Learn Calculus: Self-teaching Tips & Resources

[Ethan Hummel]

Hello everybody, I am currently a sophomore in high school and I am very interested in teaching myself Calculus. I have a good grounding on Algebra and Trig. I am here today to seek guidance of what would be the most effective way and proficient way to go about teaching myself Calculus. I have a textbook by James Steward its called Calculus 5th Edition(very original name ). I would preferably like to take an online course but study at my own pace and I would like to get it done within 3 months. I am aware of resources like MIT OCW and Khan Academy but I do not know which one to choose. Can you guys please offer me guidance also if anybody did teach themselves Calculus, exactly what way did you do it? Thank you very much for any comments in advance.

 

[Mondayman]

Is there a reason for needing to finish in 3 months?

I would recommend just opening up the book and working away. Use Khan Academy as a secondary resource if you find yourself stuck. I don't think the MIT OCW is necessary - in fact I think watching those hour long lectures is time that could be better spent just working through the book!

I am not familiar with Stewart's book but I have heard that it lacks rigor. However if you're only at the HS level maybe it will serve as a good first exposure. I'm sure someone with a better knowledge could enlighten you better than I.

 

[Ethan Hummel]

Is there a reason for needing to finish in 3 months?

I would recommend just opening up the book and working away. Use Khan Academy as a secondary resource if you find yourself stuck. I don't think the MIT OCW is necessary - in fact I think watching those hour long lectures is time that could be better spent just working through the book!

I am not familiar with Stewart's book but I have heard that it lacks rigor. However if you're only at the HS level maybe it will serve as a good first exposure. I'm sure someone with a better knowledge could enlighten you better than I.

Hey thank you for responding. I wanted to learn Calculus at a college level not high school, and I don't really want to go through the whole textbook because I find that monotonous and confusing at time.

 

[Student100]

Good luck condensing the contents of that book into three months- when typically it's studied over a year or more.

I don't like Stewart, but you already have it, so go through the text starting with chapter one. Read the book, work the examples, reason out the proofs when they're there, and then work through the exercises doing odd problems. There's no real trick to do it any faster.

Hey thank you for responding. I wanted to learn Calculus at a college level not high school, and I don't really want to go through the whole textbook because I find that monotonous and confusing at time.

Huh? What do you mean?

 

[Mondayman]

I wanted to learn Calculus at a college level not high school, and I don't really want to go through the whole textbook because I find that monotonous and confusing at time.

Well, you're going to have to at some point. Video or live lectures are not a substitute for working through examples, proofs, derivations, and the problem sets. They can only supplement material.

And as Student100 pointed out, that is a lot of information to absorb in three months and really isn't recommended. Especially if you plan to go into engineering or sciences.

 

[NathanaelNolk]

I don't think the MIT OCW is necessary - in fact I think watching those hour long lectures is time that could be better spent just working through the book!

I strongly disagree. In high school I used the OCW lectures and it really helped with the examples. It prepared me for more abstract textbooks. I could tackle Spivak after having a working understanding of Calculus (still in high school). I'm not saying reading a textbook is bad (quite the opposite, actually), but I think actual examples worked out by a professor that knows his subjects well is in no way a 'waste of time'.

Hey thank you for responding. I wanted to learn Calculus at a college level not high school, and I don't really want to go through the whole textbook because I find that monotonous and confusing at time.

What exactly do you want to achieve by self-learning Calculus? As an example, I really wanted to get into QM as a high school student so I self-studied Calculus, Linear Algebra, ODE's and mechanics. Do you have some similar goal (a concrete one, I mean)?
If you just want to get a flavor of higher mathematics, I suggest just watching Khan Academy, OCW lectures or this wonderful series. Otherwise, get down to work and read through Stewart (although I don't really like that textbook).

 

[Jeff Rosenbury]

I did this in the '80s with a workbook from the local library and a CRC. Then I skipped the Calc I in college and got in a kerkufle because their class registration program only checked math skills for entering Calc I students. I earned a bad reputation as a smartass. I don't think I've ever had Trig.

