3 Ways to Learn Calculus on Your Own
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- Опубліковано 21 лип 2023
- In this video I talk about three different ways to learn calculus. I give some books you can use and also some other tips for learning. Do you have any advice for people who want to learn calculus?
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Thank you:)
1:08 with mathbooks
4:20 buying math courses
5:24 math videos on youtube (might not be as effective)
6:54 Making own routine/gameplan with the use of these 3 strategies
Probably gonna be the first 2 and additional online resources.
Take 3blue1brown’s essence of Linear Algebra series. I never understood the determinant was about space (1d, 2d, 3d, etc) in my linear algebra class until 3B1B illuminated that. I feel like we got a little bit on vectors, then the matrices just popped up as a separate thing.
Larson, Stewart, and Thomas... Remember that it's very likely your local library has a copy of these so if you're worried about money check one out there first! Libraries are one of the best ways to help yourself on a math journey.
You have the best math study suggestions ANYWHERE, MS!!! Could never get better advice from ANY math expert or scholar even if I tried. Thank you lots, Math Sorcerer!!! :) :) :)
I just got the James Stewart Calculus book, I'm glad too hear it was a good pick. Thank you for your videos, it helps me stay excited about math. I appreciate your work.
One nice thing about the Larson textbook from a self-study perspective is that it has an accompanying website with additional resources (videos, exercise solutions, etc.) that is (at the time of this writing) free to access without any sort of subscription or registration.
Larson is what I used to learn Algebra, Trig, and now Calculus.
I'm 16 years old and I'll start chapter 7 in James Stewart's Calculus Book which is techniques of integration, I'm learning from this book and from a professor on youtube called Professor Leonard, I cannot emphasize how helpful those lectures are!
Can you link the course/ lectures please?
@@tapal9779
Calculus 1:
ua-cam.com/play/PLF797E961509B4EB5.html
Calculus2:
ua-cam.com/play/PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-.html
for more go to the playlist section in his channel
@@saeedsaleh6873 thanks!
Good job. I also did that in high school using the HBJ book that I borrowed from the library. Now, My son is doing the same with my guidance. He is also learning Calculus on his own, but he is using the MIT material (Someone told me that Leonard is better) and the 20 Minutes Cal book (easiest book I can find for kids). He watches 30 minutes of lecture daily and does 10 problems before I let him play his Minecraft game. He will start doing the MIT Cal homework after watching both the video lectures and going through the "20 Minutes" book.
Ayy I'm 16 years old too, I'm also started to learn calculus , its just great to see ppl my age doing this thing , beest of luck buddy .❤
Calculus is extremely difficult, but we're all thankful you made a video on this topic. We will continue supporting you no matter what happens.
No it’s quite easy tbh well sure you need to be quite good at algebra and know most trig identities but then integration is very simple. Then derivatives follow normal rules so they’re no problem. So if you want a calc 2 level it should take you like 4 weeks when you do power series too
I am learning calculus from Thomas and Finney as well as lectures on calculus 1,2,3 by Professor Leonard.
His lectures are amazing.
Have a playlist link?
Calculus 1;
ua-cam.com/play/PLF797E961509B4EB5.html
Calculus 2;
ua-cam.com/play/PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-.html
Calculus 3;
ua-cam.com/play/PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7.html
I'm taking DE this coming semester, I have been binge watching your lecture videos and it was always a good platform to be exposed to those topics for the first time. By branching out to other resources, I get more clarity of course. But your lecture videos really did help students like me to comprehend calculus whether while taking the class or previewing it before the semester. Thank you bro
Hey, I noticed that you always show the 5th edition by Stewart and I was wondering what your opinions were on the 8th edition.
I was always a huge Physics nerd but while majoring in Engineering in college I had to, of course, take Calculus with Stewart's textbook and I absolutely fell in love with this subject more than any other, I wasn't aware of how elegant and just how incredibly useful this mathematical branch was. I fell in love with Physics originally because of how deeply ingrained with the physical world around us it is. But Calculus takes that so much further and applies to literally everything that's continuous in our reality - from a business minimizing amount of material used all the way to finding the direction of electric potential from integrating an electric field. I just found it to be life changing, honestly, haha.
Thank you so much for your tips, teacher
I have Thomas and Finney 9th edition for calculus
Sir stay with us like this. Thanks.
I used the exact copy of Stewart's Calculus shown in the video and Schaum's Calculus. together they are very thorough.
