Don’t Let Calculus D(e)rive You Mad

I was always one of those people who thought some people were naturally good at math and if I wasn’t one of those people then there was nothing I could do about it. I thought I wasn’t “a math person” and would use that description as an excuse. Is math one of my weaker subjects? Sure but that’s mostly because I let years of bad habits get in the way of my current work. This caught up to me in my first semester of calculus (calc I) at university, where calculus was my worst class. Here’s the thing: if you’re not “a math person” make yourself one. In my second semester of calculus (calc II) I improved my mark by an entire letter grade (something I never thought possible). How? Through hard work and by understanding that I would have to work harder than some people because of my past study habits.

Know your pre-calculus well! You will struggle so much if you forget the basics. My prof said not having a good grasp of the basics is the number one reason why students will struggle with calculus. Invest time before/at the beginning of the semester to really review the stuff you learned in high school. (Khan Academy is the best way to review, in my opinion. They have challenge questions you can do for each section. Try a couple of questions for each section. If you can’t answer the question easily, watch the accompanying videos for that section first. Do this for sections you forget or know you struggle with.) Be confident in your basic mental math too, especially under pressure. I wasn’t allowed a calculator on any of my midterms or finals for calc and you don’t want to waste time on easy math that you should know lightning fast anyway.

Attend every lecture, especially if you’re even slightly confused. If you’re behind, try not to get even more behind by skipping class (obviously use your own judgement, but don’t skip unless it’s totally necessary). Don’t sit near the back of the class if you know you won’t pay attention.

Don’t just sit there and copy down notes. Be attentive in class and follow along with examples the best you can. If you get lost at a certain step in a problem put a star beside it. After class, study and attempt the problem on your own. If you still don’t understand, go to a TA or prof for help. They will be able to provide better help if they can see exactly where you got lost.

Keep your notes simple. I would use either blue or black pen for the majority of my notes and use one other colour to emphasize parts of my notes (indicate where I got lost, circle important follows, highlight which section of the textbook the class was at, etc.) Keep your notes neat and leave a gap, if you fall behind during a lecture (just remember to get the notes from someone else later). I also recommend using a grid paper notebook, for when you need to draw graphs.

Get a mini notebook! I bought a tiny notebook for cheap and filled it with a (very) condensed version of my notes, throughout the semester. I wrote down common derivatives and integrals, shapes of common graphs, important theorems and formulas, etc. This is especially helpful for calc II, because you’ll have all the necessities from calc I handy.

Advice for using Maple for math labs (if this applies to you): Pay attention to tutorials and ask questions. Complete as many assignment questions as you can in the lab/when a TA is present. If you have any other assignment questions to finish up make sure you work on them at least a few days before they’re due, so you have time to ask for help if you need it. Also, Maple can be a stupid program. You could be missing just one number, letter, or symbol and it won’t work. Or you could have it exactly right and it still won’t work (retyping your input in a new worksheet usually helps). To remedy these issues, I would work on assignments with friends and compare what our worksheets looked like. Oh and TAs love if you give your variables funny names or change the colours of your graph, because they’re all nerds (and so are you, so embrace it).

Do as many practice problems as you can. Calculus is a class where you learn by doing. Do questions till you understand the concept. If problems are recommended, treat them as if they’re actually due (otherwise you’ll just tell yourself you didn’t have enough time to do any practice problems). My number one mistake was not doing enough practice problems and just assuming I knew how to answer the problem (if you can’t answer the entire question from start to finish, then you don’t actually understand the concept).

Please don’t fall behind. Stay on top of things and prioritize what needs to be done (i.e. treat practice problems from the chapter you just learned on equal footing with the lab report you have due – if you treat it as a priority, you will get it done). But, if you do fall really behind, don’t wait until it’s too late to ask for help. Just remember, there’s always something you can do (even if you feel like you don’t know anything and there’s not enough time for any practice problems before your midterm). Identify what you need to learn before you can do anything else (i.e. work on understanding basic integration before you try to do something more complicated like trigonometric substitution) and fit in as many practice questions as you can.

Don’t give up! If you don’t understand a concept right away you just have to keep trying! For practice problems, try to find an answer without looking at your notes. If you can’t figure it out from there, look in your lecture notes and textbook for any relevant formulas, examples, or similar questions. Try to answer the problem again. If you get it, be sure to fully complete another practice problem without any outside references. If you can’t figure out an answer then you should seek help from another person!

Don’t forget everything you learned at the beginning of the semester – review, review, review! Check out this explanation on the curve of forgetting. If you continually review what you learned, for only short periods of time, you will remember so much more and save yourself time in the end!

Utilize the resources available to you. I have a list of online resources at the end of this post, but don’t overlook what’s right in front of you. Go to your prof’s office hours, ask a TA for help, and take advantage of any tutoring or study groups. My uni has a math and science centre where upper year students are always available to help other students with practice problems. If you join a course union, they sometimes offer free tutoring.