Work problems. Work more problems. Calculus (especially integration) takes practice. I'm so rusty, I doubt I could solve even a basic integral without a text of some kind.

 

[Mondayman]

Video lectures don't work for me. But you're right that they aren't a waste of time, especially for someone self studying calculus for the first time. I take that back.

I recall reading here that for every hour of lecture, you should put in atleast 2-3 hours of working problems.

 

[micromass]

I recall reading here that for every hour of lecture, you should put in atleast 2-3 hours of working problems.

I'm not disagreeing with you or anything, but your statement needs further qualifications. Because I can do very simple and stupid problems for 2 hours straight, and it will gain me very little. So just solving problems isn't really good enough. The problems need to convey important concepts and techniques and be somewhat challenging. Typically, one would start with very simple problems, and end with more difficult ones. Creating your own problems is very helpful too!

 

[NathanaelNolk]

I recall reading here that for every hour of lecture, you should put in atleast 2-3 hours of working problems.

I think that for Calculus, you should put in even more. Take integrals for instance. While you may understand how integration works on a conceptual level, if you don't do a lot (and I mean a lot) of them in the early stages of your learning, then you won't really have a good basis for later applications of said integrals. Of course, when you get to more abstract (read theoretical) courses, you don't have to drill such concepts, but you still have to do a lot of problems to really understand said concepts.

Typically, one would start with very simple problems, and end with more difficult ones. Creating your own problems is very helpful too!

This is especially true. To use my previous example, doing two hours of integrals involving only powers of x would be really stupid.

 

[Mondayman]

This is very true. You gain more from 5-6 hard questions that challenge your understanding than 50 simple computations.

I actually meant to add that someone hoping to complete all of this in a mere three months would probably have to go beyond the 2-3 hours. I may be wrong, but it just seems like a lot of information to absorb in a short span.

 

[NathanaelNolk]

This is very true. You gain more from 5-6 hard questions that challenge your understanding than 50 simple computations.

I actually meant to add that someone hoping to complete all of this in a mere three months would probably have to go beyond the 2-3 hours. I may be wrong, but it just seems like a lot of information to absorb in a short span.

If the OP only wants a superficial understanding of these topics (i.e. not doing any so-called 'hard' problems at all), then I think it is quite doable. If instead the OP means mastering Calculus to a level with which he can use it in various contexts, then I don't really think so, especially if he also covers multivariable calculus.
To elaborate on this, I'll use my own example in high school. I live in Switzerland where calculus, probability and analytic geometry (alongside trig) are the core subjects on the final exam of high school. In the calculus part, most students understand how to compute limits, derivatives and integrals, and can usually analyze functions (extrema, sketching, optimization problems) and use some integrations techniques to solve basic problems with integrals (volumes of solids for instance). At the end of the calculus sequence though, many don't really understand what the integral means and why it actually works (continuity and such). It's usually the same with derivatives where we end up with students learning all the differentiation rules, without realizing why it works that way.
Of course this doesn't apply to every students, those taking maths as a specialization even do Linear Algebra/basic ODEs so they have a deeper understanding of the tools of calculus.

 

[IGU]

Hello everybody, I am currently a sophomore in high school and I am very interested in teaching myself Calculus. I have a good grounding on Algebra and Trig. I am here today to seek guidance of what would be the most effective way and proficient way to go about teaching myself Calculus.

Top high school math students use Art of Problem Solving. Get their Calculus book and work through it.

I have a textbook by James Steward its called Calculus 5th Edition(very original name ). I would preferably like to take an online course but study at my own pace and I would like to get it done within 3 months.

Stewart is not worth your time. AoPS does online courses too, but they cost a lot more and won't go at a pace to get it done quickly.

Can you guys please offer me guidance also if anybody did teach themselves Calculus, exactly what way did you do it?

My kid taught himself calculus out of Apostol (volumes I and II), but it took much longer than three months. Don't try that unless you are very good and want serious rigor. Whatever you do, make sure you find good problems and work them yourself.