Awesome Self-Teaching Calculus Book

[claytonh4]

Awesome Self-Teaching Calculus Book!

Hey everyone! Sorry, I would've put this in the learning materials section but it said I can't access it; I don't know if that's for admin only or what. Anyways, I'm going to be a high school senior, and I took heed to everyone's advice about gaining a solid foundation in mathematics before pursuing knowledge in physics; so, I got this calculus book to get a leg up (I'm taking calc. and stat. this year, but wanted to get a head start this summer) and I must say, it's an amazing help and guide for anyone, especially high school students or college freshman who want to learn calculus.

The book is called: Quick Calculus 2nd Edition: A Self Teaching Guide by Daniel Kleppner and Norman Ramsey, both of whom are/were physics professors at MIT and Harvard respectively.

This book is great because it was written by physics professors specifically because not enough physics students had a good calculus background, so I thought it'd be great for myself and any other prospective physics student. It's designed so that you basically teach yourself through a combo of concepts and problems. The great part is, after you answer a problem or question, the book gives you the right answer; and, if you answered correctly, you are prompted to move on to another section; if you answered incorrectly, it directs you to a worked out and explained solution, and furthermore for you to try another, making it very interactive rather than a simple textbook.

For anyone who wants a good calculus background, I highly recommend it!

 

[joeoettinger]

I completely agree that Quick Calculus is awesome! It's a GREAT self-teaching guide by two physicists, one of them a Nobelist. It's only defect is a number of errors (19) in the text.

I kept a list of the errors, and I found 2 websites with lists of the book's errors.

I, and apparently many others think IT'S THE VERY BEST CALCULUS SELF TEACHING GUIDE. Use this list, but don't let it keep you from reading the book!

Here's the list:
1. p32, frame 60, answer to tan φ question is b/a, noy a/b
2. p107, frame 206, d/dx(u/v) = vu’– uv’/v^2, not uv’– vu’/v^2
3. p111, frame 211, reference should be to Appendix A5, not A4
4. p119, frame 226, reference should be to Appendix A8, not A9.
5. p120, frame 228, should read “If right, go to 231.”
6. pp148-9, the same constant is called D0 in box 287, D in box 288.
7. p149, frame 288, t = 1/c ln cD/B should be t = -1/c ln cD/B
8. p164, frame 310, 1/2 sqrt(u) should be 1/(2*sqrt(u))
9. p164, frame 312, last line should be -cos 3x, not cos 3x
10 p166, frame 316, solution is ln(x^2+4)+c, not ln(sqrt(x^2+4))+c
11. p173, frame 330, No option listed is correct. Answer is -15.
12. p186, frame 354, In the first equation, and subsequently on the page, the x has been mistakenly omited from Δx. It's an distracting ommision when new material is being introduced.
11. p187, frame 355, there should be two terms y2 in the line that has the 2Δ/6 in it;
it should read (2Δx/6) (y0 + 4 y1 + y2 + y2 + 4y3 + y4 + ...)
12. p188, frame 357, should be I = ∫x^3dx not I = ∫x^4dx
then result is 2500, not 20,000 (1/4 x^4 over interval 0 to 10)
13. p189, frame 358, using Simpson's rule gives 2500 not 2501.33
14. p202 frame 378, last equation should end with dy]dx, not dx]dy
15. p206 frame 383, solution is 8/3 - 4a, not Cbaq^3/12
16. p231, Appendix A8: A reference to frame 109 on p.58 would be helpful for the last line of the proof. Also, no justification is given for the next to last line, where the limit of the natural log of an expression is said to be the same as the natural log of the limit.
17. p248, number 48’s hint should read Appendix B1, not B3.
18. p249 should be -1/2*e^(-x^2)]
[17. p253 Wolfram: "Integral doesn't converge. Cauchy principal value = 0."]

Most of these errata are from:
https://www.bishopoconnell.org/uploaded/Academics/summerassignments2012/AP_Physics_C_Summer_Assignment.pdf
Some are from:
http://www.kurup.org/blog/2003/12/11/errata-for-quick-calculus/
And a few are from me. If you find any more errata, or any errate in these errata, please let me know.

 

[claytonh4]

Thanks for your reply! I too have noticed a pretty extensive number of errors in this book as you have mentioned, so thank you for the errata list! Other than that, I definitely like the layout and teaching method.