Study in a productive environment. This varies by person but personally I need a quiet environment, with ideally no noise or only instrumental music, bright/natural lighting, and nothing to distract me (I hide my phone and only have one pen or pencil out). If you like to listen to music when you study, math is one of those subjects where you can listen to music with words.

Improve your test-taking skills. (1) On an exam, understanding a concept is no use if it takes you forever answer the question. Do lots of practice problems till you immediately know how to answer any kind of question. Speed can be key on exams. (2) My strategy is to flip through the exam booklet as I get it. I answer the questions I can do easily, first, and leave the really difficult ones till the end. (3) Show all of your work! Don’t lose marks because you didn’t show all of your work. (4) Expect your exams to be challenging and prepare accordingly. Overlearn the material. Prepare specifically for the exam by completing past exams/practice exams in an environment that mimics the test-taking environment.

Get every mark you can, because the little marks make a big difference. If you don’t know how to answer a question on an exam, write down any formula or theorem that could relevant. If you try to figure out a solution and know that it’s most likely incorrect, but don’t have enough time/knowledge to find the correct answer, just leave your work there (don’t erase it). There’s always a chance you could be on the right track or nice markers will give you a point or two for trying. Something is always better than nothing.

Focus on the applications of calculus (it’ll make the semester a whole lot more interesting)! A physics major won’t necessarily use calculus the same way a bio or chem major might, but that doesn’t mean some calculus isn’t useful for all of those majors to know. I’ve always planned to major in biology and looking ahead at classes I will need calculus for biostatistics and genetics classes. Never tell yourself something isn’t useful because then you’ll never treat it like it’s useful. Also, my prof taught a whole lecture about how calculus could be used to account for all the variables that could affect population if a zombie apocalypse ever happened, so obviously calculus has at least one really important use :)

Resources

A bit of advice: These are called resources for a reason. It’s okay once in a while to use some of the resources to find a full solution for a practice problem, but don’t abuse it. It is so so easy to just look up the answer but you’re only hurting yourself in the end.

Desmos (Online graphing calculator - I’ve made it through so far without actually buying a graphing calculator)

Khan Academy (Step by step videos and practice questions! You can go your own speed with the videos! My top recommendation!!!)

Paul’s Online Math Notes (If your prof doesn’t provide you with decent lecture notes, these ones are great!)

Symbolab (They have a calculator for derivatives, integrals, series, etc. and I like the way they split up the steps to solve.)

Slader (find your textbook on here and they’ll give you all the solutions to questions!)

Textbooks: I used the Single Variable Calculus: Early Transcendentals (8th edition, by James Stewart) and it was awesome. The way it was set up and all the examples really helped me (I just wish I had used it more)

This post by @quantumheels is seriously fantastic (and she has lots of good advice for other topics too, one of my favourite blogs)

My Other Posts:

AP lit tips, high school biology, how to ace intro psych, organization tips, physics doesn’t have to suck: how to enjoy and do well in your required physics classes, recommended reads, reminders for myself, using your time wisely on public transport, what i learned from university (first year), what i learned from high school

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More Posts from Swirlspill-study and Others

swirlspill-study

7 years ago

[ 02.05.16 • 4/100 DAYS OF PRODUCTIVITY ] 4 days till my exams yikes D: my first exam isn’t even geography but the subject is so content heavy so I’m studying first even though I have 8 days to the exam ahhhh didn’t really bother putting a super nice set-up for the picture because meh good luck to those having their mid-years or their finals!!

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swirlspill-study

7 years ago

Sometimes, when we are presenting, our bodies act completely irrationally. Sweating, stuttering, or just shutting down completely are all things I have encountered during public speaking; behaviour that is usually connected to extreme danger and fleeing behaviour. Completely unnecessary, as your teacher won’t kill you (hopefully), but trying to convince your body to be just as rational is a tough task. Turns out that this is exactly what we’re going to do.

The basis for this (personal) advice all lies in my musical training, where posture is extremely important. Performance practice lessons have taught me one important thing: you can trick your body into thinking it’s okay, and with that, your audience. disclaimer: I have posted this information before in a slightly different way. Regard this as an updated version. Hopefully one with better spelling.

hoooooow???

Stand up and try to follow these instructions. I’m your only audience right now, so mistakes aren’t a problem.

Start by relaxing your shoulders. Many people tense their shoulders when they’re anxious, which is a very natural reaction. However, tension in your shoulder automatically reaches through to your back and arms, and even your neck, tensing up your entire upper body. It’s confirming to your brain that yes! this is scary! Well, brain is wrong and we’re going to prove it wrong by relaxing our shoulders. Just let them hang down (make sure you don’t start leaning forward though, it should be just your shoulders). Doesn’t that immediately feel more relaxed?

