"Work hard, go to the lecture, do homework, ask questions, use instructor's office hours, work in group, go to the tutoring center, practice the sample exams ... " are probably the keys of success in most of undergraduate courses from my point of view. Well, these kinds of advice are too theoretical and general. I wonder how to give more specific advices to students who will be taking my classes. I think they should be from the view of students. So, I asked some former students how they were successful in my class. The short anwer was "working hard". But they were very generous to share more detailed advice/study methods to prospective students that I copy below under their permissions. There is no such best method of studying, you have to figure out what works best for you, but the below advices are super helpful and practical in my opinion.
I deeply appreciate Sarah Hohensee, Katelyn Rousso, Grant Tooley, J. Zhang, and J. Zhan for their generosity to share with us their experiences and advice.
From Katelyn Rousso (Major in Bioengineering, Fall 2021)
How to be successful in APM 2555 (with an A)?
Katie: To be successful in APM 2555, I highly recommend doing all the homework and attending lectures in person if you have the option. Although the homework may not be graded, doing the problems prior to lecture and coming to class with questions about problems you didn’t understand is very helpful. To prepare for exams, I recommend setting aside time to study and review your homework, redo problems you struggled with the first time, and read the book to further understand sections that are more difficult for you.
What is your advice to prospective students in this course?
Katie: Practice the homework! The more you practice problems and redo ones you struggle with the more prepared you will be for the exams when you are under time restraints and feeling stressed. Focus on problems you didn’t understand the first time and look for similar problems in the book that may not have been assigned as homework. Also, it is very helpful to review some content from Calculus II such as integration by parts.
Which sections are most difficult? How do you study them?
Katie: The sections I found most difficult were the sections in Chapter 4 and Chapter 10. For Chapter 4, I found it very helpful to read through the book before exams to review important theorems and concepts such as subspaces and basis. For Chapter 10 about Laplace Transforms, practicing the problems is key. Reviewing the problems in 10.3 and 10.4 and doing all the problems on the practice final exam will be very beneficial.
From Sarah Hohensee (Major in Bioengineering, Fall 2021)
How to be successful in APM 2555 (with an A)?
Sarah: To be successful in this class, I definitely had to put in the work. I did all the homework and reviewed the practice material. I also found it helpful to be present in class each week to learn the new material. I wasn't sure if I would have an A in this class, but by putting in the work it turned out well and successful.
What is your advice to prospective students in this course?
Sarah: My advice would be to keep working even when it is difficult. Just because you are struggling, does not mean that you will never get it. Keep trying, and even ask for help to figure it out. I found it helped me to stay as positive as possible, even if I struggled to believe I could get it right.
Which sections are most difficult? How do you study them?
Sarah: I found sections that involved a lot of memorization to be difficult, such as those with formulas and complicated trig knowledge. To study, I honestly don't know what I did most of the time. I find studying math to be a bit difficult, but I try my best to do as many homework and review problems as possible and repeat the process to make sure I understand the concept of the problem and how I should go about solving it. In general, I find it is best to study hard sections by doing more problems and working through them before you test.
From Grant Tooley ( Winter 2020)
Me: How to be successful in APM 2555 (with an A)?
Grant: In order to be successful in a class like APM 2555 it is important to show up and participate in the lectures. Being present in lectures is helpful to gain general knowledge of the topics that are being discussed, but asking questions and taking notes in-person keeps your mind active and shows if you actually understand the material. Asking questions is always a great idea if you are having trouble understanding any of the work and it may even help the professor reword his explanation in a way that benefits you and the class as a whole.
Me: What is your advice to prospective students in this course?
Grant: My advice to future students in this class is to do the homework. The homework is where you get to practice the material you have learned and become familiar with the process of how to solve each problem. Although the homework can get repetitive, repetition is very important in this class. Many of the sections build upon one another. It is important to become competent with previous sections that have been taught to be able to focus on the new material when it is presented. This keeps you from falling behind too far in the class. Another piece of advice is to find people in the lectures you can contact outside of class. This is beneficial because it can help you receive quick responses to simple questions you may have and could be easier than emailing the professor then waiting for a response.