Nice, I just got started with calculus
Thank you so much for these videos! I am your new UA-cam channel subscriber! Just found out your channel through recommendation when i was searching some math videos on UA-cam! I myself is also teaching my self some math, although I have yet reached the point to start on calculus course. But it is good to know what I will need to do after I start learning them. I am currently in the middle of learning basic trigonometry(maybe high school to college level?), after I am done with those im gonna review my notes and do some integrated courses on Khan academy( which is where i learn math from), then I will be also teaching myself some high school statistic and probability, cuz i feel like its gonna be useful somewhere. After all these, I will do one more course, precalculus before I dive into the calculus. From there I will probably change abit of my study style, and try something new to countermeasure the difficult lessons i will be learning. Since what i have done so far is just to build my math foundation, I want to have to steady base before I build more on it. Your videos are really informative, so I will be staying around here and see what can help me!
Comparison and contrast of different solution methods for algebra and calculus problems is a set of videos that I think would be useful for many learners.
He looks like newton
I used and use all the methods you described..
love that mouse plush on the book shelf!
I used to think I didn't understand trigonometry but after around a year I realized that what I didn't understand is how specifically a calculator calculates each ratio. Thank you for this video I have been thinking about starting to learn calculus.
You usually learn Taylor Series to get familiar with the general concept, and in principle, that could work for what calculators do behind the scenes to find each trig ratio. But they aren't very computationally efficient. Usually it's the CORDIC algorithm that calculators use in practice.
I self-studied with Larson/Edwards for one good reason: they run a website which has the worked out in detail solutions for the odd-problems. Those details really helped. And for all editions they've ever made, I think. The Stewart does have a Student Solutions Guide with the worked out details, but can be hard to get. Unfortunately, the learner cannot buy the Instructor Solutions Guides from publishers.
I just bought your Cal 1 course right now. I took preCal last semester, I am a junior taking Cal 1 next month. I'm hoping by taking your course during my downtime that I will feel more prepared than I did during preCal. I can do hours of work every day and still fail the exams, I feel like Naruto taking the Chunin exams. My B.S in software engineering at Sam Houston so I still have a lot of math left. :(
Calculus are very hard for me but i'm in a such particular situation.
I basically skipped high school and got into university but i dropped out because some health issues and now i'm back.
Go man, you can do it!
@@verdienthusiast3868 Dude I have a applications of derivatives test next friday with optimization and related rates its way too hard for me. i need at least 1 month to learn this part.
I am from a non-math background, so my experience has been little different. I think having and doing pre-requisites helps. So, when started learning I went this path:
Pre-Algebra > Algebra > Pre-Calculus > Calculus 1 > Calculus 2 (current level) > Calculus 3 or Differential Equations (planned) > Linear Algebra (planned) > Statistics (planned). Yes I took course on online platform and in addition to it free lectures on youtube, but practiced a lot. It is a very slow process, it took me 1.5 years since the beginning but I want to really understand rather than just skip ahead. Most books are available for free to download like openstax and understanding gets better only through practice and problem solving. Everyone is different and one should do what suits one. Thanks.
What resources are you using brother?
@@karannalawat4826 Well, For Algebra I used Blitzer book, which is available online. For Calculus 1 I used Stewart and for Calculus 2 also Stewart, available online, although need some searching. I prefer online videos like Khan Academy for Algebra but for Calculus I used 2 different online sources- MIT Opencourseware and Khan academy. MIT's Calc 1 course is based upon Stewart's book. However, I would say this my method is a slow method not at all suitable for grad students who have time constraints. One advice I will give you, it is important to combine the lecture with theory in the book. E.g., if you are studying Limits from a teacher online, immediately study the theory and example from the book and complete the chapter's theory part. Then move to exercises which is the backbone of math problem solving. MIT open courseware has assignments and exams on their website that provide challenging questions to practice as well. Good luck.
Hi, your video is great! would you suggest a way to self-study differential geometry? My undergrad degress is Statistics and currently I am studying MSc statistics as well. My dissertation topic is related to statistics on manifold. However, I have no solid background in maths, I studied linear algebra, calculus, ODE, and self-studied some real analysis.
Salam..from Indonesia..
Salam from Philadelphia, USA 🇺🇸
Sosis from Turkey 🇹🇷
Salam from Germany :-)
Salam from Georgia 🙏
Walekum assalam.
I think the more algebra someone learns, the more calculus is going to open up. I also people think should watch calculus videos even if they understand 0 percent of it. It might be discouraging to watch something you don't understand or try to work through problems you can't understand. But when it become discouraging, go watch the math and do the math you do understand. Then return to the math book/videos you don't understand. When I start to self study math, I realized I knew more math than I thought. I don't say that to make myself seem better. I also suggest if you are in math classes in college, taking non degree or audit math classes for math classes you don't have yet. I mean suppose you are in bs education with specialization in math degree program. You're have Calculus 1,2, and 3, Take non degree or audit a Calculus 2 class before its required in your bs degree program.. Yeah, I think I'll skip around in the Steward Calculus book and skip to the limits. Limits seem kind of easy. Very basic functions are easy. Here's one from Calculus by Steward: f(x)=6--4x. or this one: f(x)=x+2 over x squared --1. Very easy and basic stuff.
