# Self teaching Calculus for physics?

• Parkour
In summary: So, it covers all the basic principles and techniques of calculus that are necessary for introductory physics. It is considered an introductory calculus textbook and there is a significant amount of calculus covered in this book.
Parkour
Summary:: I want to teach myself physics and was wondering if Thomas' Calculus is a good book to learn the Calculus I need to learn introductory physics.

Hi,

I am following a guide by Susan Rigetti (https://www.susanrigetti.com/physics) which aims to help and give sort of structured learning to people who want to self learn physics at the undergraduate level. It says to start out with an introduction to mechanics from "University Physics with Modern Physics 15th Edition" whilst also learning calculus from "Thomas' Calculus 14th Edition". I was wondering is this a good introductory book for calculus and how much of it do I need to know to learn undergrad/introductory physics?

University Physics with Modern Physics 15th Edition: https://www.amazon.com/dp/0135159555/?tag=pfamazon01-20

Thomas' Calculus 14th Edition: https://www.amazon.com/dp/0134438981/?tag=pfamazon01-20

Here is the contents of the Thomas' Calculus:

1. Functions
2. Limits and Continuity
3. Derivatives
4. Applications of Derivatives
5. Integrals
6. Applications of Definite Integrals
7. Transcendental Functions
8. Techniques of Integration
9. First-Order Differential Equations
10. Infinite Sequences and Series
11. Parametric Equations and Polar Coordinates
12. Vectors and the Geometry of Space
13. Vector-valued functions and motion in space
14. Partial derivatives
15. Multiple integrals
16. Integrals and vector fields

Another question: How much of calculus does this book cover based on reading the contents? Is this an introductory calculus textbook? How much calculus is there?

vuthanhcrazy and Delta2

I'm not familiar with Thomas's book, but it is introductory calculus. And, yes, by the time you finish your first courses in Classical Mechanics and Electromagnetism you will need all of that material.

vuthanhcrazy and Parkour
Another good book for this purposes is

R. Courant, Differential and integral calculus (2 Vols)

vuthanhcrazy, Parkour and Dr.D
You do not have to get the most recent edition, so you should be able to find a cheap copy. Freshman calculus is differentiation, integration, limits,sequences and series. Sophomore calculus is vector calculus.

vuthanhcrazy and Parkour
Thomas has been used for generations and it remains a good book. I do not recommend Courant, as it is much more detailed and you do not need it as a companion text to University Physics which you mention.
(It comes to me that I may be confusing Courant with Courant and Hilbert.)
Courant and Hilbert is much harder and you can always learn that later if required. Thomas gives many problems. Thomas will provide many exercises which you will need to practice and get comfortable with.
In answer to your question. Thomas is a good (I would say excellent) introductory calculus book, and plenty calculus is there if you want to learn physics out of University Physics, or any other freshman level calculus based physics course.

vuthanhcrazy and Parkour
I didn't mean Courant&Hilbert which is much more advanced than Courant's introductory analysis textbook, which helped me a lot when I had to learn math for doing physics in the first few semesters. In my university there was not a separate math course for physicists but we had to attend the analysis lectures 1-4 as well as linear algebra for mathematicians. Of course, we never had the math at hand what was needed in the physics lectures, because in the math lectures everything was neatly proven and in the most modern way (e.g., the Riemann integral was a nogo for the math professor; he introduced the Lebesgue integral, and the Riemann integral was just a problem on a problem sheet in the problem sessions of this lecture). Of course, later I was pretty thankful for having attended such a course for mathematicians, because the more rigorous and general approach can help also to understand the more subtle points in theoretical physics (particularly of course in quantum mechanics). On the other hand to just start doing theoretical physics, a more practical somewhat less general introduction to analysis and linear algebra is better.

vuthanhcrazy, Parkour and mpresic3
For understanding Young & Freedman’s University Physics (or any other similar calculus based first-year physics book) you don’t actually need to know much calculus. Basically you need to understand the concept of derivatives and integrals, how they relate to a graph of a function, and how to calculate them for simple functions like polynomials.

I never used Thomas, but it looks like the first 5 or 6 chapters should be enough for most purposes.

Many students in the US take the first semester of intro physics alongside Calculus I.

vuthanhcrazy and Parkour
Parkour said:
How much of calculus does this book cover based on reading the contents? Is this an introductory calculus textbook? How much calculus is there?
It covers the material in a three-semester calculus sequence, taken by students majoring in math, physics and engineering, at a typical US college or university. Calculus I probably covers chapters 1 through 5 or 6, Calculus II continues to chapters 10 or 11, and Calculus III covers the rest. Calculus I and II are normally taken in the first year, and Calculus III in the first semester of the second year.

