I Need Calculus Book Recommendations please

In summary, the conversation is about a 10th grader preparing for physics olympiads and asking for recommendations on calculus books. They discuss the option of using Thomas Calculus and whether it covers all the necessary topics, including the nabla operator and contour integrals. The conversation also mentions Khan Academy and MathIsPower4U as additional resources for learning calculus. The importance of not skipping important concepts and the value of textbooks and instructors are also mentioned.
  • #1
tumkan
10
1
Summary:: What calculus books do you recommend? Does Thomas Calculus include all the calculus topics?

Hi! I'm a 10th grader and preparing for physics olympiads. I'm planning to learn calculus this summer, i self learned prior required topics before calculus (trigonometry, logarithm etc.) . Would Thomas Calculus be a good choice to study calculus? What books do you recommend? And I've seen some weird integrals (Umm... It is like an regular integral notation but there is a circle on it) and nabla operators in an electrodynamics textbook (i guess it was second volume of serway physics) before, does Thomas Calculus includes them? In fact i only need calculus as much as to be able to study classical electrodynamics (for physics olympiads). I will probably study griffiths' electrodynamics. So my purpose is to learn calculus to understand the book, electrodynamics.
 
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  • #2
Have you checked Khan Academy? I suspect it would be more helpful for learning it quickly.
 
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  • #3
jedishrfu said:
Have you checked Khan Academy? I suspect it would be more helpful for learning it quickly.
No, i haven't. Thanks a lot for recommendation. By the way does it include nabla operator, contour integral etc ?
 
  • #4
Another resource is MathIsPower4U.com

Its a collection of videos on many math topics including Calculus 1,2, and 3 as taught in first year college. The ten minute videos present a problem and then work through the solution.

Here's the Calc 3 table of videos:

http://mathispower4u.com/calc-iii.php

As far as nabla being discussed, I'm sure its covered in one or more of the videos under gradient problems.
 
  • #5
Do you really think that suggesting Youtube videos instead of studying a textbook is good advice? I'm surprised!
 
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  • #6
vanhees71 said:
Do you really think that suggesting Youtube videos instead of studying a textbook is good advice? I'm surprised!
Me, too.

tumkan said:
Would Thomas Calculus be a good choice to study calculus?
Generally speaking, yes, although there are a lot of different editions out there. I have Thomas-Finney 8th Ed., Part II. As I recall, one of the original authors, George Thomas, died quite a while ago, and some newer versions have been written in part by Jearl Walker.
tumkan said:
And I've seen some weird integrals (Umm... It is like an regular integral notation but there is a circle on it) and nabla operators in an electrodynamics textbook (i guess it was second volume of serway physics) before, does Thomas Calculus includes them?
The integral symbol with a circle is the line integral over a closed path C. The nabla symbol means gradient (see https://en.wikipedia.org/wiki/Gradient), in the context of vector functions.
 
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  • #7
vanhees71 said:
Do you really think that suggesting Youtube videos instead of studying a textbook is good advice? I'm surprised!
Me three.
 
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  • #8
tumkan said:
I'm planning to learn calculus this summer
So, I'm assuming you are relatively new to calculus? If so be careful about going too quickly. Things like contour integrals are best left until you have a really good understanding of the more basic concepts. If you skip important things it can be really hard to go back and learn them the "right" way. This is why the structure of a good textbook, class, or instructor is really valuable. Honestly, I don't know anything about Olympiads, but there is great wisdom in being able to recognize what you aren't prepared for yet. This is the nature of education, there is always more to learn, and some of that should be delayed until you are ready for it.
 
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  • #9
vanhees71 said:
Do you really think that suggesting Youtube videos instead of studying a textbook is good advice? I'm surprised!
They both have value. I agree that Khan academy is a good thing to study, but I also agree that you don't really know math without studying textbooks too. Khan academy is the modern equivalent of an instructor drawing on a chalkboard. Then, in my day, that instructor will tell you to read chapter 4 in the book for next week.
 
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  • #10
Mark44 said:
Me, too.Generally speaking, yes, although there are a lot of different editions out there. I have Thomas-Finney 8th Ed., Part II. As I recall, one of the original authors, George Thomas, died quite a while ago, and some newer versions have been written in part by Jearl Walker.

The integral symbol with a circle is the line integral over a closed path C. The nabla symbol means gradient (see https://en.wikipedia.org/wiki/Gradient), in the context of vector functions.
thank you very much sir
 
  • #11
DaveE said:
So, I'm assuming you are relatively new to calculus? If so be careful about going too quickly. Things like contour integrals are best left until you have a really good understanding of the more basic concepts. If you skip important things it can be really hard to go back and learn them the "right" way. This is why the structure of a good textbook, class, or instructor is really valuable. Honestly, I don't know anything about Olympiads, but there is great wisdom in being able to recognize what you aren't prepared for yet. This is the nature of education, there is always more to learn, and some of that should be delayed until you are ready for it.
Sir I'm a little bit confused here. Of course i am not planning to directly jump into such complicated parts like contour integral, it is like at the end of the second volume as far as i remember. I just mentioned it because i saw it in an electrodynamics textbook. Should i delay learning calculus? I'm afraid to learn concepts incorrect because as you mentioned it is hard to turn back and correct them. And besides i want to pursue in such areas like physics and mathematics in the future. I don't want to ruin it. However i also need to know calculus in order to solve problems and understand physics topics (physics olympiads). I've been studying olympiads for a while without knowing calculus but next year I'm going to enter another stage, which calculus knowledge is required. As i told i don't want to make any mistakes, do you have any general advices? And is it okay to start with thomas calculus?
 
