 10 minutes before class, where he’d go over problems, really helped clear up some confusion.
Another tip is to take advantage of the partner work in class. Many people in this school don’t talk to one another, but this class is one of the few where you’ll have the chance to work in groups. Be sure to exchange phone numbers, Instagram handles, and/or emails so you can reach out when studying for exams, doing homework questions, or catching up on notes if you miss class. My last piece of advice is to review your notes and memorize the different tests. I lost a few points on an exam for misnaming the ratio test.
Math has always been a strong subject for me, so my challenge with this class was less about the content and more about OpenLab and Webwork. Most classes donât include participation in the grade, but we do in this one. My best advice is to get familiar with OpenLab and complete the discussion posts and comments. There are a few videos explaining how to create posts and type out math equations if you need help. Another thing to note is that OpenLab sends everyone in the class an email each time someone posts or comments, which can get annoying, but you learn to manage it. My other issue was with WebWork. Sometimes the questions can’t be solved or require you to type in the answer a certain way so it can be accepted. Or the question can be tricky or difficult to understand. My advice is to work on WebWork early so you have time to figure out any confusing parts and bring the problems to the tutoring center or the professor. You might even have time to use the WebWork help feature for assistance.
I thought calculus 2 would only be a bit harder than calculus 1. But no. This class is not for the weak, problems are always multi-stepped and it’s not always clear what the next step is. One thing that makes this math class different is that this class requires abstract thinking more than previous math classes. Most of the time you will be asked to find your own path to answer questions.
Memorizing formulas is also crucial to succeeding in this class. You will be asked to remember a ridiculous number of formulas and standard integrals. In addition to these, you will also be required to recall stuff from algebra, calculus 1, trigonometry, and geometry. If there ever was a time when you cheated on a test instead of understanding the material, this class is where it comes back to bite you.
Try not to take morning classes, especially this not class. Even if you had enough sleep the night before chances are, you will still be tired. Being tired in this class will cost you, much more than other classes. Because of the abstract nature of calculus, not understanding the concept thoroughly will leave you feeling lost very quickly. Calculus builds on itself, so if you miss one idea, itâs like trying to build a house on a shaky foundation, it wonât stand. Stay alert, stay engaged, and donât be afraid to ask questions. Asking questions in class or during office hours can clear up confusion early before it snowballs.
The hardest topics for me were series and sequences, especially when dealing with convergence tests. At first, it feels overwhelming because there are so many different tests to rememberâRatio Test, Root Test, Comparison Test, Alternating Series Test, and so on. My advice is to practice each test individually until youâre confident about when and how to use it. Create a âcheat sheetâ
summarizing the conditions for each test. Practice recognizing patterns in series problems, so you can quickly identify which test applies. And remember, just because something looks intimidating doesnât mean itâs impossibleâbreak it into smaller parts and take it one step at a time.
To wrap it up, approach this class with discipline, practice a lot, and donât get discouraged. Itâs tough, but if you put in the work, you just might pass.
Entering MATH 1575 can feel overwhelming, but with the right preparation and support from your professor, it is possible. If I were to speak to incoming students, hereâs the advice Iâd give: One thing I wish I had been told at the start of this class is to practice foundational concepts before moving on to more complex topics. A strong understanding of algebra, trigonometry, and limits of functions is essential, as these are the building basics of calculus. Reviewing Calculus 1 concepts, such as derivatives and basic integrals, will also help ease the transition into more advanced topics. Donât overlook these early stepsâthey lay the groundwork for everything that follows. A particularly challenging topic in the course is integration techniques. It can feel overwhelming at first with methods like u-substitution, integration by parts, partial fractions, and trigonometric substitution. My advice is to practice each method individually, focusing on when and why it is used. For example, integration by parts is ideal for solving integrals involving products of functions. Volumes of solids are another tricky topic that can be intimidating. Visualizing the object, setting bounds correctly, and understanding the geometry are critical. Regular practice will help you to better approach these questions and recognize patterns in problems more easily. Another important factor for is to have a practice of functions and their graphs. Concepts like domain, range, and transformations are critical, even if they arenât explicitly taught. These skills of practicing will improve your understanding of limits, derivatives, and integrals and help you verify solutions through visualization. Lastly, always stay organized and manage your time well. Review notes regularly, attend every class, and practice daily. Do not hesitate to ask for help from classmates or your professor. With persistence, effort, and help from the professor, students are able to do well.
