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Calculus *BEST* Calculus 3 Textbook for self study

Hello, currently I am a high school senior who will be going to college in the fall and since my school ends in may and college starts in mid-August. I am planning on self-studying calculus 3, so I can test out of it and go straight into partial differential equations.

The textbooks that the colleges that I applied to use are the CALCULUS — Early Transcendentals, Stewart, Brooks/Cole. books. From other posts I was able to infer that this textbook is mediocre at best, is this true? what about Vector Calculus by Peter Baxandall and Hans Liebeck?

Also at the moment, I am using Larson calculus textbook for my BC class and for EM I am using Fundamentals of Physics by David Halliday.

I would like to use a textbook that focuses less on computations and more on theory and is full of rigor because I actually wish to learn and not just waste my time doing plug and chuck into the formula.



Thanks for the help!
 
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I would like to use a textbook that focuses less on computations and more on theory and is full of rigor because I actually wish to learn and not just waste my time doing plug and chuck into the formula.
Thanks for the help!
Spivak.
Apostol part 2 (assuming you know stuff in part 1),
A Course of Pure Mathematics - G.H Hardy,
Baby Rudin,
Real analysis part 1,2 - Terence Tao (I have never read these books but they are written by Terence Tao).

There is also Analysis on Manifolds by James Munkres but that's too hard for you.
 
Spivak.
Apostol part 2 (assuming you know stuff in part 1),
A Course of Pure Mathematics - G.H Hardy,
Baby Rudin,
Real analysis part 1,2 - Terence Tao (I have never read these books but they are written by Terence Tao).

There is also Analysis on Manifolds by James Munkres but that's too hard for you.
Thanks, I will look into these books but my only problem is where am I supposed to find them as some of theses are from the 70s.
 
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Wrichik Basu

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If I'm correct, Calculus 3 is Multivariable calculus. If so, then you can use this book:

images (1).jpg


It was referred to me by one of my seniors, and later I have seen several professors recommend it as well.
 

Attachments

If I'm correct, Calculus 3 is Multivariable calculus. If so, then you can use this book:

View attachment 217947

It was referred to me by one of my seniors, and later I have seen several professors recommend it as well.
thanks and I was looking into volume 2 of Apostol but it combines linear algebra and multivariable calculus so am somewhat worried about how where to start with(typical in a university those subjects are separated)
also I should change the title and thxs a lot

<Moderator's note: Problematic copyright remark removed. Here's an official way to purchase the book in question: https://www.amazon.com/s/ref=nb_sb_ss_c_1_13?url=search-alias=aps&field-keywords=shifrin+multivariable+mathematics&sprefix=Shifrin+Multi,aps,234&crid=12I5BMGFVQXJ0.
As mentioned below (#7), there are also valuable texts online available for free.>
 
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Thanks, I will look into these books but my only problem is where am I supposed to find them as some of theses are from the 70s.
All the books I mentioned are available on Amazon (want link ?); they all are pretty standard textbooks. Book by Hardy is freely available at Internet archive (well, you can find others also but I am not sure if its legal or not; Internet archive is not super clean).

thanks and I was looking into volume 2 of Apostol but it combines linear algebra and multivariable calculus so am somewhat worried about how where to start with(typical in a university those subjects are separated)
also I should change the title and thxs a lot

Edit:do you know where i can find a pdf for the textbook as otherwise its in $200 price range >_>
If you read Apostol from part 1 - part one is single variable calculus not high-school calculus - you will get a pretty good understanding of both Linear algebra and calculus/analysis. Shifrin's book also combines linear algebra and multivariate calculus, all multivariate calculus books do that to some extent.
 

fresh_42

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My favorite recommendation for free sources, especially on the change between high school and college are:
https://openstax.org/subjects
https://open.umn.edu/opentextbooks/SearchResults.aspx?searchText=Calculus
and maybe a bit more advanced (and in development)
https://www.ams.org/open-math-notes/omn-search-results

In case you want to prepare self-study, it might also be worth to read our insight articles about this subject, which I've listed here:
https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947
 
Thanks, everyone and I have a question would it be better to just take the classes over the summer(I am sure that the university offers summer courses) or just self-study??
 

mathwonk

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one problem i see with your plan is you intend to study rigorous calculus of several variables without having a rigorous background in one variable calculus. I.e. the Larson book you have used for BC seems itself rather plug and chug, possibly inferior to Stewart . If you do indeed place out of all 3 calculus courses in college, you will probably never acquire the more rigorous version of any of them which is offered in some honors level college courses. although the level of some college courses has been adjusted down to mesh with students' high school level preparation, some college instructors teach at a higher level, and in these courses students who try to skip beginning level college courses, relying on their high school preparation, often struggle. I suggest you get some guidance from a knowledgable professor at the college you will attend, but I would not recommend jumping from a Larson course in elementary calculus, straight to an Apostol or Shifrin level course in several variables. I used to hate teaching the fall semester version of college level calc 2, since the students were mostly entering freshmen, with AP preparation from high school, essentially none of whom had sufficient background to handle my course. Nonetheless it is quite possible you can survive the partial diffeq course without the rigorous background you propose for yourself. You really should talk to the the PDE prof as well as those profs who teach the lower level calc courses to find out how they fit together. We can recommend rigorous books to you, but we cannot say how suitable they will be for your program.

