How to Self Teach and Prepare for Calculus

In this short video I answer a question I received from a viewer. He is trying to learn calculus on his own so that he can prepare for his calculus course. Do you have any advice? If so, please leave a comment below.

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[danielmrosser]

The best preparation for calculus is a solid understanding of college algebra and trigonometry— the sole purpose for the course entitled “pre-Calc” is to prep you for the Calculus. Pre- Calc is the first calculus course! This reminds me of the aphorism “if you want to learn algebra, take a course in Calculus!” The message is that algebra and trig are the bedrock principles for Calculus. If you have weaknesses in either subject, it will be revealed when you take a course in Calculus since so much of this beautiful theory requires proficiency in algebra and trig. When you open almost any book on Calculus you’ll find the first chapters will cover topics in algebra and trig, the subjects covered in pre-Calc.

[saiello]

I'm in my mid 50's and have been casually learning the basics of calculus because I simply missed out in my younger years and I want to see what all the fuss is about...! 😋 My advice is to get some solid context behind calculus, learn some of the history and philosophy behind it and how and why it came to be. The universe is best described by how much and how fast it changes in relative terms rather than describing it in absolutes and calculus is the best tool we have to this end. This was my starting point. There are a lot of videos on YouTube that give you "the big picture" and I would recommend these. There is no doubt that learning any subject in a contextualised way helps dramatically.

[aliensoup]

Total immersion, and don't skip around subjects. Calculus is highly structured, so every concept is dependent on what comes before. Start from the beginning and don't proceed until you are totally proficient with the current lesson. If you have difficulty understanding a concept, find another source of instruction. When I self-studied Calculus I was using at least 6 different sources of information including online textbooks, university lecture series, online testing programs, and tutorial videos. I did the same thing for linear algebra. Then do lots of problems, and don't quit until you have solved the problems and understand your mistakes and where you had trouble. By the end of the process I was proof-reading Calculus 3 content for an online textbook.

[allthesepollitos]

Without a doubt be solid with algebra and trig. I’ve seen so many students stuffer in calculus because they have a very weak algebra/trig foundation. “You can always be better in algebra”

[douglasstrother]

A book has many advantages: no batteries required (still works w/o WiFi); it's tangible (make notes); it's structured (start at the front), unlike search engine results; and it should have a bibliography, if you want to explore subjects in more detail or from a different perspective.
Skim through the whole thing, cover to cover (preface to index), before diving into the first chapter. The geometric nature of Calculus makes it easier to digest than other branches of higher mathematics; so learn how to draw examples of definitions, theorems, problems, etc.

Learning Math, Physics or any other stuff like this is little different that learning a musical instrument or a sport. At first, you'll feel clumsy, but with practice, you'll be surprised how much you can learn.

Turn all of your electronics off, and find a quiet place to work. Watch "Attitude, Concentration & Effort", by The Math Sorcerer, then turn your electronics off!

[SuperTommox]

I'm starting calculus in Italy next Fall. Here it's called mathematical analysis. Can't wait!

[ffcac]

I started recently with calc III on my own and am hoping to go through linear algebra, DEs, and then Analysis over the summer. I have a bit of olympiad experience (I got top 5 in Canadian Math Olympiad and top 20 in the USA Math Olympiad this year), but I really haven't formally gone past HS math. I honestly am just excited to go further in Math in uni come September :)

[pinedelgado]

Math Sorcerer, you are the Love ALL your videos!!! Thanks for hosting, producing and posting THIS ONE!!!! :) :) :) :)

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[surrealistidealist]

Get a little study group together, even if it's just with one friend, and/or at least find a mentor. The key here is to learn how to TALK about math and make your lessons and studies be as conversational as possible! This makes it all more understandable, memorable and meaningful!

I would have avoided so many pitfalls if only I had a second pair of eyes giving me feedback, or even just to help me feel better when stressed or lonely.

Conversation can be its own form of high-frequency, low-stakes self-testing. And that's essentially the most potent way to learn and grow that I know.

And personally, I recommend trying to make your studies as interdisciplinary as possible, at least as a long-term plan. Making connections between disciplines can be another fun and meaningful form of high-frequency, low-stakes self-testing, and it can also be done through conversation.

