# Calculus book for 14 year old physics enthusiast

• Manuel Cardoso
In summary, these books may be a good starting point for someone who is wanting to learn calculus:-Precalc 2e-Calculus for Scientists and Engineers, by James Stewart-Calculus: Early Transcendentals, by David Denby-The Calculus Book, by Herbert Robbins
Manuel Cardoso
Hello, I'm trying to learn calculus, what books would you recommend?
For a beginner.

"Question" is possibly the worst subject line you could have used. I suggest changing it to "question about calculus books".

I also suggest a forum search since that question has been asked here numerous times.

malawi_glenn
phinds said:
"Question" is possibly the worst subject line you could have used. I suggest changing it to "question about calculus books".

I also suggest a forum search since that question has been asked here numerous times.
I corrected it.

berkeman, phinds and malawi_glenn
Depends on what you already know. Do you know precalc and trig?
This site has some free online books on algebra, trig, precalc and calculus.
https://openstax.org/subjects

Here are some recent threads regarding calculus book recomendations
https://www.physicsforums.com/threa...et-standard-vs-early-transcendentals.1017424/

fresh_42
Manuel Cardoso said:
Hello, I'm trying to learn calculus, what books would you recommend?
For a beginner.
https://openstax.org/subjects

They are meant to close the gap between school and university. You can also solve a simple exercise:
Figure out what a function is, and what it means that it is continuous.

You can use our forums to get help with this task. It is a simple example of what calculus means.

malawi_glenn
malawi_glenn said:
Depends on what you already know. Do you know precalc and trig?
This site has some free online books on algebra, trig, precalc and calculus.
https://openstax.org/subjects

Here are some recent threads regarding calculus book recomendations
https://www.physicsforums.com/threa...et-standard-vs-early-transcendentals.1017424/
You beat me to it.

malawi_glenn
In truth though, look into Khan Academy and work through the videos on Algebra, Trigonometry, Precalc and Calculus then use any good Calculus book as a supplement.

There are also high school AP and IB study books for Calculus which you can use as supplements.

PhDeezNutz and malawi_glenn
i like this free book;
https://babel.hathitrust.org/cgi/pt?id=mdp.39015017417141&view=1up&seq=7&skin=2021this is a very gentle introduction to the ideas of calculus, intended for high schoolers. in vol.1, chapter 3 treats differential calculus for polynomials, i.e. tangent lines to their graphs, and appendix 3.12 and 3.13 discusses very gently the fundamental theorem of calculus in that case, i.e. the fact that the slope of the area function A for the graph of a function f, equals the height of the graph of the function f. I.e. if A is the area function for f, then the slope of the graph of A, is the height of the graph of f, or A' = f, where A' is the "derivative" of A.

After part 1, which treats mostly polynomials, part 2 treats exponential, log, and circular functions sin and cos. The appendices to part 2 discuss the power series expansions of sin and cos and the euler formula relating complex exponentials to sin and cos. There is a minimum of discussion of formal limits and an emphasis on the underlying ideas of approximations. This is the most elementary and still mathematially honest introduction to calculus I know of.

Last edited:
jedishrfu
jedishrfu said:
In truth though, look into Khan Academy and work through the videos on Algebra, Trigonometry, Precalc and Calculus then use any good Calculus book as a supplement.

There are also high school AP and IB study books for Calculus which you can use as supplements.
Don't misguide young enthusiasts! It may help to watch movies like Khan Academy from time to time, but they are not a substitute for working actively (!) through good textbooks, and high-school books are rarely good books unfortunately. When I was at high school picking up a book on "mathematics for engineers" was a revelation, because all of a sudden I understood, why the "math" taught at school in fact works and that one can understand it. I'd thus recommend to look for these kind of books, i.e., math books for introductory university courses but not necessarily for mathematicians. The latter you can read, when you get interested in the more formal aspects but it's not so easy to get used to this mathematical rigor without having some intuitive ideas what the whole thing is about.

apostolosdt and fresh_42
idk watching videos can somewhat supplement attending a lecture. But sure, one should not entirely just watch videos, same as one should not only attend lectures. One has to make the material your own intellectual property. The advantage of watching a video is that you can pause and go back, the disadvantage is that you can ask questions but you do not get an immediate respons.

jedishrfu, fresh_42 and vanhees71
phinds said:
"Question" is possibly the worst subject line you could have used. I suggest changing it to "question about calculus books".