Of course, things are likely different at elite schools like MIT and Caltech.

vuthanhcrazy, Parkour and vanhees71
George B. Thomas Jr. wrote the standard US engineering calculus book at MIT in the mid 20th century. It sold so well and was so well regarded, that the publishers did not want to let go of the cash cow. Thus it has been rewritten many, many times, even since his death in 2006, still, quite misleadingly, bearing his name. These later books bear almost no resemblance to any of the books actually written by Thomas, which themselves also went through several rewrites, and were greatly changed.

Since these are popular books, sold for university courses where the latest editions are often required, the price of a "Thomas" calculus book is related mostly to the edition number, not the quality of the book. Hence you can find earlier editions than the 14th on used book sites like abebooks for under ten dollars.
e.g.
https://www.abebooks.com/servlet/BookDetailsPL?bi=30359730186&searchurl=spo=120&sortby=17&tn=calculus&p=5&an=george+b.+thomas&sp=1&cm_sp=snippet-_-srp5-_-title16

I myself recommend getting as old an edition as possible, preferably from the 1950's, and authored only by Thomas himself, alone. If not available, the first coauthor to join him that I recall was Finney, and I recall liking their joint book, the 9th edition, blue cover. Later editions that i taught from, with added names like Hass, Weir, Giordano, I considered some of the worst books I ever had to teach from. I am not an expert on the 14th edition, since there are too many editions to know them all. Nonetheless, even if these later books are perfectly acceptable for you in quality, I would not recommend paying a high price for the 14th edition when you can get the 9th by Thomas and Finney, or better, the 3rd or so by Thomas alone, for under ten dollars.

https://www.abebooks.com/servlet/SearchResults?isbn=0201531763&cm_sp=mbc-_-ISBN-_-allhere is the full, list so you can search for yourself:

https://www.abebooks.com/book-search/author/THOMAS,-GEORGE-B-,-JR-?cm_sp=brcr-_-bdp-_-authorBy the way, I am retired college mathematics teacher, so my opinion may differ greatly from yours as to what book is most useful, so I recommend you go to a university library and look at calculus books. However one reason I disliked the later editions of "Thomas, Weir, Hass, etc..." is that they left out helpful, important connections between concepts like volume, work, and center of mass, which make some calculations much easier, and I would think are important to physicists. I.e. in the later editions some of these concepts were presented, but without their applications, which made the presentation unmotivated, and less useful. I don't recall the exact details now, but I do recall thinking that the logic and flow of Thomas' original presentation of some key concepts was lost. Even if you disagree totally with me as to their usefulness, and like all these books, I suggest it makes little sense to pay top dollar for the very latest edition in the series.

I see by looking at your linked self - teaching physics site, that the author has exactly opposite opinions to mine- she likes the latest "thomas" written by entirely other people, best, and she likes the similarly ghost written "stewart" calculus, issued 6 years after stewart's death, by two other authors, second best. she does not give her reasons, but you may agree with her.

Some research reveals that Mrs. Rigetti is also not a physicist, but has studied it.

Last edited:
vuthanhcrazy, Parkour, madscientist_93 and 1 other person
I didn't really like the book that much as it was a bit too verbose. Also it's kinda too pricey. I learned from the MIT OCW Scholar courses instead, which are free (and I think brilliant).

18.01 Single-variable Calculus
18.02 Multivariable Calculus
18.03 Differential Equations

These cover everything in the Thomas book and more. Also they have video lectures, recitations, problem sets, etc which are much easier and much more fun.

vuthanhcrazy and Parkour

vuthanhcrazy and vanhees71

## 1. What is the importance of learning calculus for physics?

Calculus is a fundamental mathematical tool used in physics to describe and analyze various physical phenomena. It allows for the precise calculation of quantities such as velocity, acceleration, and force, which are essential in understanding and predicting the behavior of objects in motion.

## 2. Can I learn calculus for physics without any prior knowledge of calculus?

It is possible to learn calculus for physics without any prior knowledge of calculus, but it may take more time and effort. It is recommended to have a basic understanding of algebra and trigonometry before delving into calculus.

## 3. What are the main concepts in calculus that are relevant to physics?

The main concepts in calculus that are relevant to physics include derivatives, integrals, limits, and differential equations. These concepts are used to model and analyze physical systems and make predictions about their behavior.

## 4. How can I apply calculus to solve physics problems?

Calculus can be applied to solve a wide range of physics problems, such as determining the velocity and acceleration of an object, finding the area under a curve to calculate work or energy, and solving differential equations to describe the motion of a system.

## 5. Are there any resources available for self-teaching calculus for physics?

Yes, there are many online resources available for self-teaching calculus for physics, such as video lectures, practice problems, and interactive tutorials. Additionally, there are textbooks and study guides specifically designed for learning calculus for physics.

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