# USAPhO Calculus textbook

• Other

## Main Question or Discussion Point

Hello, I am preparing for a physics exam which takes place next year. The scope of this test is mechanics, e&m, thermodynamics, relativity, waves, and modern physics. The exam doesn't require anything farther than Calculus 1, but it is still a rigorous exam. So I am looking for a calc 1 textbook that has some applications to physics in it. I am looking for a decent understanding, nothing too hard. I have heard Richard Courant's Intro to Calc and Analysis Volume 1&2 has what I described in it. Will this cover calc 1 enough for the physics exam? On this website, there are some sample problems for you to go look.
https://www.aapt.org/physicsteam/2019/exams.cfm
Just go click USAPhO exam.

Related Science and Math Textbooks News on Phys.org
If you have any other book suggestions then the ones I asked, it will be much obliged.

Just gonna bump this - if my question's not clear I'm just looking for a calc 1 textbook that has nice explanations. Wondering if Courant's Volume 1 hits the mark. Thanks again.

vanhees71
Gold Member
2019 Award
I like Courant's analysis textbooks, but I don't know, whether it's what you need to prepare for this contest!

Sorry for the lack of my incompetent question. Let me rephrase this to:
What calc textbook will meet most of these requirements?
4.7 Calculus
Finding derivatives of elementary functions, their sums, products, quotients, and nested functions. Integration as the inverse procedure to differentiation. Finding deﬁnite and indeﬁnite integrals in simple cases: elementary functions, sums of functions, and using the substitution rule for a linearly dependent argument. Making deﬁnite integrals dimensionless by substitution. Geometric interpretation of derivatives and integrals. Finding constants of integration using initial conditions. Concept of gradient vectors (partial derivative formalism is not needed).
Source: https://ipho2018.pt/content/syllabus

Thanks again

PAllen
2019 Award
Sorry for the lack of my incompetent question. Let me rephrase this to:
What calc textbook will meet most of these requirements?
4.7 Calculus
Finding derivatives of elementary functions, their sums, products, quotients, and nested functions. Integration as the inverse procedure to differentiation. Finding deﬁnite and indeﬁnite integrals in simple cases: elementary functions, sums of functions, and using the substitution rule for a linearly dependent argument. Making deﬁnite integrals dimensionless by substitution. Geometric interpretation of derivatives and integrals. Finding constants of integration using initial conditions. Concept of gradient vectors (partial derivative formalism is not needed).
Source: https://ipho2018.pt/content/syllabus

Thanks again
Well I can recommend an ancient one that is very readable, has loads of good exercises, both theoretical and computational, and covers all that and more, yet is not too big. However, I have no idea if it can still be found.

Calculus and Analytic Geometry, by Fisher and Ziebur (second edition)

Last edited:
This actually looks like a solid book. I am surprised I haven't heard of this book before. Also I found this book on archive.org if anyone else is wondering. Thank you