Keep your feet a little bit apart, firm on the ground. This sends the message to your brain and audience that a single push will not have you fall over. Standing with your legs closely together simply isn’t as stable, and you want to radiate stability and confidence. Even if you’re feeling dizzy, this simple way of pretending will keep your feet on the ground. Literally.

Chin up, back straight, eyes at the audience. I used to tend to look at the ground, or to lean forward. No, no no! You want to maintain an open posture, and to address the entire audience. When you do this, you’ll look more secure, and maybe you’ll even notice people will listen to you more closely. Make sure you address the entire room, and not just one spot. if you’re scared to look at faces, look at the back wall. But not just one spot, find some nice different wall spots to look at.

What to do with your hands? I know I used to put my hands in my pocket, or fidget with something. Instead, try to talk with your hands more. When you’re using gestures, people will usually pay more attention to what you’re saying, and they’ll sometimes understand more easily (if you’re interested as to why, message me).

Do not hide. This is special advice to musicians, too. I used to hide behind my music stand because it was nice and safe. During public speaking it’s easy to hide behind some notes or to stand behind other people of your group, maybe. Don’t. Remember, fake the confident posture till you make it.

When you’re finished, don’t stop pretending just yet. When people ask how it went, always say it went okay. This is so so so important! Because if you’d say “ugh it was awful!! So many things went wrong, I suck at presenting!” they’ll start thinking hmm, yeah, there were indeed some mistakes… Could have been better. Whereas if you just say it was okay or good, or even decent, they’ll hardly even question it and will most likely remember the positive aspects, as humans tend to do.

I promise this works, at least to some extent. It may not help you get rid of anxiety right away, especially in really severe cases, but it can help you feel more at ease in front of a group. After that, you can start working on other things, such as volume, intonation, powerpoint use etc.

Just take a few seconds before you start talking to breathe, focus on those muscles, and to follow this with an amazing presentation (and a good grade).

You can always send me an ask for advice on public speaking! Even though I’m not a professional coach or whatever, I have overcome my speaking anxiety and maybe I can be of any help at all <3

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swirlspill-study

5 years ago

as i get farther along this academic road, i can see that people are becoming increasingly secretive about their grant proposals, statements for faculty applications, fellowships, etc. what is your policy on sharing these things? i ask because i think you are a Normal Human Being who is a Decent Person, and sometimes this secrecy or tendency to distrust makes me sad!

i understand and i really dislike it as well, but i think it’s important to remember that much of that distrust comes from real and historical patterns of intellectual theft (which hit disproportionately across academia). it’s shitty! the world is a better place when we can share openly and help each other get through the absolute absurdity of the academy! but i can’t think badly of anyone who chooses not to spread their materials around. even though they’re not the same kind of work as, say, a book chapter or an article, we put a lot of labor into documents like proposals and applications, and i think it’s okay to be protective of that labor.

that said, i’m really open with mine, particularly with people that i actually know. my roommate’s getting a big folder of fellowship and job application materials from me, for example, which is partially bc i love him & the other younger premodernists in my program and want them to succeed, and partially bc i want to save our shared advisor some work. my fellowship group have swapped and given feedback all our job materials, and juliana @caffeinebooks & i exchange proposals all the time. i’m happy to share things like cover letters and research statements with people that i know, because i want to save them some of the angst i went through (which was already ameliorated by the folks who did this for me). it’s harder to muster that kind of generosity towards people i don’t know, because, as selfish as it sounds, i spent 9 hours getting the wording on that cover letter right and i’m enough of an asshole to want to reserve the fruits of that labor for people i know and love, at least until i’ve moved on to other forms of labor. i was not planning on sharing my job materials until i got a job. now i’m cool with it.

i feel an obligation to pay forward a lot of the help that i’ve gotten on my materials from people who shared theirs with me. but i also understand not being comfortable doing that, or only being comfortable doing that in certain ways. the giving and the getting should be balanced, IMO, but i think it’s up to the individual to decide what that balance looks like for them.

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swirlspill-study

7 years ago

· 2/1/2016 ·

Biology flashcards from this morning. Good way to start the year.

How is everyone’s day? I love studying the human heart, it’s the best topic in my syllabus. I can’t understand any other sciences though so adios, my inner Christina Yang.

It’s a beautiful day to save lives.

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swirlspill-study

4 years ago

I need advice. I've always had a problem with my grades. I've failed a lot of classes, not because I don't understand, just because I'm so depressed I can't find the motivation to do a single thing. I know that this year I NEED to get good grades. Report cards are almost out. Im more depressed now then ever. I have bad grades at the moment. I just recently learned that I have to put my cat down, and that is making it hard for me to even speak, let alone get stuff done. Any advice

/hugs/ I’m so sorry to hear that you’re going through a rough time. Especially with your cat.