Me: Which sections are most difficult? How do you study them?
Grant:The section I found most difficult in the class is some of the more complex Laplace Transform material, such as convolution. The way I studied this material was completing the homeworks and reviewing any notes. The homeworks were the most beneficial for me because it helped me work through the problems by hand and figure out any areas that I struggled with. I would then look up videos or review my notes to further understand and correct any issues I was having. Another way I studied the material was asking questions to the professor and my friends. This supplied me with different techniques on how I could better comprehend the sections. It also allowed me to hear different explanations of the topics and would help me change the way I approached the material.
From J. Zhang (High school student, Winter 2020)
Me: How to be successful in APM 2555? What is your advice to prospective students in this course?
J.: Largely the same as what I wrote for MTH 2775, with the notable exception of the bit at the end about proofs (me: see here for his advice on MTH 2775). I don't remember encountering many questions asking me to prove something in this class. Rather I would add:
Many test questions are incredibly similar in nature to homework problems. As such, you can almost always apply similar or the same methods to these problems to solve them. Learning to recognize which processes are applicable in which situation is the primary source of difficulty in this course.
Me: Which sections are most difficult? How do you study them?
J.: Some of the harder problems in the course come from Laplace transforms and finding particular solutions to differential equations. These areas, notably, are not hard because the concept is difficult; rather, in this course, Laplace boils down to a table for you to use, and particular solutions are found through a process which is basically the same set of rules to apply in every instance of the problem. Instead, these problems are difficult in practice because of all the algebra which is required. In the case of particular solutions, this often involves solving a system, which can waste a copious amount of paper. This is where having a strong foundation in the linear algebra portion of this course comes in handy. This is mostly just a slog to get through, but having the requisite practice will enable you to do these problems quickly and accurately. With Laplace transforms, you can get an even more unwieldy amount of work, but these mostly involve high school level algebra. You'll be dealing with lots of fractions and factoring and sometimes partial fraction decompositions. Success in those areas is largely based off having ample experience with your homework to recognize the patterns that you can algebraically manipulate into a form which is more agreeable to your Laplace transform table.
From J. Zhan (High school student, Winter 2020)
Me: How to be successful in APM 2555 (with an A)? What is your advice to prospective students in this course?
J.: It is very important to understand the concepts in APM 2555. Of course you’ll need to memorize some formulas like other calculus classes, but understanding is more important. Paying attention in class and taking notes is very helpful in this class. There are many new definitions and new ideas in this class, and many of them build on each other, so having an organized notebook helps a lot. It allows you to check the formulas or theorems when you forget about them. Everyone has their own way to organize their notes, so it’s always easier to read something from your own notes compared to looking for it in the textbook. Taking notes in class doesn’t mean simply copying down everything, make sure you’re paying attention when professor Tran is explaining them. Understanding the idea is more important than writing things down.
Other than paying attention and taking notes in class, doing the homework is also helpful. Homework problems are more similar to the quizzes and tests compared to the examples in class. Don’t do the homework just to get it done. You can practice the new concepts when doing homework, and you’re able to see which part of the section is harder for you. More practice also helps you to do the problems faster when taking a test. This class is not that hard, just make sure not to make any simple algebra mistakes when you’re doing calculations in this class.
Me: Which sections are most difficult? How do you study them?
J.: Section 10.5, piecewise and periodic continuous input function, was hard for me. It is a new idea to rewrite a piecewise function using unit step function. After learning the definition of the unit step function and understanding the few examples professor Tran gave in class, it’s easier to rewrite the functions. I don’t recommend you to memorize it because once you get it it’s not hard anymore. Paying attention and understanding things is very important, and you can always ask the professor for help if you have questions.