I agree on your statement because key is to Memorizing information might get you through a test, but truly understanding the concepts allows you to apply them in different situations. Break concepts into smaller parts and connect them to what you already know. To don’t struggle yourself use Resources like office hours, study guides, online tutorials, and classmates are there to help you succeed. Donât try to do everything alone.
1) Before entering MAT 1575, I wish I was told to review concepts from MAT 1475 and recall any math material such as algebra, trig and geometry to catch up to a new material faster. I had an idea that math in general is built upon previous topics, but I did no think that it would heavily rely on past mathematical courses. For example, I did not think that I would have to review geometry concepts when stepping in to Calculus II, however topics like trig substitution, area of curves and volume of revolved 3d solids utilize some geometrical shapes and Pythagorean theorem. Also, basic idea of limits and L’HĂ´pital’s rule is definitely good to know from Calculus I that is used in convergence/divergence tests that deal with limits as we take an improper integral for example. Overall, my advice would be to have Calculus I topics fresh in the mind as it would be useful to catch up to Calculus II topics right away without taking days to review derivatives and limits.
2) I find trig substitution topic especially tough, because as we take an indefinite integral, we can’t use u-substitutions or integration by parts as our beginning method, therefore we have to go back to trig functions and identities to replace variable “x” with “theta”, so that we can break down the integral by canceling out some of the trig functions. That’s where the challenge starts, since it’s important to memorize trig functions, their derivatives/integrals, integral identities and Pythagorean theorem to find hypotenuse and convert “theta” back to variable “x” for our final answer. This plethora of memorization is crucial for trig substitution and even 1 missing symbol can leave us astray. In general, topic of trigonometry is very sensitive, in case that we have to remember bunch of functions by which we need to cancel out terms. Furthermore, we can’t forget about integrating as we go along with our trig substitution method. However, good technique to have been to make connections among these trig functions and find easier study method to recall them faster. Always good to review trig concepts, as they would definitely come back to haunt you in Calculus II course.
3) Prior knowledge that I have been carrying throughout college, is to not procrastinate and paying attention in class, because topics are built upon each other and it’s good to stay on top of everything. Also, studying about a week in advance is a good practice to have for tests and especially finals. Another piece of advice that I can give, is to talk to classmates and staying during office hours can increase awareness on the course which helped me a lot, especially math courses. Staying “present” throughout the semester is important, because having notes and staying in contact with classmates and professor can be crucial factor in passing the course.
I didn’t understand how crucial it was to keep up with the content when I first started MATH 1575. It seems like you’re always playing catch-up if you skip a week of math since it goes quickly. Consistent practice is the best advise I can provide. At least try a few issues each day; you don’t have to do a lot of them. Learning things gradually is considerably simpler than learning everything at once the night before an exam.
Sequences and series were one of the most challenging subjects for me, particularly when it comes to determining convergence and divergence. There are several tests to monitor, including the Integral, Ratio, and Comparison tests. It all seemed to be a blur at first. Creating a summary document that included each test, its requirements, and usage instructions was helpful to me. When working on practice problems, concentrate on identifying the characteristics of a series and selecting the most effective test. At first, it’s difficult, but with practice, it becomes easier.
I also wish I had realized how much trigonometry and algebra are used in this course. It is common to use trig identities, factor, or simplify equations. Reviewing such abilities early on is helpful if you lack confidence in them. Later, when things grow more difficult, it will save you a great deal of worry.
