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The Best Way To Master Calculus
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Күн бұрынIn this video we talk about learning mathematics and integration. Do you have advice for people? If so please leave a comment below.
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@byronwilliams7977 5 ай бұрын
I failed Calculus in Canada when I was in high school. I hope this helps. 1) Cover the exact same course material in a For Dummies Book series. Generally speaking the questions are easier, and the explanations are not nearly as rigorous. 2) Then cover the exact same material in "The Humongous Book of calculus problems" by W. Michael Kelley. Make sure you compare your solutions and explanations in the book. 3) Then move on to something more rigorous. I used the MIT Opencourseware Calculus videos/coursework; they were newish at this time. Do the exact same videos until you can reliably solve the test problems consistently getting 100%. 3) The most important thing is that you do so many questions, and get them correct that you can't help but get a perfect score. 4) The other thing is to prepare for a higher degree of rigor than you will be subjected to. Obviously I didn't go to MIT, but I had access to their tests. If possible, always work hand in hand with the solution manual until you understand every line of every solution. If you need more advice, please feel free to reach out. Also get a course, you can see the material in advance so it won't adversely affect your GPA.
@user-so5vl9ee6g 5 ай бұрын
Thank you so much!
@LeisureSuitLaurent 5 ай бұрын
Damn man, I would have just used Khan Academy and Waterloo's CEMC. Or those MathSmart books to pick up on the pre-reqs to calc (from grade school to G12). But you went for quality, I just went for "good enough". We used the James Stuart textbook at Waterloo for the science calculus, it comes with a solution manual. Pretty good! The math profs were way too crazy abstract though, probably forgot what it was like to be a student learning that stuff for the first time. I had a lot of issues with how math was taught in Ontario...Not sure if you're from there. Lot of us got our asses handed to us in undergrad during the double cohort years.
@doctorstrange2736 5 ай бұрын
@@LeisureSuitLaurent I’m in Ontario . I’m a student in a masters Analytics and machine learning program. I’m revising calculus for machine learning. Great to hear from you folks .
@elmoreglidingclub3030 5 ай бұрын
“Sometimes, you just have to get the pencil moving.” Dang. That is seriously good advice for learning anything. Thank you so much for sharing that.
@massivemario 5 ай бұрын
I came here to point that out. I had a teacher few years ago, it was a private teacher so she came over to teach me at home weekly. She always said to keep writing something, and that was probably the best tip I had ever gotten in maths. I had the first calc2 test today, it went pretty average, I was aiming for 100/100 since that's the only way I could pass calc1 (thank you @themathsorcerer for this tip from your other video) but it didn't really feel like I was really solving much. Most of the time in my test today I just had the pen moving and writing down stuff that pops into my head just as soon as the pen hits the paper. I just had to watch this video after what I experienced today...
@thea.igamer3958 5 ай бұрын
Differentiation is mechanics. Integration is art.
@evelyn-ed7nn 5 ай бұрын
it def requires more creative thinking lol
@terencemeikle534 5 ай бұрын
I spent the whole of January doing nothing but integrals. I got addicted, I guess. There's a satisfaction in integrals that differentiation simply can't match.
@sir_albaxious1909 5 ай бұрын
TELL ME WHAT IT IS. INTEGRALS' SYMBOL HAS A SPECIAL PLACE IN MY HEART! TELL ME!!!
@terencemeikle534 5 ай бұрын
@sir_albaxious1909 You got me there; it's one of those things that are tough to explain. I suppose it's like an integral could be compared to bathing in warm spa water and sipping on a piña colada, but differentiation is like a cold shower with carbolic soap, followed by a rub-down with a scratchy towel. 🍹 🍸 or 🚿 🛁.
@UnconventionalReasoning 5 ай бұрын
@@sir_albaxious1909 Differentiation is entirely mechanical: use the basic differentiation rules and repeat over and over with the Chain Rule. Integration is more of a puzzle. The "inverse function" is always more complex than the "direct" function, most easily seen with multiplication/division and powers/roots.
@waltercoady-jz2rf 5 ай бұрын
I agree. When I was in university, I loved integration. Much more involved and fun than derivatives.
@chriswilliams5291 5 ай бұрын
Something so satisfying about derivatives and integrals. I really enjoy math problems that make you think and are not just tedious plugging in numbers into a large equation.