Would love to see a similar video on Linear Algebra. I actually find it harder than calculus. I can’t even visualize dimension greater than 3.
I would love a similar video on Linear Algebra, too. Vectors! Ugh!
@@qbtc Thanks!
For some reason, I really got hung up trying to teach myself calculus using Stewart's textbook when I got to the chain rule. Larson worked better for me, but others' mileage may vary.
I used the Larson book. It's great, but I think when you get onto vector calculus at the end of the book, the explanations of things like div/curl are a bit too sparse. There are some very good videos on YT explaining these concepts well though (3blue1Brown for example did a great explainer).
I would say that learning exclusively from videos is a bad idea. The concepts won't sink in without doing a lot of exercises. But rather than getting a Larson or Stewart book, you could use the workbooks from Chris McMullen or the big Shaum's Outline which has tons of fully worked problems in addition to exercises for you to do.
I'm procrastinating so much about starting to learn calculus, that I can't stop watching videos about "how to learn calculus". I guess I'll know where to start 😂
When do you know if it's time to try proof-based calculus?
I’ve learned integration and derivatives through old A level exams black pen red pens videos and a German book which I found in my library
question limits of solutions in algebra perhaps calculus itself will solve them if allow it to unfold in your mind following its operations? unanswered question are your teacher / study buddy ask what problems can not be solved trig or algebraic is it fail point or limit of subsystem analytics?
Learning Calculus on your own is difficult if you don't have a solid Algebra background. On top of those thick textbooks, I would recommend "The 20 Minutes Series" and "Schaum Calculus" books for practice.
Hey Math Sorcerer what do you think about apps or sites like Mathway? You put in the math problem and it shows you step by step how to do it. The books and sites like Mathway can be good for self teaching, and helps a lot when you get really stuck.
I learned calculus with the book of JAMES!! its really good.
Teacher I need some help with Probabilidade e Estatistica(i dont know how its this word in english btw), Im not good enought, and its really hard for me to undestand, can you recommend any book to study this subject?
:)
Imho calculus is proof of compactified time.
The universe evolves one Planck second at a time. Iterated.
Why there are so few linear equations. Iteration tends to attractors.
Love from India ❤
Hoi, from The Netherlands.
Do you suggest repeating past solved problems for retention?
Yes definitely!!! It’s a good way to get in the groove also when you are returning. Nothing wrong with working out stuff you already know🔥
Just a daily reminder. Math isn’t a spectator sport. To learn, you must do.
Hello guys, I'm very new here. I'm from Romania and I learnt a bit of maths here. it might sound very strange but i really want to learn all the maths, like, all the basics of the maths (not to an Olympic level, but have a grasp about maths)
In my country the level was pretty high, we learnt limits and integrals in highschool. But i was never a quick student in sciences. I study languages now at uni but it would really like to enjoy maths in my free time. Is there a book i can starts with?
Thank you from the bottom of my heart in advance
What about Thomas' Calculus? Why didn't you recommend this book?
Do you think visualisation is a great tool for beginners so use of softwares like Mathematica or matlab or maple or some apps on mobile like desmos. May be you can make a video of how to use these software to enhance and suppliment and even get a sense of experimentation and play to what we are learning. This is what learning is all about anyways. Finally also talk on how to maintain a notebook physical or digital like one note or app like anki flashcards. Where the difficult problem once encountered are all categorised and solution along with insights or any graphs that was created using the software is saved. This abridged note of difficult problems if revised daily twice once before going to sleep and once immediately on waking up will be a game changer. It can also be reviewed on any mobile device during commute. Will 10X performance and expertise. Please make a video elaboting and showing how these tools can be leveraged
I have to look into, gradience, curl, divergence, laplacian ... and ... forgot the others. Also tensors. Trying to learn what they are, but I can't seem to get an anwser of what they actually are. So now my strategy is to take my favourite book on higher mathematics (how we call it in germany) and spend every evening an hour of riddling what I'm actually reading ... Wish me luck, lol
If you are familiar with the ways you can multiply vectors, those first three terms you mentioned are really just extensions of the same idea, with a vector of derivative operators (the DEL operator) taking the place of the one vector. Have it act on a scalar function, that generates the gradient. Divergence is like a dot product of a vector field with the del operator, and curl is like a cross product with the del operator. The Laplacian is a combination of two of these, the divergence of the gradient.