My main recommendations are to stay ahead of the curve, practice as much as you can, and go over whatever trig or algebra you’re lacking. Everyone struggles, so it’s acceptable, but if you persist and seek assistance when necessary, you will succeed. I wish you luck!
If I were invited to speak on the first day of MATH 1575 (Calculus II), my most important advice to incoming students would focus on one critical topic: understanding derivatives and the rules for differentiation. Derivatives are not just part of Calculus I; they are the foundation on which a significant portion of Calculus II is built. Without a strong grasp of derivatives, you will struggle to keep up, as nearly every new concept in Calculus II piggybacks off this knowledge.
In Calculus I, you learned how to compute derivatives using rules like the power rule, product rule, quotient rule, and chain rule. Additionally, you learned how to differentiate functions such as logarithms, exponentials, polynomials, and trigonometric functions. Calculus II requires these abilities; they are not optional. You will learn new and more complex concepts in Calculus II, including integration (the opposite of differentiation), integration techniques, and solving practical problems like arc lengths, areas, and volumes. You must work with derivatives and comprehend how they relate to functions in order to comprehend any of these subjects. For instance, when solving an integration problem using substitution, you must correctly identify derivatives within the function to proceed. Similarly, integration by parts, another key technique, relies on your understanding of the product rule for derivatives.
To put it simply, if your derivative skills are shaky, youâll find yourself re-learning basic Calculus I concepts while trying to keep up with the more complex material in Calculus II. This can easily become too much to handle. Before class starts, I advise you to study and become proficient in the differentiation rules. Spend time solving problems, especially ones that involve tricky applications of the chain rule and product rule. Understand not just how to differentiate, but also why the rules workâthis deeper understanding will make integration techniques much clearer when they come up in the course.
Lastly, I would advise you to embrace the perspective that Calculus II is a subject that builds on itself. Calculus 1 knowledge is not abandoned; rather, it is expanded upon. You’ll position yourself for success and make Calculus II’s difficult material much more approachable if you go into the course confident in derivatives. Also allow yourself to make mistakes and adjust to them, if you find yourself not understanding, office hours and before class are good times to hash out difficult problems and ask those critical questions that will open up conversations that lead to clarity.
One topic in this course that has been the bane of my existence was finding the volume of a solid when the curve is rotated about either the x or y axis. Prior to this everything came easy to me but this have been proven to be quite challenging.
Within this topic, there exists 2 methods to solving. That being the disk method and the shell method. I suggest to master this topic (I for sure have not), would be to do many examples as well as seek online resources. You can also consult with your professor.
My main go to online resource would be The Organic Chemistry Tutor. Since I wrote S.A.T’s, he’s been my teacher. He is well versed in every subject among different STEM subjects.In addition to him, again, one can get clarification from your professor or see a tutor.
Hey Gabriel. I think we do have challenges with the same topic lol. And the problem is really finding the rotation and setting up the function. After that it is straight calculations
**Success in Calculus 2: Advice for Students**
Calculus 2 can feel daunting due to its depth and complexity, but success is achievable with the right strategies. Looking back, there are several key pieces of advice that would have made a significant difference in my experience. Consistent practice, mastering challenging topics, and having strong foundational knowledge are all critical to thriving in this course.
The most important piece of advice I wish I had received at the start of the class is to practice consistently. It is not enough to follow along in lectures or feel comfortable with the material during class. Mastery comes from actively solving a variety of problems, including those that push you beyond your comfort zone. Waiting until exams to dive deeply into the material is a common mistake. Instead, setting aside daily time to review concepts and work on problems will help solidify your understanding. Additionally, seeking out supplemental resources, such as online tutorials or study groups, can clarify tough concepts and enhance your learning.
One of the most challenging topics in Calculus 2 is the *convergence and divergence of series*. This topic requires understanding several tests, such as the Ratio Test, Root Test, and Integral Test, each with specific rules and applications. Students often struggle with recognizing which test to apply to a given series. My advice is to memorize the conditions for each test and practice identifying patterns in series to choose the right approach. Creating a flowchart or decision tree can simplify this process. Practicing diverse examples and counterexamples is crucial for building confidence in this area.