First thing is first: take time. From what you’ve written, it doesn’t sound like the content of your classes is causing you trouble. Rather, it seems like there’s external factors that’s preventing you from studying - circumstances which are triggering your depression etc.

Studying with depression is difficult. Consider professional help as an option. Rely on your support network. Learn to forgive yourself for not performing at your best because of your mental illness. Remember - it is something to be managed; not a barrier to your success.

I’d also consider speaking with your faculty/ advisor etc. There may be formal avenues of review or adjustments to where/ when you take your exams and/or deadlines that may help relieve the stress in the interim as you get back on your feet.

Here’s some tips re: motivation

Five Practical Study Tips to Keep Motivated in School by @nag-aaral/ @sadgirlstudying (working link by @pas-au-talent)

Motivation by @areistotle

Motivation masterpost by @elkstudies

Motivation masterpost by @artkidstudies

Tips for avoiding burnout and staying motivated by @coffeesforstudiers

And for dealing with failure:

Dealing with Failure

Shit Grade? Feeling better after a terrible exam

This response

And this one

And this one here

On Bad Semesters by @post–grad

This Masterpost by @areistotle

How to Fail by @psychstudyblr

Good luck - give yourself time. Focus on “how” (not just a demand - ‘need’) to get exams. Celebrate your victories - not matter how small. Because it’s going to be a slow process. But you’ll get there. It may not be the ‘perfect’ solution or the perfect ‘result’ you want - but hell, we’re human. It keeps things interesting.

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swirlspill-study

7 years ago

Just Some Notes 📝📝📝 One More Day Until My Break, I Can’t Wait!!!🙆‍♀️🙆‍♀️🙆‍♀️

Just some notes 📝📝📝 one more day until my break, I can’t wait!!!🙆‍♀️🙆‍♀️🙆‍♀️

(DAY 9/100 OUT OF ONE HUNDRED DAYS OF PRODUCTIVITY)

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swirlspill-study

6 years ago

5 sites every med student should know about!

Folllow my studygram:Studyspiration

When it comes to medicine, understanding the principles is key, however it might be quite difficult to understand even though you attend lectures and read all the chapters, which is pretty normal since most of the times neither professors or text books make any great sense - therefore these different sites, or youtube channels can help you out a great deal. Here are a collection of some that I have found useful and that pretty much everyone I know makes use of.

1. Dr. Najeeb (https://www.drnajeeblectures.com/). You will often find medical students talking about this guy. He is probably what would be called a superhero between med students and that is for a good reason. His website features tons of videos that explains pretty much everything. He does it in an interactive way where he engages the audience and draws on the whiteboard so that you can follow along. This does cost money - however if you can split the bill between some of your friends, or you can use some other students login (if they are that generous ofcourse)

5 Sites Every Med Student Should Know About!

2. Kenhub (https://www.kenhub.com/). Now this website is amazing for studying anatomy or the central nervous system (I think they are working on expanding their content, but this is what they have for now). It is very good because it gives you a simple overview over what you need to learn. The content on here consists of videos, articles and many quizesses which I loved during anatomy.

This website costs a monthly fee (there are also other options for payment), however you can split this with some friends as well, I shared my account with my study buddy.

3. Khan academy (https://da.khanacademy.org/). You have probably stumbled across some of their videos on youtube, however they also have a website where all of these videos have been compiled and they have made up this “interactive” system where you gain points for finishing videos. this is for FREE. Yes you heard right free.

4. Anatomy zone (Youtube channel) Now this is almost an essentiel for every semester that you do. In almost all of your courses you need a little bit of anatomy, and thankfully this youtube channel has got you covered. It is soo good! I mostly make use of this channel, because honestly they just do it so well and its free.

5. Armando Hasudungan (Youtube channel). This very talented artist, makes all the medical concepts become illustrative and thereby making the understanding of the principles that we cannot see become more easy.

Study hard, study smart and stay motivated,

Love,

Dunia

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swirlspill-study

7 years ago

✨30.09.17 last minute math revision notes~ uni is starting on monday, i’m filled with 49% anticipation and 51% crippling fear tbh

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swirlspill-study

7 years ago

12/21/15 || Last week’s spread ☺️ Loving my new cloud stickers. ☁️✨

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swirlspill-study

4 years ago

Home Page - Academic Phrasebank

Academic Phrasebank is a phraseological resource for academic writers organised according to the main sections of a research paper or dissertation.

This website is helpful, especially if you’re new to academic writing! You can select what section of your study you’re writing about and then it provides you with example phrases for different parts of that section. I find this super useful when I feel like I’m repeating myself or I know what results I want to describe but I don’t know how to say it. Here’s an example below: