Here's the type of textbook I'm looking for. Does it exist?

[Lane4]

I am a college physics grad. For many subtopics of precalculus or calculus, the following statement applies to me:

"I can easily solve problems that involve X, but I can't really tell you what X is or why it matters."

I'd like to spend some spare time to gain a strong understanding of the central concepts of precalculus or calculus that I only learned superficially.

Can anyone recommend a text to work from, based on the following criteria?

- Covers precalculus or Calculus BC material.
- Focused only on the fundamentals and central concepts. For example, I want to understand integration by substitution, but I don't need or want to review every substitution technique.
- NOT focused on (1) tricks, (2) rote problem solving, or (3) teaching general problem solving techniques
- Ideal for self study

Thanks!

 

[Xtensity]

There is a website I am using which many have heard of.

http://www.khanacademy.org/

I'm using it right now to learn Calculus. It's all 1 guy making all of the videos, and in each lesson he tries to explain it in a way so you can have intuition on why you're doing what you're doing.

Sal received his MBA from Harvard Business School. He also holds a Masters in electrical engineering and computer science, a BS in electrical engineering and computer science, and a BS in mathematics from the Massachusetts Institute of Technology.

Imo, it's a much better way of learning than traditional textbooks. In terms of calculus I believe he only covers the first 1-2 semester of college calculus in around 150-160 videos.

The various subjects he covers on his site:

It's not a textbook, but it is a very good source of learning on your own. All the videos on his site are separated nicely so you can find what you're looking for specifically.
Best thing of all, it's 100% free and he's dedicated his life to his site in hopes of providing better educations for students worldwide. Covering subject from K-12 and a bit into college.

He is helping to change the world with his site and has received quite large donations from people such as Bill Gates.

Good Luck.