@alevyts3523 5 ай бұрын
Each element in calculus has a visual interpretation, a real physical or technical object, or a process. It helps a lot. And makes it easy.
@myahoeft2930 5 ай бұрын
I just declared as a math major as a junior in college. I always enjoyed my calculus I and II classes and I got along with the math teachers. The classes are small which I like. I bought myself an essentials of Calc workbook and I recently bought your Calc III course using your link. I'm nervous because I'm one of very few women pursuing math at a University that isn't math focused. Thank you for your resources! I love your channel!
@TinyMaths 5 ай бұрын
As cliche' or as dumb as it may sound, a lot of practice can really make a difference. And here's something I have found useful when practicing a lot. If you have a large number of examples; go through as many of them as you can (if not all), and then start all over again from the beginning; I promise you, if you have say, 100 on your list, you will have completely 'forgotten' how you did many of them, and I would sometimes end up trying to solve the same problem in different ways, not realizing that I used another solution (until I looked back at my previous workings). I did that when practicing integration, and I found that I kept being tripped up in the same way on some of the same questions. But, over time, I began to remember what to look for in a given situation, irrespective of the specific integral, and what kind of rabbit-hole traps to be aware of. The repetition of the integrals really solidified different techniques used for different scenarios. Although you're repeating the integrals, it seems that, on a different level, you're actually repeating the techniques, and begin recognizing more and more, where they can be used. That helped me a lot.
@Douchemaster_McChest 5 ай бұрын
Practice, practice, practice is the best advice. If the teacher assigns just a few problems from a section as homework, just don't do the minimum. Do them all (or as many as you can.) Also, if your book has, say the odd numbered problems' answers in the back of the book, use it to check your answers, but don't use it as a crutch. Once you start getting the correct answers, you will feel more confident. When that happens, you can start tackling the even numbered problems (and any others that don't have answers in the back of the book) and your confidence will carry over to those too, even though you won't have a way to check your answers for those problems. Also, like what was pointed out in the video, once you start doing enough of the same type of problems, you will start to see a pattern and realize what the best technique is to use to solve a particular problem. After you do a whole bunch of problems for a specific type of integration technique and feel comfortable with that technique, move on to the next technique's problems. Rinse and repeat for each. Once you've done that, hopefully you will be able to recognize what main techniques to use to tackle any integral. Try to find a big set of integral problems that involve a random selection of problems involving all the major techniques. Eventually it will become second nature on what to use to solve most integrals. Other advice is if you are really struggling, seek help in study groups or an outside tutor. If your University has a Math Study Lab that is run by upperclassmen, graduate teaching assistants, or Professors in their spare time, use that too, as these Math Labs are a resource to get on-campus free help.
@richoneplanet7561 5 ай бұрын
Practice the 4 different kinds of integration problems and identifying them for a test - calc 2 was the funnest 👍
@morbloe4559 5 ай бұрын
Where he’s talking about pattern recognition is important to me. It took me so long to realize there is no “master algorithm” to determine what integration method to use, it’s just pattern recognition. Another beautiful thing I’ve noticed as a beginner, is that certain integration techniques seem to have “personality’s.” For example, U-sub reminds me of a sledgehammer, trig sub reminds me of… something else.
@pichirisu 5 ай бұрын
Could you add on to this by making a video on how to best visualize calculus, or any kind of math? It would be very appreciated.
@douglasstrother6584 5 ай бұрын
Check out 3blue1brown
@Tensor-An 5 ай бұрын
I am on a journey to trying to find a formula for integral for product functions. Recently I thought I was about to come to that formula, but guess what? I have re-discovered new aspects of calculus, like directional derivative, gradient, co-ordinate transformations, Jacobian. It was a dead end, but I learnt new things about calculus. I'm not a smart person by any means. I just like thinking about them. My way of learning calculus is the hard way. If it doesn't make sense, keep thinking about it. Most of the revelations happen when I am bathing in the morning 😂
@sir_albaxious1909 5 ай бұрын
Relatable. My math journey is on finding a general way to solve Factorials. I rediscovered the Triangular Number Formula and Some Combinatorial Identities. I decided to learn Calculus because I want to understand the Sequence at which a circle's circumference falls onto the x-axis (tbh I still can't make my question certain). I think it is one of the best decisions ever made in my life because I soon realized that the essence of calculating my sequences is the essence of differentiation.
@GeorgeofVA 5 ай бұрын
Practice does make perfect. However, I find that when I get stuck on a subject it is because I don't understand the the underlying concept. Undergraduate calculus is usually presented as a rule based, or procedural topic. It may help to look up and incorporate the fundamental core reasons and use for the topic. Good luck.
@moksh1106 5 ай бұрын
My advice is visualising the concepts, the graphs And also try to memorise the method of solving a question
@Kozakjosh 5 ай бұрын
I'm taking calculus for the first time in two weeks! What great timing.
@tmann986 5 ай бұрын
ALWAYS CHECK IF YOU CAN DO U-SUB BEFORE ATTEMPING THE CALC 2 INTEGRATION TECHNIQUES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! and don't forget the +C.
@m1nd2pap3r2 5 ай бұрын
Trig sub is SO satisfying when it works out though. Filling out the entire page with a solution, and then checking the back of the book to see that you got it right is addicting. I’m self-taught in calc so I definitely still miss some basic things that are taught in a classroom I’m sure
@lotuttv 5 ай бұрын
THANK YOU FOR EVERYTHING YOU DO ❤
@AtulKumar-cu3mz 5 ай бұрын
You're the Richard Feynman of Mathematics ❤
@terencemeikle534 5 ай бұрын
Yeah, you're spot on. Since I got recommended the Sorcerer's videos, I've experienced a complete renaissance in my interest in math. I'm an old duffer, but this guy has given me back some of my youth. What a wonderful communicator he is!
@moksh1106 5 ай бұрын
Richard Feynman is the only man known that has scored a perfect score in "Putnam"
@davidhill8163 5 ай бұрын
Great advice, your courses are amazing.
@kugif3927 5 ай бұрын
I got a 99.7% in calc one. Entering calc 2 I felt completely overwhelmed and lost. I did hundreds of problems and got a 97% on my first exam. It really is always about practicing doing problems like crazy.
@joelweidenfeld471 5 ай бұрын
I will tell you why calculus 1 + 2 are hard and 3 not so much.....Differential then Integral calculus are difficult ONLY because of the way they are taught...THE PRINCIPLE OUTWEIGHS BY FAR THE utility of progressive examples. ... Thus for 1 and 2 it would not at all disturb me if they spent a full quarter of the semester moving extremely slowly until the differential and integral are understood.... ITS A QUICK path to a F when they are flying INTO the problems and half the class doesn't understand what the hell tbey are doing. Calculus 3 is in fact easier because by the time you get there , if you get there , you have a clue...
@UnconventionalReasoning 5 ай бұрын
For many learners, "Practice, Practice, Practice" is ineffective and inefficient. A better approach may be emphasizing the algebra, de-emphasizing the numbers, concentrating on the algebra, and deconstructing each problem into sub-components.
@rusi6219 5 ай бұрын
Yeah that's a good approach, collapsing every problem to the point the only requirement is trivial math
@Rest.all.is.secondary 5 ай бұрын
Sir please try solving jee advance exam maths portion Please.
@SuperMrgentleman 5 ай бұрын
Will he do the needful?
@Rest.all.is.secondary 5 ай бұрын
@@SuperMrgentleman think so
@SuperMrgentleman 5 ай бұрын
@@Rest.all.is.secondary that was a joke sir
@fSFan333 5 ай бұрын
i wish i could just practice solving integrals, but our calculus course is a little bit different, it first focuses alot on measure theory and then it's all about fourier transformation and differential forms. While I do think it's possible to get better by practice in this specific calc course, I still find it pretty hard to come up with solutions at times, because it's really more of proof writing than actually calculate something.
@bradleybeauclair8282 5 ай бұрын
I'm honestly convinced that the best way to do calc 2 is to do every problem in the book by finding the answers step-by-step through ai, or your udemy courses, or chegg, or hire the professor, and just do every single problem (all 10,000 of them) 100 times each. Then go learn pure theory to understand why what you have 99% memorized, at this point, makes sense.
@user-sw7rw3px6n 5 ай бұрын
i had a rough experience with calculus 1 but i will say 2 wass fine
@LeisureSuitLaurent 5 ай бұрын
That's unusual, Calc 2 was way worse, but I guess when you had the fundamentals of Calc 1, it made 2 easier? Or you developed good calculus strategy.
@83jbbentley 5 ай бұрын
il calcolo infinitesimale è una razza di forti e persistenti.