One way to get a feel for the program at your college would indeed be to take a summer class, but be aware that summer versions of classes tend to be easier and less rigorous than winter versions, mainly for time constraints but also for generally less well prepared students. Still it offers more familiarity with the system than self study.
 
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one problem i see with your plan is you intend to study rigorous calculus of several variables without having a rigorous background in one variable calculus. I.e. the Larson book you have used for BC seems itself rather plug and chug, possibly inferior to Stewart . If you do indeed place out of all 3 calculus courses in college, you will probably never acquire the more rigorous version of any of them which is offered in some honors level college courses. although the level of some college courses has been adjusted down to mesh with students' high school level preparation, some college instructors teach at a higher level, and in these courses students who try to skip beginning level college courses, relying on their high school preparation, often struggle. I suggest you get some guidance from a knowledgable professor at the college you will attend, but I would not recommend jumping from a Larson course in elementary calculus, straight to an Apostol or Shifrin level course in several variables. I used to hate teaching the fall semester version of college level calc 2, since the students were mostly entering freshmen, with AP preparation from high school, essentially none of whom had sufficient background to handle my course. Nonetheless it is quite possible you can survive the paertial diffeq course without the rigorous background you propose for yourself. You really should talk to the the PDE prof as well as those profs who teach the lower level calc courses to find out how they fit together. We can recommend rigorous books to you, but we cannot say how suitable they will be for your program.

One way to get a feel for the program at your college would indeed be to take a summer class, but be aware that summer versions of classes tend to be easier and less rigorous than winter versions, mainly for time constraints but also for generally less well prepared students. Still it offers more familiarity with the system than self study.
I will look into to that and the textbook they use for calculus 3 is Early Transcendentals, Stewart for regular and for honors it's the Thomas' Calculus: Early Transcendentals but neither of those books go into depth proof wise as Apostol or Shifrin.(I might be wrong but the course description said no proofs)

Also thanks for the advice
btw I have a question why isn't Apostol or Shifrin like the default calculus textbook for college?
 
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I have a question why isn't Apostol or Shifrin like the default calculus textbook for college?
I guess it is so because it might be a waste of time to teach non-maths students with those books (atleast Apostol).
 

mathwonk

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because most students cannot handle apostol/spivak after coming in with only AP high school preparation. college is a business, and we cannot survive if we don't admit students with only AP preparation even if we think that is not adequate academically.
 
because most students cannot handle apostol/spivak after coming in with only AP high school preparation. college is a business, and we cannot survive if we don't admit students with only AP preparation even if we think that is not adequate academically.
I mean it would be hard but not impossible if they work at it. I mean why should one take the easy route >_>
 
I guess it is so because it might be a waste of time to teach non-maths students with those books (atleast Apostol).
But won't Spivak be useful for engineering majors?
 
because most students cannot handle apostol/spivak after coming in with only AP high school preparation. college is a business, and we cannot survive if we don't admit students with only AP preparation even if we think that is not adequate academically.
Ok, I get your point but I really wish to study through Apostol/Spivak/Courant....
So what should I do, should I just restart at calculus 1 with those and work my way up to multivariable or is there another route?

btw the point you made about AP(BC) not being actually calculus 2 is true in a sense.
but my teacher made the class a calc 2 class, so we learned things such as work, force, integration techniques, parametric and polar,3d space and atm we are doing vectors then series and some other things
 

mathwonk

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just to give a very simple test, can you define what it means for a function to be continuous at a point? or to be differentiable? can you define what it means to have a limit at a point? can you prove that the function f(x) = x^2 is continuous everywhere? can you prove that a function which is continuous everywhere on the interval [0,1] is bounded? can you define what it means for a function to be integrable on the interval [0,1]? can you prove that if f is a continuous function on [0,1], then the function F(x) = integral of f from 0 to x, is differentiable? can you define the exponential function and prove it is differentiable? Now you are getting some idea of what we discuss in my calculus class.
 
