If you're reading this, I'm going to presume that you are a student in high school or college preparing to take calculus, or physics, or perhaps chemistry or engineering. You've had lots of math - algebra, geometry, trigonometry, perhaps a few semesters of calculus.
However, you've never really had to use all this math to reason with. When presented with a page of integrals you can (possibly with a few minutes to review) manage to work through most of them correctly, but when presented with a problem in words and pictures, especially one that depends on relations you're struggling to master (like the laws of physics) you have no idea how to proceed to reduce the problem to just doing some particular integral.
There are also a bunch of things that you just plain don't know. Maybe they were covered one time in one course that you've taken. Maybe your book, or your class, or your teacher just failed to cover them. Maybe you were absent that day. Who knows?
However it came about, you find yourself in a course where you really need to know those things, to have them at the tip of your fingers, ready to pour out intelligently onto paper as you solve problems that are difficult enough if you do know well all of the things required to solve them.
This short book is for you. It is written in a lecture note, summary/review style that should make it fairly easy to find things that you need to know quickly, and filled with the actual derivations and short explanations that support the material so that you can actually understand it and not just memorize it. If you keep it handy - on your laptop, in your backpack - it can be a quick and easy way to look things up or review them while doing your homework in various science courses or studying for exams.