Finally, strong prior knowledge in *algebra* and *trigonometry* is essential for success. These skills, though not taught in the course, are foundational for solving problems involving integration, series, and polar coordinates. Weaknesses in algebra or trigonometric identities can make even basic problems feel overwhelming. Reviewing these topics beforehand ensures you have the tools to tackle complex calculus problems with confidence.
In summary, regular practice, strategic preparation for challenging topics, and strong foundational knowledge are the keys to succeeding in Calculus 2. With persistence and the right approach, the course can become a rewarding experience.
I agree with you Ethan when you say it is not enough to follow along in lectures because I found myself copying the notes but not actually processing what was being taught. It really does help to take some time out and teach yourself any material that confuses you or that feels challenging.
What do you wish that you had been told at the start of this class, to help you succeed?
This I wish that you had been told at the start of this class, to help me succeed is know by hard the formula for each assign topics and make some. Struggling with concepts at first doesnât mean you wonât get there. Be patient, and give yourself time to grasp the material.
A little effort every day helps you stay on track and prevents last-minute stress.
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 especially challenging is indefinite integral that has the trig equations on it.
The steps to achieve it is Steps to Solve a Taylor Series:
Maclaurin series as the Taylor series centered around a=0
A Maclaurin series is the specific instance of the Taylor series when
a=0.
Remember that we can choose any value of
a in order to find a Taylor polynomial. Maclaurin series eliminate that choice and force us to choose
Remember that we would always use the formula
to build each term in the Taylor series. Since
]
a=0 in every Maclaurin series, this formula simplifies to. Finding the nth-degree Maclaurin series
Example
Find the seventh-degree Maclaurin series of the function. f(x)=sin(3x)
Since weâre finding the series to the seventh-degree, weâll use
n
n from
0 to
7
What is the most important prior knowledge (not taught in the class) that you need in order to succeed? Why is it important? Self-Learning Skills
Why Itâs Important: In any subject, the material taught in class is limited, but concepts often build upon each other. To truly understand, apply, or master a topic, you need to learn how to explore beyond the class syllabus.
Examples of Self-Learning:
Knowing how to research concepts online (e.g., using resources like academic papers, videos, or forums).
Developing critical thinking to connect the dots between topics.
Practicing âactive learningâ through problem-solving, summarizing, and teaching others.
Honestly, I was really prepared as I was registering for this calculus II class. Most of the people I know who have taken the class before told me it is challenging, and I should get ready for it. Some even said it was the hardest math class they had to take. But I am proud to say that this has actually been the least challenging math class I had to take and so for two reasons. The first reason is that from the very beginning of the class I started studying hard for it and the second one I had a great professor. I knew how to take advantage of the second reason because his explanations were so simple, direct and clear that it was easy to follow along. The class was engaging and at each class, I stayed awake, focused and active throughout the class making sure I understood the concepts and got every little detail to my brain. When I go home, I do not need to do extra work besides the homework. I think the part of the class I really had to study harder for is âApplication of Integrationâ. I would suggest that any upcoming student do not skip a single class during this chapter. This part is challenging not because it adds concepts from the previous chapter but because you do have to be a pragmatic and analytic thinker. So do not hesitate to do look for more assignments besides the homework to study or even go on YouTube to watch video of people resolving those applications. I think knowing how to find the derivative of a function is the most important prior knowledge needed to succeed in this class. This is important as from the beginning to the end of the semester, in every chapter we had to calculate the derivative or find the anti-derivative of functions. And I also believe that having a good notion of derivatives wonât just help you with Math 1575, but also for more advanced math classes.
