Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
Differential Geometry
Understanding the definition of derivative
Reply to thread
Message
[QUOTE="lriuui0x0, post: 6212406, member: 663788"] As far as I understand, when we want to differentiate a vector field along the direction of another vector field, we need to define either further structure affine connection, or Lie derivative through flow. However, I don't understand why they are needed. If we want to differentiate ##Y## in the direction of ##X##, since each ##X_p## is itself a derivation operator, we can already do differentiation? Consider the following definition for differentiate ##Y## along ##X##. Write ##Y## in components ##Y = (y^1, \dots, y^n)##, each ##y^i## is a scalar function and differentiate it along ##X## we get ##Xy^i##. Do it for all components we get ##XY##. I believe there's problem with this definition, which might relate to coordinate dependence. Can somebody explain to me why is this an ill definition? With many different concepts in differential geometry, it gets confusing on what is coordinate dependent and what is not. [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Differential Geometry
Understanding the definition of derivative
Back
Top