# Does Three-dimensional space has any use in real analysis particularly in measure the

1. Mar 13, 2012

### woundedtiger4

Hi all!
I am self teaching myself and due to no money plus time I can't join University, but I want to study maths on my own, therefore please guide me.
I have adapt a route calc1->calc2->calc3->differential equation->introductory linear algebra->introductory abstract algebra-> real analysis->measure theory->probability theory, so that I can study topics as stochastic process, brownian motiion etc. is this route sounds OK?
currently I am studying calc2 and I was wondering if I really need to study three dimensional spaces and/or vectors or not, does it not use only in computer graphics, physics etc sort of stuff?

2. Mar 13, 2012

### micromass

Staff Emeritus
Re: Does Three-dimensional space has any use in real analysis particularly in measure

Yes, you absolutely need to study it. Things like partial derivatives, multiple integrals, PDE's have quite some application in stochastic processes.

3. Mar 13, 2012

### mathwonk

Re: Does Three-dimensional space has any use in real analysis particularly in measure

think about what you are doing. you are studying science, the structure of our world. is the world at least three dimensional? does that answer your question?

4. Mar 13, 2012

### Sankaku

Re: Does Three-dimensional space has any use in real analysis particularly in measure

Your question has already been answered. However, I would also suggest you do linear algebra before Calc 3 and ODEs.

Last edited: Mar 14, 2012
5. Mar 13, 2012

### micromass

Staff Emeritus
Re: Does Three-dimensional space has any use in real analysis particularly in measure

Ah yes, I missed that. i definitely agree!

6. Mar 14, 2012

### woundedtiger4

Re: Does Three-dimensional space has any use in real analysis particularly in measure

Thanks a tonne for the reply. I am studying Calculus at http://tutorial.math.lamar.edu/ and in calc 2 & 3 it covers some linear algebra such as "Vectors - Basics, Magnitude, Unit Vector, Arithmetic, Dot Product, Cross Product, Projection
Three Dimensional Coordinate System - Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates, Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates."
This webstie also offers a separate course on linear algebra and the highest level of this course is Euclidean n-space and Eigenvalues and Eigenvectors.
Don't you think that I will cover sufficient linear algebra in Calc2 & 3 and therefore I will not need to study separate lin. algebra?

P.S. Actually Paul's notes are excellent but I don't know why I am not getting anything in three dimension (also I tried to read the lin algebra on his website but it's still going over my head :( ) therefore now I am studying these particular topics in the early transcendentals - calculus by James Stewart (chapter 12 & 13)

Last edited: Mar 14, 2012
7. Mar 15, 2012

### Broccoli21

Re: Does Three-dimensional space has any use in real analysis particularly in measure

Calc II and III will definitely not be sufficient linear algebra background. And I agree with the previous posters. Do some linear algebra before ODE (and get some in before calc III if possible).

8. Mar 15, 2012

### woundedtiger4

Re: Does Three-dimensional space has any use in real analysis particularly in measure

Thanks a tonne for your valuable advice. Hopefully, I will finish Calc2 by this week and then I will start calc3 along linear algebra. Can you please recommend any good book or website which takes the reader from beginner level to some upper level?

Last edited: Mar 15, 2012