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OP, why do you want to rush and take calculus 3 r? Does your university have a placement or departmental finals that you don't want to take? At my college, Calculus 1 and 2 have the same final and it's very difficult. I was lucky enough just to take calculus 2 final since my calc 1 credit transfer.
 
calculus 3, so I can test out of it and go straight into partial differential equations.
You can really go straight to PDE after calc 3? Interesting. I had to have ordinary differential equations and a semester of matrix/linear algebra done before I could take PDE. I always figured that was kind of the standard. Though, from what I remember, the linear algebra probably wasn't necessary, and, I suppose that, if using an applied book like Haberman's, you could get by on the ODE theory if you learned to solve first and second order and Cauchy-Euler equations.


At my college, Calculus 1 and 2 have the same final
The same final? Are you sure you have that right since you only had to take the one? It might be all part of the same kind of standardized test, but the students take a different section of it. I can't imagine how it'd make any sense otherwise.
 
Yes, every section of calculus 1 and 2 take the same final. I think they do it since a lot of PhD students teach the class. They want to make sure everyone has the same fair test because there are some that make the tests easy. Starting calculus 3, PhD or professors have the right the right to make their own tests ad quizzes. I know University of Pittsburgh does it and at my University too! I go to University at Albany. Kinda curious They let you take PDE after calc 3?? I’m getting a math minor and my goal is to take PDE too. However, I need to take Linear Algebra, ordinary differential equations first then take partial differential equations.
 
Yes, every section of calculus 1 and 2 take the same final. I think they do it since a lot of PhD students teach the class. They want to make sure everyone has the same fair test because there are some that make the tests easy.
I understand what you're saying now. All the sections of calc 1 take the same calc 1 final, and all the sections of calc 2 take the same calc 2 final. It was done that way at my university as well.

That's a bit different from what you originally said, which was

Calculus 1 and 2 have the same final
meaning that calculus 1 and calculus 2 students have the same exact final, which of course doesn't make any sense. There wasn't enough context for me to put together what you meant.
 
OP, why do you want to rush and take calculus 3 r? Does your university have a placement or departmental finals that you don't want to take? At my college, Calculus 1 and 2 have the same final and it's very difficult. I was lucky enough just to take calculus 2 final since my calc 1 credit transfer.
The reason I wish to rush is so I can start doing some sort internship/research as a freshman and teaching my self, more calculus(calc 3) seems like a fun way to spend my summer imo. Plus it should also help me get into some grad level math classes as an undergrad.
 
Yes, every section of calculus 1 and 2 take the same final. I think they do it since a lot of PhD students teach the class. They want to make sure everyone has the same fair test because there are some that make the tests easy. Starting calculus 3, PhD or professors have the right the right to make their own tests ad quizzes. I know University of Pittsburgh does it and at my University too! I go to University at Albany. Kinda curious They let you take PDE after calc 3?? I’m getting a math minor and my goal is to take PDE too. However, I need to take Linear Algebra, ordinary differential equations first then take partial differential equations.
I would probably take them at the same time
 
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You can really go straight to PDE after calc 3? Interesting. I had to have ordinary differential equations and a semester of matrix/linear algebra done before I could take PDE. I always figured that was kind of the standard. Though, from what I remember, the linear algebra probably wasn't necessary, and, I suppose that, if using an applied book like Haberman's, you could get by on the ODE theory if you learned to solve first and second order and Cauchy-Euler equations.




The same final? Are you sure you have that right since you only had to take the one? It might be all part of the same kind of standardized test, but the students take a different section of it. I can't imagine how it'd make any sense otherwise.
I meant ODE sorry about that and I planning on taking them alongside Linear algebra and they offer a test out option all the way to ODE
 
My friend who is a freshman now got to do research in 4 weeks (Physics something to do with black holes). Yet, he still was in my calculus 2 class. You can check his youtube channel on how he did it. https://www.youtube.com/channel/UCdMUoX-RTX1z_C2ow2lpkEA

Anyways, I don't think taking the test option to get to ODE will help you get research as a freshman.
 
My friend who is a freshman now got to do research in 4 weeks (Physics something to do with black holes). Yet, he still was in my calculus 2 class. You can check his youtube channel on how he did it. https://www.youtube.com/channel/UCdMUoX-RTX1z_C2ow2lpkEA

Anyways, I don't think taking the test option to get to ODE will help you get research as a freshman.
but it still should give me an edge up

Edit: I watched your friends video and it was something I didn't consider before but I would still like to challenge myself and as your friend was saying about those that failed to waste a year on a class, its similar for me as I don't wish to waste valuable college time during my undergrad not constantly challenging myself and wasting money and time on something that I can teach myself because it would give me more options in regards to my studies.
 
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