@bspain1637 5 ай бұрын
I went to get your Calc II course but when I tried to pay I was told I didn't qualify for the 80% discount.
@TheMathSorcerer 5 ай бұрын
Weird, try having the link from my website or in the description of this video
@bspain1637 5 ай бұрын
@@TheMathSorcerer I guess I'll have to wait until Udemy has a sale again. I can't afford the $95 price point at the moment...
@bspain1637 5 ай бұрын
Sorcerer's courses on sale at Udemy as of March 19 '24
@eze1196 5 ай бұрын
have a question: If every time I go to solve a math exercise and I don't get it because it is too difficult, I look at the answers/ask for help or solve it with some "cheat" method, am I really learning anything? And if I don't learn anything, how do I solve the exercise without help or without having to spend 1 day trying to solve it on my own?
@user-yj7mw9od3k 5 ай бұрын
Can u do review on 48 hours of honors calculus
@heartburn6160 5 ай бұрын
Do I need to take Trigonometry before taking calculus?
@Sirslicey 5 ай бұрын
Yes, calculus relies on trigonometric concepts just as it relies on algebra.
@axelromero5529 5 ай бұрын
From personal experience, the university I attend requires trig before calculus I so you have to take trig where I am at, not to say it's different for other universities. There may also be a prerequisite where trig is integrated with pre-calulus - under a name other than trigonometry. I found that trig did give me some basic understanding to topics in calculus I and beyond so if it is not required to take trigonometry, I would recommend taking it either way.
@LeisureSuitLaurent 5 ай бұрын
You should be familiar with it. You will have to derive and integrate sin/cos/tan/csc/sec/cot functions. And you might have to know some basic identities to flip equations around into integratable form =/. Do you need an entire class on it? I never had one, they were just built into my high school curriculum. But you should know those functions and some basic identities. My universities just started in at Calculus I.
@heartburn6160 5 ай бұрын
Thank you!@@LeisureSuitLaurent
@heartburn6160 5 ай бұрын
I appreciate the time you took to reply and the advice. Thanks.@@Sirslicey
@joelweidenfeld471 5 ай бұрын
Gottfried Wilhelm Leibniz (1646-1716) the last “universal genius and his mother was a Schmuck...
@sir_albaxious1909 5 ай бұрын
For me: Understand 'Calculus with Analytic Geometry' by Earl W Swokowski.
@topdog5252 5 ай бұрын
It is the advice I have heard... just do zillions of integrals! Just Do It!
@atulyashaurya2495 5 ай бұрын
Hello sir. I want an advise. I want to learn college maths (real analysis and algebra) on my own. I am a beginner. Is it sufficient to watch video lectures + solve lots of problems or should i read at least one book? Please help.
@allrounder2367 5 ай бұрын
What is the name of this guy (the youtuber on which channel i am commenting)? And what is his nationality as well? American? British?
@amarjeetkaur6881 5 ай бұрын
Sir Can you please recommend me some books on number π.
@Ancin47 5 ай бұрын
Hello! On KZfaq, who’s the closest person to you for Biology and Chemistry?
@user-so5vl9ee6g 5 ай бұрын
I'm completely lost and confused between mathatics and electrical engineering I love them both but I feel more comfortable towards mathematics, is there any bright future for mathematicians in the marketplace? Or shall I go with electrical engineering?
@sir_albaxious1909 5 ай бұрын
There is another option. How about applying math in electrical engineering? It helps yk.
@LeisureSuitLaurent 5 ай бұрын
Engineering is industrial application - you'll find more jobs there. They're both good degrees, diff strengths/weaknesses. Engineering is more specialized right. But electrical should be in demand because of all that chip war going on now - which NVDA and TSMC are absolutely cleaning up.
@kevin-gg8ir 5 ай бұрын
Trig sub....Arrgh!
@luisramrod9121 5 ай бұрын
Now I want to take integration insanity course, so I can become an integration god.
@luisramrod9121 5 ай бұрын
Cal 2 is my Achilles heel
@BC-2 5 ай бұрын
Who's gonna be the judge of if I've "mastered" calc?? Some know nothing teacher who can't explain it themselves beyond "duuuhhhh, that's just how it is..." No thank ya
@tassotzobiko1135 5 ай бұрын
I am the first !
@ajj-qi7jg 5 ай бұрын
am i the only one thinking he looks like jeff bezos with hair
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