As for tensors, I like to think of them as super-vectors, where there is more than just a list of numbers to identify the algebraic object. Usually, a tensor will be a square matrix, in the applications I'm familiar with, which keeps track of how the quantity in question is an interaction of multiple spatial dimensions, and each component is uniquely determined by corresponding to each two out of three of the spatial dimensions (e.g. xx, xy, yy, xz, yz, and zz). Applications I'm familiar with, are the stress/strain tensor from statics and the inertia tensor from dynamics. Tensors can also go beyond this, and be a cube matrix, or even a matrix of matrices.
@@carultch wow, thx for the extensive answer :-) Yeah I encountered the Inertia Tensor and didn't really get why it is a "tensor" or what actually makes it a tensor. "identify the algebraic object", "keeps track of how the quantity in question is an interaction of multiple spatial dimensions", I'll keep your description in mind when looking over the topic!
"each component is uniquely determined by corresponding to each two out of three of the spatial dimensions (e.g. xx, xy, yy, xz, yz, and zz)" so basically the tensor is constructed in a way that gives you a "response" for how it interacts for example with vectors or generally objects and their special dimensions?
You could make a review of Calculus Simplified by Oscar Fernandes. I thought It is a good reading to learn for begginers.
planning to read either spivak or apostol after studying stewart. which one to pick?
Oh I dunno. I have both hmm. Can you afford both? They are both kind of pricey is the problem lol.
@@TheMathSorcerer Can afford them both but how would you rate each text in terms of dryness? Do you recommend studying the two books at once?
Four Resources I am using 1) Math Sorcerer Udemy Courses 2) Essential Calculus - Chris McMullen 3) Bob Miller’s Calculus for the Clueless and 4) Klotz Online Math Notes
You have a ton of books in the background. Seriously, have you processed each and every one of them from the first to the last page? Or are you like me, that you buy books because you love them and "they will be useful somehow sometime"? 😅
A big problem for me was that I'd heard a lot of this stuff and picked up rules by just watching random videos over the years, so I knew some calculus but not enough to actually solve any problems. That made it a lot more boring to actually try and learn calculus systematically, which I'm doing right now with Stewart's book. Has anyone else had problems with this?
Yeah I could see that happening. Pretty cool you learned like you did 🔥
Just a hypothetical question...
Would it be possible to finish Calculus by James Stewart in 4 months?
I don't think that would be beneficial
You need to slow down if what you're doing is self study
So that you won't be overwhelmed and burnt out
And that is the worst thing that might happen for a learner
man you look exactly like cinematic mad genius
Books for international students please! These US books aren't available for us in Europe
Hogs are thick, but books are voluminous.
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NAMASKARAM FROM BHARAT 🙏🏻🧡🙏🏻
I suggest my students that use videos to pause the video and solve the problem then play the video to check their solution.
Have you had a look at calculus for dummies? Whats your opinion on that?
I think the best way is to start from real analysis
That's... unconventional. I took calcuus in high school from a teacher who loved pure mathematics and took a very theoretical approach (heavy on rigorous definitions and theorems and proofs). It was great preparation for going on to become a math major, but I don't think it's the best way to teach or learn Calculus for most people.
Yep. I Did that aswell. But I think that taking a proof writing class and pre calc before is a must. Or.. you just want to struggle a lot.
Calculus is pretty ez
Book combined with video courses is really a nice way for someone who doesn't have any other options. But the real difference is being able to ask a student and/or lecturer stupid questions. Not those where they respond with "nice question" .. no, no, those where everyone looks at you like "How can he ask such a question? Is he stupid?" (so you might already have gotten this answer from StackOverflow, so you don't even need to go outside of your comfort zone for this line of questioning, lulz). Ah yeah, also try to tackle the things you are not comfortable with in a productive and effective way :-) Wish you all the luck, my beloved fellow math sufferers and you too Prof. Math Sorcerer ;-)
really? really? Years of practicing different maths but it seems just with 2 books makes the difference... yeah... perhaps if I let my hair grow it will simplify the whole calculus theory... This is great, by the 2 books, study these and you will be able to pass all exams in college! Yeah
Why the math sorcerer always talks about calculus and algebra but never on Statistics & probabilities and PDE/ODE??
You shaved! Rip beard :-)
I agree with everything you have said. However, I feel you have left out one "newly" important idea. That is utilizing ChatGPT. If you get stuck in the book, ask ChatGPT or have it recommend a video on the concept to get across the idea. I would use Google, but it would take a long time to find exactly what you are looking for especially if you do not recognize it. ChatGPT has its draw backs, but utilized correctly, it can help you quickly to overcome your hurdle. My two cents...
Yes! ChatGPT might be useless at *doing* math, but it's great at explaining mathematical concepts. I like to use it as a kind of tutor to bounce my understanding off of, too.