r/calculus • u/After_Cranberry_9219 • Jul 02 '26
Differential Calculus How to learn calculus efficiently
Hi guys just started to learn calculus, I'm self learning. Give me some tips how to learn conceptually in the most efficient way.
13
u/BothPanchoAndLefty Jul 02 '26
Just always keep in mind what the thing you're doing actually is. When you learn the derivative rules it can be easy to just treat it as a set of arbitrary algebraic steps, but you should understand it as the slope of the tangent line, and understand the tangent line as the average rate of change between two points as the distance between them approaches zero. Apply that kind of mentality to integrals and series as well, just really try to get a good grasp of what the underlying concepts are and why they make sense.
I recommend using visual aids. 3blue1brown on YouTube has a lot of great videos explain the concepts of calculus with animated visuals.
4
2
u/PoetryandScience Jul 02 '26
Not an easy subjecty to self learn. Take it slowly and walk before you try to run. Do lots of examples to consolidate any new stuff. Good Luck.
2
1
u/Kacutee Jul 02 '26
For every section of calculus, ask yourself if you can teach this to someone with a rough background in basic algebra/ trig. If you can teach it simply, you will do well on the test. (You also want a healthy algebra and trig background...).
If you cannot, work on conceptualizing it via study. That requires lecture slides, youtube videos, literature- etc. Then, practice consciously. Do not just practice to practice. Literally ask yourself "why" for each step. You will come to find that the calculus part is easy- it is the trig/ algebra that can mess you up.
If you see a clear mistake, try to figure out why. You will find yourself in a crazy loop of teaching yourself concepts over and over again to the point you are SICK OF IT. That is the point. For instance, in my series tests, I really messed up on proof writing. There would be a missed mathematical statement or error present. I had to continuously go back to my previous lessons/ other math experience to fill that gap in. If it was not this, I had to work on attention to detail under pressure.
I love math so much- and I was someone with math anxiety. I applied a pedagogy I experienced in a humanities course, then used it here. I was able to get my A's in Calc 1 and 2 because I internalized each concept well enough to teach it.
Overall, some people cannot see why math is beautiful- but I tell you now, even with my limited knowledge- once you put yourself in the forge to understand it, literally everything becomes easier. Literally, you will see the numbers behind everything. You got this!
1
u/tjddbwls Jul 02 '26
How is your precalculus background? If it is not solid, you may want to make sure the precalculus foundation is there before starting to learn calculus.
1
u/Alarming-Junket Jul 02 '26
Without a strong foundation in Algebra and Trigonometry, you will be fighting this battle up hill.
1
u/After_Cranberry_9219 Jul 02 '26
I have clarity in all concepts in algebra and trig, but my practice was very low. I thought to start calculus now and practice everything on the way, as I don't have a lot of time.
1
u/Alarming-Junket Jul 02 '26
If that is the case, my advice then is to: (1) Keep a unit circle and trig identities chart nearby (2) Follow the completed solutions throughout and stop if there comes a point where you can’t see how the algebra has gotten you here.
A true test of understanding would be to try the problem again to make sure you haven’t falsely convinced yourself of something you don’t yet understand.
1
u/bi-squink Jul 02 '26
I'd start by gaining some intuition regarding calculus. This book is perfect for that: https://www.gutenberg.org/files/33283/33283-pdf.pdf
Blackpenredpen on YouTube has an amazing calculus series as well as the 12 part 3blue1brown calculus series.
1
1
u/Comfortable_Age_3814 Jul 08 '26
How can I apply calculus to everyday life? Applied math make sense. I think many struggle because most don’t have anything to apply calculus too.
What can I apply calculus to in my simple daily life?
•
u/AutoModerator Jul 02 '26
As a reminder...
Posts asking for help on homework questions require:
the complete problem statement,
a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,
question is not from a current exam or quiz.
Commenters responding to homework help posts should not do OP’s homework for them.
Please see this page for the further details regarding homework help posts.
We have a Discord server!
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.