  • #12
The best edition of Thomas is the 3rd edition (red book). Followed by the Thomas/Finnly 9th? (the one with the blue cover with a big light house picture).

I would suggest buying both the 3rd and 9. They are really entirely different books. Read the 3rd edition for explanations, work out some of the problems, then open up the 9th and compete more exercises. If you find something in the 3rd edition difficult to understand, then refer to the 9th edition.
 
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  • #13
tumkan said:
Sir I'm a little bit confused here. Of course i am not planning to directly jump into such complicated parts like contour integral, it is like at the end of the second volume as far as i remember. I just mentioned it because i saw it in an electrodynamics textbook. Should i delay learning calculus? I'm afraid to learn concepts incorrect because as you mentioned it is hard to turn back and correct them. And besides i want to pursue in such areas like physics and mathematics in the future. I don't want to ruin it. However i also need to know calculus in order to solve problems and understand physics topics (physics olympiads). I've been studying olympiads for a while without knowing calculus but next year I'm going to enter another stage, which calculus knowledge is required. As i told i don't want to make any mistakes, do you have any general advices? And is it okay to start with thomas calculus?
I would absolutely go ahead learning calculus. You'll just want to do it in order, follow the plan of someone that teaches it. Like in a textbook or online course. I'm not a expert on the textbooks, but Thomas is as good as any IMO.
 
  • #14
Like other people have said video lectures though helpful often don't result in permanent knowledge.
That being said I personally taught myself calculus for physics by going through MIT OCW's 18.01SC and by reading sections of multiple calculus books. I particularly enjoyed Simmons' Calculus with analytic geometry and a Russian text by Tarasov. I personally never had any patience for overly flashy watered down super expensive modern calculus textbooks.
As for the other integrals that you mention they are the subject of multivariable and vector calculus which is absolutely necessary if you want to study electromagnetism. Again I didn't use a particular textbook but followed MIT OCW's 18.02SC (which is again excellent) and solved lots and lots of problems from multiple sources.
If you have any questions or doubts you can always ask in the homework forum.
 
  • #15
tumkan said:
Sir I'm a little bit confused here. Of course i am not planning to directly jump into such complicated parts like contour integral, it is like at the end of the second volume as far as i remember. I just mentioned it because i saw it in an electrodynamics textbook. Should i delay learning calculus? I'm afraid to learn concepts incorrect because as you mentioned it is hard to turn back and correct them. And besides i want to pursue in such areas like physics and mathematics in the future. I don't want to ruin it. However i also need to know calculus in order to solve problems and understand physics topics (physics olympiads). I've been studying olympiads for a while without knowing calculus but next year I'm going to enter another stage, which calculus knowledge is required. As i told i don't want to make any mistakes, do you have any general advices? And is it okay to start with thomas calculus?
No, don't delay to learn calculus. It's much less complicated than often advocated. It takes time to really learn it properly. In my opinion there is no other way than to study from a good textbook. Listening to some good (!) online lectures (and I don't mean something like Khan Academy but a real math lecture; Khan Academy can help to get used to practice calculational skills, and this is very important particularly for physics too, but it's not math).

I don't know, what's needed for olympiads. For physics you need of course a good deal of calculus and analytical geometry (i.e., vector calculus) and ordinary and partial differential equations. It's also good to study physics in parallel to see which mathematics is needed.
 
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  • #16
vanhees71 said:
No, don't delay to learn calculus. It's much less complicated than often advocated. It takes time to really learn it properly. In my opinion there is no other way than to study from a good textbook. Listening to some good (!) online lectures (and I don't mean something like Khan Academy but a real math lecture; Khan Academy can help to get used to practice calculational skills, and this is very important particularly for physics too, but it's not math).

I don't know, what's needed for olympiads. For physics you need of course a good deal of calculus and analytical geometry (i.e., vector calculus) and ordinary and partial differential equations. It's also good to study physics in parallel to see which mathematics is needed.
I think a lot of people get turned off by the reputation of being hard that calculus has. It's really not that complicated (atleast the computational part). It's just a change in way of thinking from discrete to continuous phenomenon.
 
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  • #17
DaveE said:
I would absolutely go ahead learning calculus. You'll just want to do it in order, follow the plan of someone that teaches it. Like in a textbook or online course. I'm not a expert on the textbooks, but Thomas is as good as any IMO.
Thank you very much sir.
 
