Learning Calculus Without Paying for a Tutor
I spent about six months last year going through standard calculus material while building an open study system I ended up sharing with a few friends. The Diy Calculus Guide emerged from that mess of PDFs, YouTube links, and handwritten notes. It is not a polished product. It is a structured path that takes you from high school algebra through multivariable calculus and differential equations. The guide is organized by topic progression rather than by textbook chapter. Most people try to work through Stewart or Thomas cover to cover and burn out around Chapter 8. The guide skips that trap. It starts with limits because everything else builds on them, then moves to derivatives, integrals, series, and finally vector calculus. You need a few resources alongside it. I recommend Paul's Online Math Notes for worked examples, MIT OpenCourseWare 18.01 for lectures, and a graphing calculator like Desmos or GeoGebra for visualization. The guide tells you exactly which video corresponds to which concept and which practice problems actually matter.
How It Actually Works in Practice
Here is what happens when you follow it. You pick a topic, watch the assigned lecture once, read the corresponding notes section, and then do the problem set. The problem sets are tiered. The first ten problems teach the mechanic. The next five test whether you actually understand it. The last two are edge cases that show up on exams. I ran into a specific issue when someone tried to use the guide to prepare for an AP Calculus exam in three weeks. The guide is designed for a semester-long pace. Rushing through it blindly would leave gaps in their understanding of series convergence tests. What I did was pull the first four weeks of material and compress it, adding targeted practice problems for integration by parts and partial fractions since those are the highest-yield topics on the AP exam. That person scored a 4. Not a 5, but a 4 after three weeks of solid work is reasonable.
What Beginners Miss
The biggest mistake I see is skipping the algebra review. People jump into derivatives without being comfortable with polynomial long division, factoring quadratics, or manipulating rational exponents. You cannot do implicit differentiation cleanly if you spend three minutes just trying to isolate y. The guide includes a two-week algebra warm-up at the beginning. Do not skip it. Another counter-intuitive thing: you should learn logarithmic differentiation before you feel ready for it. Most courses introduce it late, but it is the cleanest way to handle functions like x^x or complicated products of terms. Learning it early saves you from doing tedious product rule expansions over and over.
Get the Full Details
Technical Nuances Worth Noting
When you get to the section on convergence tests for infinite series, the guide emphasizes the ratio test first because it is the most broadly applicable. But the ratio test fails for p-series and alternating harmonic series. If you only memorize one test, you will get stuck. Learn the comparison test and the limit comparison test alongside it. They are faster for most standard problems once you get used to them. For multivariable calculus, the chain rule with multiple variables trips up almost everyone the first time. The guide walks through a specific notation approach using subscripts that makes tracking which variables depend on which other variables much less error-prone. I use this method myself when I am grading assignments. It catches directional derivative mistakes that students keep making.
Limitations and When It Fails
This guide does not replace classroom instruction for students who need direct feedback on their work. If you are self-studying and you make a sign error in a triple integral, the guide will not tell you. You have to compare your answer to a solution manual or use an online checker. I also found that the guide assumes you have access to a decent computer or tablet for graphing. Working entirely on paper is possible but slower and more frustrating. There is no spaced repetition system built into the guide. You will forget integration techniques if you do not revisit them. I built a simple Anki deck for my own use that maps to the guide's topics. It takes about two hours to set up and then maybe ten minutes a day to maintain.
Where to Get It
You can find the current version of the Diy Calculus Guide on GitHub under the repository name diy-calculus-guide. There is a README with installation instructions, though it is mostly just a collection of linked PDFs and markdown files. The math content is licensed under Creative Commons Attribution-NonCommercial 4.0. Feel free to fork it and add your own problem sets if you want something tailored to a specific course. If you want the full thing downloaded as a single PDF, there is a build script in the repo. Run it with Python 3 and the required dependencies listed in requirements.txt. It took me about forty-five minutes to assemble the first clean version, and I have updated it a few times since. The latest commit adds corrected solutions for the Green's theorem problem set, which had errors in the original version.
