Autodidact Calculus: A Junior's Summer Challenge

[beanrique]

Hey, I'm just a young inspired junior who is wondering how I can achieve learning calculus on my own during the summer. Also, I'm wondering if any of you have gone out your way to learn a subject by yourself and how you accomplished it

 

[jedishrfu]

I used the Schaum's outlines series and worked all the problems in the topic I was studying. For Differential Calculus its pretty straightforward learn about limits and then learn the rules of differentiation and practice with a lot of problems. Learn to cross check your answer to gain confidence in what you've done. Integral Calculus is a bit more involved as integration is somewhat of an art that you can acquire after having done a variety of problems learning the tricks of the trade. More advanced Calculus gets into double and triple integrals and the areas of where these are used (eg physics, engineering...) and also vectors.

There's a good series of videos on this website that might help:

http://mathispower4u.yolasite.com/

Another resource is Khan's Academy videos (https://www.khanacademy.org). They are bitesize (aka 10 mins videos on one topic) and perhaps with a Schaum's outline you can learn a topic and then use the Schaums for additional problem sets.

 

[Axel Harper]

When I decided to teach myself some calculus, I used Thomas' Calculus with Analytic Geometry (blue cover with a lighthouse). It's a very straightforward and well-written book' and it's also cheap; I bought a copy for 1 cent. There are also great resources online. Someone already mentioned Khan Academy. A math professor wrote textbooks for calculus i, ii, and iii, hosted here: http://tutorial.math.lamar.edu/. Here's a link to a very good (and free!) precalculus book if you need to brush up: http://www.stitz-zeager.com/. Finally, male sure you do the practice problems - just as important as reading the book.

 

[xiavatar]

The first time I self learned a subject was really calculus. I taught myself calculus using an old advanced calculus book they used to use at MIT in the summer before senior year. I basically spent two weeks reading 24/7 of that during my summer break, and I learned to write proofs by noting careful details, in a notebook, of how they proved each and every theorem in that book. After I finished reading the book in those two weeks, I basically spent the next two to three weeks doing every single problem in the book, and the way I verified whether my proof was right or not, was by scrutinizing particularly hard problems for several hours, while working on other problems. I usually skipped the routine exercises, since they don't really teach you much except motivate memorization of techniques by repetition. But if you need to do these type of exercises, go for it! The types of problems you should focus on are the theoretical ones because these will immensely help you with understanding how certain ideas come about. And don't be discouraged if a certain idea might take you a couple hours to days to understand, its all part of the learning process. Try to figure out why the idea works by yourself, and then ask someone. Never ask someone for help unless you have spent at least a week thinking, and you still don't understand the idea.Also don't feel hesitant to teach yourself other subjects. After I finished the calculus book I taught myself Abstract Algebra, Graph Theory, Mathematical Logic, Set Theory, Number Theory, Statistics, Linear Algebra, Ordinary Differential Equations, Fourier Analysis and Differential Geometry. And all of this was done in one year. You'll be pleasantly surprised how quickly you can pick up learning a subject after teaching yourself something for the first time.

 

[xiavatar]

I suggest you try Essential Calculus with Applications by Richard Silverman. It's a nice little book that is easy enough for someone to start teaching themselves Calculus. And good luck. :)

 

[beanrique]

Thanks for the replies. The way that math is taught in my high school and in other, feels more like a chore than a fun and wonderful subject. I got inspired to find the beauty of math when I watch a Numberphile's video explaining why people hate math
Here's a link to the video if interested

https://www.youtube.com/watch?app=desktop&persist_app=1&v=Yexc19j3TjE

 

[Yellowflash]

Check out Spivak's Calculus book or try the calculus courses on MIT OpenCourseWare.