I wish that I wouldâve been told to ask for help when needed. I felt stuck a lot in this class and I didnât attend any office hours because of my schedule but I shouldâve still made an effort to reach out to the professor. I had learned some of the material before but in different methods so I shouldâve asked the professor for the help which I very much regret not doing but I think future students should. I was told this class was easy but I found it a bit challenging. Therefore, donât wait until the last minute to try to learn the material. Ask for help the moment you feel like you donât even know how to start solving a problem.
I found derivatives a bit challenging. I used to be pretty good at it but over the summer I forgot everything and lied to myself and told myself I’d remember it when I see it but I didnât. It took me time to try to remember it again and teach myself it because at times I didn’t understand it the way the professor taught it. I would advise future students to remember how to derive before coming into this class as well.
The most important prior knowledge not taught in this class was the chain rule and the derivatives of the trig functions. It was necessary when it came to integrating. Itâs something that shouldâve been memorized before coming into this class. Like I said before, I lied to myself and said I knew how to do this but I forgot how to so definitely go over those topics because they are very important. A lot of the problems tend to include trig functions in them that can stump you so try to memorize as much as you can.
I totally agree with what you are saying, especially about asking for help right away. I think a lot of us feel stuck but hesitate to reach out, whether it’s because of time or thinking we can figure it out later. It’s so important to make the effort to ask the professor or classmates for help as soon as you feel lost, instead of waiting until the last minute.
Welcome to MATH 1575! This course is both exciting and challenging, and I’d like to share with you some advice I might have wished to hear your first day to help along the way.
Okay, well let’s first of all talk about preparation. The most important prior knowledge that you will need for this class is a strong foundation in Calculus I concepts, primarily, derivatives and integrals. Understanding how differentiation and integration work will afford you the ability to focus on the more technical topics that you will now face such as trigonometric substitution and integration by parts. If you’re not entirely solid on these topics I would at least read over them much more in detail early, and often.
One of the topics that have posed a big challenge in this course is series and convergence.
It’s conceptually heavy, and a fine sense of pattern intuition is mixed with rigorous mathematical argumentation. My advice for mastering this topic is rather simple: start with the basics, understand what a series is, and practice on whether a series converges or not. Memorize some major convergence tests, such as the Ratio Test or a Comparison Test, but don’t just memorize, they are there for a reason. Practice makes perfect it would seem.
Work as many examples as you can, and then review your work by explaining the reasoning behind your answers to a friend or classmate. And last but not least, I would like someone to tell me just how important it is that you are really consistent with WeBWorK assignments. These aren’t just busy work, they will directly prepare you for your exams. Make sure not to fall behind, and if you start feeling lost, be it in office hours or some of your classmates, there’s always someone you can turn to for help. Really, this can make the most of a study group to keep you on top of your game with regard to these concepts that were tricky, and kept motivated. Math 1575 is challenging but rewarding. If you prepare, persevere, and practice, you will do wonderfully in this class. Good luck!
If only there was a person that I know that had taken this class before so I could have been warned on how challenging Calculus 2 is. I been all over the place and was stressing before this class even started in the first day. I been trying things by myself lately without any help from anyone, but it was the worst choice that I went for. Asking for help is important to learn new ways and I wish I could go back and ask for help because all of us are in this together. Itâs okay if it makes you feel not so smart by asking a lot of help. I regret it and overthink too much that I want new students who are going to take this class to know that help will always be there. Derivatives was a challenging topic to learn, sometimes I would find ways to remember by looking back at problems that I did but the numbers are different. I forget things and overdoing a problem that should be simple to do. I wasnât that prepared for this class because Calculus one was just the beginning of Calculus two. Thereâs a lot to learn and things will get harder as moving on to different topics. Take the opportunity to attend office hours or someone who can do tutoring. For what I want for students is to stay on top, do homework in time and learn faster ways to help improve your skills in math. Anyone can do it, just need to put effort into your studies. In order to succeed next time, I must make time for myself and try to do easy problems first then save the harder ones to spend more time on them. Not only to remember but to know how to solve that problem.