Learn how to cycle between high, medium and low levels of difficulty. It's probably best to spend most of your time at whatever's only moderately difficult for you. But easier topics and problems can help you perfect what you already know and prepare you for challenges that really make you grow. Harder topics can make you more motivated to do the less challenging stuff necessary for mastery, and the harder stuff can give you guidance, too.

[schrodingcheshirecat]

Get good at Precalculus. A textbook at a thrift store can be picked up for a few bucks.
Get the gist of a subject by scanning the table of contents. I take notes all in my texts. do what works for you. after you finish a section. review concepts using your own words, rework some examples. get a clear picture of why the answers worked the way they did. then work a few problems to test you knowledge while getting practice. Mistakes are OK, they show you where you are slipping up. Keep trying.
tutorial videos such as The Math Sorcerer's can fill in gaps and save time.
Later, in class you'll have a level of proficiency during lectures while half of the class is catching up, . that's an addictive feeling.

[eflat]

I'm 67, at least for the next 2 months, and have been trying to teach myself math with a goal of learning enough math to work my way through a university level physics books. I live on a fixed income and was able to scrape up enough money to buy a few used math books and a ti-84 plus CE calculator. I think for my the most frustrating thing is getting answers to only odd numbered problem but get curves thrown my way on the harder even numbered exercises. For example yesterday I was working on exercises about simplifying expressions with imaginary number and putting them in a+bi form. I do fine then get toward end of the exercises and sure enough I get an even numbered problem involving irrational square roots. I will search YouTube for help but often those YouTube videos just show the easier problems I can already solve. Is there any advice on how to deal with those or should I just grind on?

[hampusandersson]

I'm 28 and applied to study physics at uni next year. I'm working through algebra 2 as a reminder and then working through pre-calc and then calc one. I find the for dummies books are very good and college algebra and trigonometry is very much a must for anyone looking after doing calculus. As I work through trig and algebra, I'm watching videos on calc to see how my subject relates to calculus helping me to get a deeper understanding

[omniyambot]

Easy! Go to Khan Academy!!! Take precal and master Algebra II. Then take the whole calculus. Sal Khan teaches deeply into intuitive stuff plus rigorous proving. Then combining practice, you will get fluid and deep understanding of subject. Yeah, buy a book, read other resources, watch youtube videos like in this channel. Actually not that easy but entirely doable. I was stupid at math until I did this. One year later I am helping physics graduates in their calculations.. I will be freshmen this coming month and I hope I'm ready!!

[samridhabarman]

Please do more videos like these 😭😭😭 i really need this motivations

[Nnn_k]

For me i started my long journey with calculus when i totally stop caring about school and was so excited to learn some pure math, i stopped caring and just foxed on having fun while learning, i got an A+ in all my exams, calculus is amazing just give yourself time to learn

[aomoussynonymous]

For learning pre-calculus, preliminary algebra (Higher algebra by Bernard Child), geometry (Elements of Coordinate Geometry by S.L. Loney), trigonometry (Plane Trigonometry by S.L. Loney) and basics of linear algebra (YouTube lectures / Linear Algebra : A modern introduction by David Poole) should be thoroughly studied in the same order. For building self confidence in calculus through practice one may study Schaum's 3000 solved problems by Elliott Mendelson. Most beginner calculus books are usually isomorphic.

[thNebula]

I have gotten through Calculus I-III with B average but still feel I need to go back and be great at writing proofs and logic before going further. I would love for there to be a thorough course from basic logic and proofs through more complex at the level of math majors.

[nyrmike]

Meason, I like the advice given by The Math Sorcerer. Just get a used book even if an earlier edition of the book that will be used by the professor in that class and read and study the book and do the exercises. There are many math channels where you can watch the videos and study the same topic in the book you have. If you use this approach I am sure you will do well. Just word of advice make sure you have a good sound background in algebra, trigonometry and basic geometry before self studying Calculus. Good luck!

[MarkKoltkoRivera]

Mason, especially if you have not taken a math class in seven years, you might want to start at the _super_-basic level. Allow me to recommend:
-- Calculus for Dummies
-- Calculus for Dummies Workbook
-- Calculus II for Dummies