Calculus

What Hacker News says

1. vector_spacesFeb 2020
   I like books by Ron Larson, particularly his Trigonometry and Applied Calculus books -- the applied calculus title (intended for social science and business majors) vs his "Calculus" book (intended for math, physics, and engineering majors) is much gentler for people seeing this material for the first time. Although I do highly recommend his Calculus book once you have the other book down.

   Gelfand also has some nice texts on Algebra, Trig, and Geometry that are reasonably cheap, especially if used.

   I'm older and went back to school later in life to study math, and these are the books I learned that material (for the first time -- I flunked math thru high school) from.

   Here are the exact titles and ISBN-10s:

   Ron Larson, Calculus: An Applied Approach, ISBN: 0618218696

   Ron Larson, Trigonometry, ISBN: 1133954332

   Israel Gelfand, Trigonometry, ISBN: 0817639144

   Israel Gelfand, Geometry, ISBN:1071602977

   Israel Gelfand, Algebra, ISBN: 0817636773

   And as others have mentioned, Khan Academy is pretty good, although I tend to prefer patrickJMT's explanations a bit more: http://patrickjmt.com/

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2. alephnerdJul 2023
   CBSE is literally just the limits and basic derivatives. It's literally Pre-Calculus as it is taught here in the California (Pre-Calculus with Limits, Ron Larson).

   With the Chinese curriculum, same story if not at a Sr Secondary School. Here's the curriculum for the Secondary Vocational Schools (aka the schools most Chinese students end up attending) - http://www.moe.gov.cn/jyb_xxgk/s5743/s5744/A07/202001/W02020...

   Notice how it caps at permutations.

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3. mhartlAug 2012
   I taught the physics core curriculum at Caltech for five years, so I'll do what I can to help. For many of the classes at Caltech, we never found a truly satisfying textbook, but when you're learning on your own that's still the route I recommend. This means putting textbooks back on your list for consideration. Buying a textbook for a full 1-2 year college-level physics sequence costs less than $200, much less if you buy used. You have parents, right? Now they know what to get you for your birthday.

   Your immediate goal should be to get a firm grounding in classical physics, which will be important for everything else you do. When choosing a textbook, the most important thing is to pick one that's aimed at scientists and engineers. That means it should be calculus-based, "algebra-based physics" being a contradiction in terms. If you don't know calculus, you should start there. (This will set you back some more money. Sounds like a plan for Christmas, Hanukkah, etc.)

   To my knowledge, none of the introductory texts are truly great, but I did some poking around and University Physics by Young, Freedman, and Ford looks like a good bet. If you need to learn calculus, Calculus by Larson and Edwards looks decent. Get the most recent editions if you can afford them, but I'm sure older editions are fine. Those two books alone should take you a year or two to consume, and they are likely to be very challenging unless you have an exceptional preparation in mathematics. But even if you get stuck occasionally, you'll still be way ahead of the curve. (I wish someone had put a calculus-based physics textbook in my hands when I was in high school. I would have been unstoppable. Unfortunately, though it now seems impossible, I went to high school before Amazon or even the Web, so it simply never occurred to anyone.)

   I recommend supplementing the textbooks with liberal use of Khan Academy videos and Wikipedia articles. More than anything, it is essential to solve a large number of exercises. Developing a good physical intuition is important, but physics is a quantitative discipline, which means being able to do calculations.

   One more thing: if you want to demonstrate your competence to the world (and to college admissions committees), it's a good idea to take the AP Physics exam (B or C) at some point. The AP Physics C exam is the best one to target if you only have enough time to take one, as it will let you test out of introductory courses at many schools. (Not at Caltech though—we have a separate system of placement exams.) Take a look at the AP Physics C website to see the syllabus. If you decide to take the exam, buying a test-prep book such as 5 Steps to a 5 AP Physics B&C is probably a good idea. If you go this route, try to negotiate with your school to get course credit for your independent study.

   P.S. At some point, read The Feynman Lectures on Physics. FLP doesn't make for a good introduction, but after you have a foundation it's gold.

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