What Comes After Single Variable Calculus

[Stratosphere]

I am currently finishing up single variable calculus, what comes next? Is multi-variable calculus the same as advanced calculus?

 

[Newtime]

I am currently finishing up single variable calculus, what comes next? Is multi-variable calculus the same as advanced calculus?

Next...as in with regard to calculus courses? Yes, usually (almost always) multivariable calculus comes next. Advanced calculus can refer to vector calculus, multivariable or analysis, it just depends on the context and personally I think the term "Advanced Calculus" is often misused. Also, since you posted this in the science book section, do you need ideas for what to read next? If so, check out the thread directly below yours called "Multivariable Calculus" or something to that effect.

 

[Landau]

It depends on what you mean by "single variable calculus" (at what level: computational or theoretical) and "to come next" (with regards to calculus courses, or math in general, or only to apply it to physics,...). After singe variable calculus at a computational level, you can also go to single variable analysis.

 

[Pinu7]

I am currently finishing up single variable calculus, what comes next? Is multi-variable calculus the same as advanced calculus?

Single Variable Calculus--->Multivariate calculus------> Ordinary Differential Equations/Linear Algebra.
(I put a slash mark between linear algebra and ODE because I suggest you learn them at the same time.)


After that there are MANY different paths to take.

 

[Landau]

I would definitely suggest learning linear algebra before multivariable calculus. I don't think you can appreciate the concept of total derivative without knowing what a linear map is.

 

[Stratosphere]

Well first sorry for the late post I went away for a little while. So I want to do theoretical physic/astrophysics, so what type of math do I need to under stand these books, and in what order do I learn them,

and https://www.amazon.com/dp/0805387323/?tag=pfamazon01-20.

I would also what to learn any other maths that I would learn as an undergrad for physics.

I am also looking for textbook recommendations.

 

[Pinu7]

Personally, I don't like any of Griffiths' books. However, most members in this forum praise them so I guess it depends on the person. You should have a MASTERY of single and multivariate calculus before you study any real physics.

As far as the General Relativity, that is a graduate textbook. I recommend you get some background knowledge on Tensor Analysis, Analysis on Manifolds, Abstract Algebra, and Lie algebra before you start looking at GR quantitatively.

Edit: I know, it is a lot; I am still learning the maths listed above.

 

[clope023]

I would definitely suggest learning linear algebra before multivariable calculus. I don't think you can appreciate the concept of total derivative without knowing what a linear map is.

yes you can, you don't really need to go into that concept either; in most schools only calc 2 is necessary to take multivariable at least in my school they teach you linear algebra in the context of multivariable calc anyway

to the OP, it usually goes single variable, multivariable, linear algebra, differential equations, partial differential equations, etc; usually advanced calculus would come after multivariable

 

[Stratosphere]

yes you can, you don't really need to go into that concept either; in most schools only calc 2 is necessary to take multivariable at least in my school they teach you linear algebra in the context of multivariable calc anyway

to the OP, it usually goes single variable, multivariable, linear algebra, differential equations, partial differential equations, etc; usually advanced calculus would come after multivariable

So since you didn't place advanced calculus in your main list there does that mean I won't need it for physics? What good textbooks are there for multivariable calculus?

 

[Landau]

What good textbooks are there for multivariable calculus?

See https://www.physicsforums.com/showthread.php?t=328703

 

[iamthegelo]

I would also what to learn any other maths that I would learn as an undergrad for physics.

I am also looking for textbook recommendations.

You're looking for a Mathematical Methods book. There's tons of them out there, choose one. I have Mary Boas' Math Methods and I love it. I also have one by Riley, Hobson and Bence - this one not so much. I think it's a matter of which author works for you. Check your library to see some books on Math Methods.

 

[Stratosphere]

Yes but no one answered my question about advanced calculus. Do I need it or not?

 

[Pinu7]

Yes but no one answered my question about advanced calculus. Do I need it or not?

"Advanced Calculus," is an ambiguous term that varies with universities. Advanced Calculus could mean anything from rigorous calculus books (e.g. Apostol) to Manifolds or more.

 

[Stratosphere]

"Advanced Calculus," is an ambiguous term that varies with universities. Advanced Calculus could mean anything from rigorous calculus books (e.g. Apostol) to Manifolds or more.

I will need Manifolds right?

 

[Landau]

You'll need everything...or not.

You just finished single variable calculus, manifolds is way ahead. No need to worry about it yet.

 

[Pinu7]

I will need Manifolds right?

Don't get ahead of yourself.
You should do:
Multivariate calculus and then
Ordinary D.Es/Linear Algebra(at the same time)


before you even TOUCH manifolds.

 

[LithiumHelios]

I'd agree with the above.

Typically something like: Partial Differentiation, Vector Integrals (i.e. Line integrals, surface integrals), del operator - grad, div and curl, certainly ordinary differential equations etc...

For the above beyond a typical undergrad math methods book (https://www.amazon.com/dp/0120598760/?tag=pfamazon01-20. Would be a good idea to have done some partial differentiation and be comfortable with vectors.


After covering those you can usually start to expand into some of the areas of Math/Physics that build of those concepts including: Fourier Analysis, Partial Differential Equations (Pretty huge subject by itself), Complex Analysis, Integral equations (along the lines of integral transforms), Vector Spaces (building on linear algebra etc).

 

[Stratosphere]

Would you say that this is a good book to go into now? https://www.amazon.com/dp/0486683362/?tag=pfamazon01-20 and after that one should I go into vector calculus or linear algebra/OD equations?

 

[Landau]

That's a great, rigorous book, but I am pretty sure it is too advanced. It uses (covers) linear algebra and advanced concepts from single variable calculus in the first chapter.

I think it's better to look at LithiumHelios' suggestions (Div, Grad,.. or Vector Calculus).

 

[Stratosphere]

How bout this book?

 

[Pinu7]

Stewart is the safe way of learning calculus, you should buy it because it is has wonderful problem sets for practice. Great for learning partial differentiation and multiple integrals.

However, when I studied more advanced mathematical texts in which a rigorous knowledge of vector calculus would make things easier which I didn't learn from Stewart.

For vector calculus, you should consider:

Calculus Vol. 2- Apostol
or(if you can get your hands on it)
Vector Calculus-Mardson