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The Ultimate Calculus Resource Guide (AP Calculus AB/BC and Calculus I and II)
It has not been too long ago I was going through the same things through which you might be going: how in the world am I going to remember integration by parts, how do I memorize all of these formulas...and what exactly is calculus? Well, maybe not any of these questions. This page will hopefully serve as a guide to provide you with links and resources that will guide you through your journey with calculus. Of course, it is possible for me to write up all of my own material, but there is so many resources out that I think would do about 100 times better of a job than my best try, so I am going to leave it up to you to find which links and which books to pick!
I will try to be as descriptive as possible about each of the links, and I hope that some of these resources will be extremely helpful for you! If you have any other recommendations, please feel free to comment, and I just might add your suggestions!
A Mumbo Jumbo of Calculus Links
I am going to try and be as descriptive as possible about each of the links so that you do not end up looking at twenty different links that might not have been as helpful as you had hoped.
1. Paul's Online Notes- He has extremely, extremely detailed notes and his notes are very clear and detailed. This link is great for anyone who is considering self-studying for Calculus or preparing for the class in advance. Unlike many university level textbooks, which might only provide one or two examples proceeding a theorem and proof sequence, he makes sure that you see a variety of potential problems that might come up regarding the topic so that you are more than prepared to tackle and understand what in the world all those theorems and corollaries might mean in your calculus class! He has this sort of lecture format for all of the normal mathematics sequences for the university level. A must-read if you are preparing for any calculus course! He also will let you print out his lecture notes in PDF format.
2. Khan Academy- Khan Academy is a great resource if you might be stuck on a homework problem. Also, this link is not just for mathematics; he literally goes through so many subjects, and this resource is really invaluable for many of the introductory college courses/ AP courses you might be heading into. Basically, he has a series of Youtube videos that will go through step-by-step questions in the topic in question and proceed with many examples. Everything is free of course, and it is great if you might just be confused on one or two topics and are looking to make sure that you get the concepts.
3. MIT Open Courseware- This is a great, comprehensive website that provides lecture notes of all the material required for a standard Calculus I/II class. This is also a great resource for study material, and they also have many practice exams (and worked out solutions!) all for free. The notes are very clean, however the material might get a tad bit technical. A must see for those who are self-studying, or would like to prepare for a calculus course. They also have many other courses (mainly for the AP level and beyond) in case you might need supplemental material for other courses.
4. Mr. Calculus- Preparing for the AP Exam? You might not have access to the multiple choice questions, but for the free response questions, this is the next best thing! This site has over a decades worth of AP short response questions, with worked out solutions! A must see for those who are taking the AP Calculus AB/BC exam.
Need some practice with your product and quotient rule? Need to look at some similar problems to your problem set in order to understand what in the world the question is talking about? This book, with 3,000 solved problems just might be your solution. No dry background material, it just gets to the point of giving you your 3,000 questions. If you are planning on getting this book, make sure you know your basic calculus rules or have a book/textbook that will provide you with reference material in case you are not sure from where the formulas/theorems are coming.
Need a little background material? This one is a slightly less intense version with 1,105 examples, but there is some basic material in the beginning so you can reference what your questions are about.
This book has so many review questions that you should have a great foundation for the exam. Also, the questions can get pretty tricky, so the book is sure to sharpen your eye for potential trick questions.