I also suggest a forum search since that question has been asked here numerous times.
Sorry I'm new here. Thank you to everyone who responded (can't reply to everyone, but thank you all)

Quick Calculus, 3rd edition by Kleppner et al.

Its structure is for learning calculus during a weekend, with a bit of effort of course! Originally written by Kleppner (MIT) and Ramsey (Harvard) for eager freshman students and subtitled "A Short Manual of Self-Instruction." (I still prefer the first edition!)

vanhees71
I have not read every single reply here, but I'll say this: be careful taking book recommendations from people here if you are not already experienced with the subject. A lot of the members here have been doing physics and mathematics so long that they have somewhat forgotten how hard it can be to begin. Additionally, some people are here just straight up gifted, and what they find to be an "easy introductory book" may be nearly impossible to learn from by yourself. This happened to me when a clearly gifted young member (who deleted his account) recommended me a Linear Algebra book, and it's been gathering dust ever since. The only reason I'm saying this is because I don't want you to waste your money.

Anyway. If you have a good grasp on Calculus I recommend getting a textbook that is targeted towards engineering undergraduates. Mary Boas' Mathematical Methods in the Physical Sciences is very applied and will give you a good foundation for Calc II and linear algebra.

hutchphd and jedishrfu
actually i think most of the earlier replies are pretty spot on for a beginner to calculus, and many are free. it is always of course a good idea to preview a book in a library before buying it.

Mr mayhem, if you still need a linear algebra book, there are many free ones recommended in various places here as well.

vanhees71
Manuel Cardoso said:
Hello, I'm trying to learn calculus, what books would you recommend?
For a beginner.
Listen to the good advice given, but here's the deal. This will be intellectually the hardest thing you have done, so don't be discouraged. It may be intellectually the most rewarding thing you have ever done so prepare to celebrate. In any event it will be worth the effort.

vanhees71 and berkeman
One last resource is the Gullberg book written by Jan Gullberg MD to help his son through college:

https://www.amazon.com/dp/039304002X/?tag=pfamazon01-20

Its a very readable book on math and the history of math up to the present with the math level at the first year undergrad level towards the end of the book ie calculus, differential equations, and linear algebra.

mathwonk said:
actually i think most of the earlier replies are pretty spot on for a beginner to calculus, and many are free. it is always of course a good idea to preview a book in a library before buying it.

Mr mayhem, if you still need a linear algebra book, there are many free ones recommended in various places here as well.
I had an applied course. Learned the most important things, namely matrix arithmetic and linear solving, etc. which is useful for my programming

## 1. What is calculus and why is it important for a 14 year old physics enthusiast?

Calculus is a branch of mathematics that deals with the study of change and motion. It is important for a 14 year old physics enthusiast because it provides a deeper understanding of the fundamental concepts in physics, such as velocity, acceleration, and forces.

## 2. Is a calculus book appropriate for a 14 year old?

Yes, a calculus book can be appropriate for a 14 year old physics enthusiast. As long as the book is written in a clear and understandable language and includes relevant examples and applications, it can be a valuable resource for learning calculus.

## 3. Do I need to have a strong math background to understand a calculus book at 14 years old?

Having a strong math background can certainly be helpful, but it is not necessary to understand a calculus book at 14 years old. As long as you have a basic understanding of algebra and geometry, you should be able to follow along and learn from a calculus book.

## 4. How can a 14 year old use a calculus book to improve their understanding of physics?

A calculus book can help a 14 year old improve their understanding of physics by providing a more advanced and in-depth understanding of key concepts, such as derivatives and integrals. It can also help with problem-solving skills and critical thinking, which are essential for success in physics.

## 5. Are there any recommended calculus books for 14 year old physics enthusiasts?

There are many great calculus books available for 14 year old physics enthusiasts. Some popular options include "Calculus for the Practical Man" by J.E. Thompson, "Calculus Made Easy" by Silvanus P. Thompson, and "Calculus: Early Transcendentals" by James Stewart. It is important to choose a book that aligns with your learning style and level of understanding.

Replies
5
Views
2K
Replies
2
Views
2K
Replies
4
Views
2K
Replies
26
Views
3K
Replies
30
Views
3K
Replies
17
Views
584
Replies
2
Views
1K
Replies
9
Views
741
Replies
5
Views
2K
Replies
32
Views
3K