Name: Calculus
ISBN: 9780471000051

Calculus

An introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

What Hacker News says

apricotApr 2025

Calculus by Thomas Apostol (also from the sixties) teaches integration before differentiation as well. Great textbook!

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wwarnerMay 2023

Calculus I, Tom Apostol

Introduces calculus using vectors from the second chapter. For me, it was a very natural and intuitive introduction to the topic.

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laichzeit0May 2022

Supposing you have at least high school mathematics under the belt:

1. Book of Proof by Hammack [1]

2. Tom Apostol Calculus Vol 1 (stop at Linear Algebra)

3. Linear Algebra by Insel, Spence & Friedberg

4. Understanding Analysis by Stephen Abbott

5. Tom Apostol Calculus Vol 2

These are books with excellent exposition, and solution manuals are available when needed. You are absolutely required to do all the exercises. To learn mathematics is to do mathematics.

Two other excellent books are Spivak - Calculus, the problems in this book are very good, but much more difficult than Apostol. For more advanced analysis there's Walter Rudin's Principles of Mathematical Analysis (baby Rudin), which on its own is too difficult as a first exposure to analysis, but there's a cool professor that recorded an entire semester of baby Rudin lecture videos [2]. This is as close as it gets without being enrolled in a university.

[1] https://www.people.vcu.edu/~rhammack/BookOfProof/

[2] https://www.youtube.com/watch?v=ab41LEw9oiI&list=PLun8-Z_lTk... (the first video is a bit blurry, it gets better)

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umanwizardFeb 2017

"Calculus" by Tom Apostol has lots and lots of simple physics applications.

I cant think of any obvious applications of calculus to the average non-technical person's daily life. If that's what you mean, you're going to have a bad time, as I think it's a misconception of what math is supposed to be for.

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MichaelCrawfordMay 2015

I'd like to go back to grad school, get my PhD, but it's been so long that I've forgotten all my math.

I'm planning to start with high school geometry. If I can find a copy, I'm going to use the same textbook as I used in high school. It was really good. Not sure about what I'll use for a trig textbook. For calculus I'll use Tom Apostol's Calculus vols I and II - that's what we used at Caltech.

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ademApr 2014

My recommendation is "One-Variable-Calculus with and introduction to Linear Algebra" by Tom M. Apostol, followed by "Mathematical Analysis". Both books form a great combination!

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