  • #18
MidgetDwarf said:
The best edition of Thomas is the 3rd edition (red book). Followed by the Thomas/Finnly 9th? (the one with the blue cover with a big light house picture).

I would suggest buying both the 3rd and 9. They are really entirely different books. Read the 3rd edition for explanations, work out some of the problems, then open up the 9th and compete more exercises. If you find something in the 3rd edition difficult to understand, then refer to the 9th edition.
The oldest edition of thomas calculus i find, published in my language, is 11th edition. Would it be a problem?
 
  • #19
tumkan said:
The oldest edition of thomas calculus i find, published in my language, is 11th edition. Would it be a problem?
What is your language?
 
  • #20
There is not just one "Thomas calculus". This is a franchise, consisting of many extremely different books, published over more than 60 years, written by many different people, mostly not including the original Thomas, who died long ago. I have taught from at least 4 or 5 different editions and studied others. The book actually written by Thomas himself is quite good, and is still sometimes available as an early edition. Others with co authors and written in the 60's seemed good to me. I also liked the 9th edition, with Finney, as was mentioned above. The 11th edition, on the other hand, by Haas, Weir and "Thomas" (who was then dead), struck me when I had to teach from it as terrible, certainly the worst of all I have seen. But I was comparing it to the earlier ones, and I am a professional. Of course you can still learn something from it, but not as much as from the earlier ones. You should look at it yourself, and see if it seems understandable and useful fo your purposes. The information in it is not wrong, it just has less information, and less insight, and (you must judge this yourself) may not be as well explained.
 
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  • #21
MidgetDwarf said:
What is your language?
Turkish
 
  • #22
mathwonk said:
There is not just one "Thomas calculus". This is a franchise, consisting of many extremely different books, published over more than 60 years, written by many different people, mostly not including the original Thomas, who died long ago. I have taught from at least 4 or 5 different editions and studied others. The book actually written by Thomas himself is quite good, and is still sometimes available as an early edition. Others with co authors and written in the 60's seemed good to me. I also liked the 9th edition, with Finney, as was mentioned above. The 11th edition, on the other hand, by Haas, Weir and "Thomas" (who was then dead), struck me when I had to teach from it as terrible, certainly the worst of all I have seen. But I was comparing it to the earlier ones, and I am a professional. Of course you can still learn something from it, but not as much as from the earlier ones. You should look at it yourself, and see if it seems understandable and useful fo your purposes. The information in it is not wrong, it just has less information, and less insight, and (you must judge this yourself) may not be as well explained.
Thank you very much sir. Do you have any other book reccomendations?
 
  • #23
tumkan said:
Thank you very much sir. Do you have any other book reccomendations?
don't overwhelm yourself with resources. it's often very crippling and unproductive.
 
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  • #24
tumkan said:
Umm... It is like an regular integral notation but there is a circle on it) and nabla operators in an electrodynamics textbook (i guess it was second volume of serway physics) before,
That's vector calculus. You must first learn ordinary calculus (calculus with functions of one variable) then move to multivariable calculus, and finally to vector calculus. Under some circumstances, multivariable calculus and vector calculus are highly related. Introductory books on calculus teach usually only calculus of one variable.
https://en.wikipedia.org/wiki/Multivariable_calculus
https://en.wikipedia.org/wiki/Vector_calculus
 
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  • #25
Is it possible to read in English? From your replies, your English is exceptionally good. Maybe you are using a translator?
 
  • #27

1. What are the best calculus books for beginners?

Some popular calculus books for beginners include "Calculus: Early Transcendentals" by James Stewart, "Calculus Made Easy" by Silvanus P. Thompson, and "Calculus: An Intuitive and Physical Approach" by Morris Kline.

2. Are there any calculus books specifically for self-study?

Yes, there are many calculus books designed for self-study such as "Calculus: A Complete Course" by Robert A. Adams and Christopher Essex, "Calculus: Early Transcendentals" by Soo T. Tan, and "Calculus: One and Several Variables" by Saturnino L. Salas, et al.

3. What are some calculus books with practical applications?

Some calculus books that focus on real-world applications include "Calculus for Scientists and Engineers" by William L. Briggs and Lyle Cochran, "Calculus: Concepts and Contexts" by James Stewart, and "Applied Calculus" by Deborah Hughes-Hallett, et al.

4. Can you recommend a calculus book for advanced students?

For advanced students, some recommended calculus books are "Calculus: A Complete Course" by Robert A. Adams and Christopher Essex, "Calculus: Early Transcendentals" by James Stewart, and "Advanced Calculus" by Patrick M. Fitzpatrick.

5. Are there any calculus books with interactive resources or online support?

Yes, there are many calculus books that come with online resources such as practice problems, interactive tutorials, and video lectures. Some examples include "Calculus: Early Transcendentals" by James Stewart, "Calculus: An Applied Approach" by Ron Larson and Bruce H. Edwards, and "Calculus: Early Transcendentals" by William L. Briggs and Lyle Cochran.

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