Gradient in different cooridinates

  • Thread starter Thread starter athrun200
  • Start date Start date
  • Tags Tags
    Gradient
Click For Summary
SUMMARY

The discussion centers on calculating gradients in different coordinate systems, specifically addressing the confusion surrounding the variables f, g, and h in the context of rectangular coordinates. The consensus emphasizes the importance of understanding the foundational principles of gradient calculation rather than relying solely on formulae. It is established that in rectangular coordinates, the values of f, g, and h are equal to 1. Participants recommend a thorough study of the underlying concepts before consulting external resources for specific formulae.

PREREQUISITES
  • Understanding of gradient concepts in vector calculus
  • Familiarity with coordinate systems, particularly rectangular coordinates
  • Basic knowledge of mathematical notation and terminology
  • Experience with first principles in calculus
NEXT STEPS
  • Study the derivation of gradient formulas in various coordinate systems
  • Learn about the application of gradients in physics and engineering contexts
  • Explore vector calculus textbooks for deeper insights into gradient calculations
  • Practice problems involving gradients in polar and cylindrical coordinates
USEFUL FOR

Students of mathematics, physics, and engineering, particularly those seeking to deepen their understanding of vector calculus and gradient calculations in different coordinate systems.

athrun200
Messages
275
Reaction score
0

Homework Statement



attachment.php?attachmentid=37440&stc=1&d=1311346926.jpg


Homework Equations





The Attempt at a Solution


I saw from a book this is a quick way to get gradient in different cooridinates.

However what f, g and h are? And how do I know that in rectangular coor. f=g=h=1 and etc?
 

Attachments

  • 1.jpg
    1.jpg
    55.3 KB · Views: 465
Physics news on Phys.org
I am always a bit suspicious about these formulae. My advice id to go from first principles, learn how to do it and then when you need then again, look it up in a book.
 

Similar threads

Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Surface integrals of vector fields, normal - does scaling matter?
  • · Replies 7 ·
Replies
7
Views
3K
What is the Maximum Rate of Change in Scalar Fields?
  • · Replies 4 ·
Replies
4
Views
2K
Directional Derivative at an Angle with a 3d Gradient
  • · Replies 4 ·
Replies
4
Views
3K
Optimization with Lagrangian Multipliers
  • · Replies 1 ·
Replies
1
Views
2K
Significance of nonvanishing gradient
  • · Replies 22 ·
Replies
22
Views
4K
Derivatives and the chain rule
  • · Replies 5 ·
Replies
5
Views
2K
Surface Element Conversion for Flux Through Uncapped Cylinder
  • · Replies 6 ·
Replies
6
Views
2K
Curl of a gradient and the anti Curl
  • · Replies 6 ·
Replies
6
Views
2K
Unit vector perpendicular to the level curve at point
  • · Replies 4 ·
Replies
4
Views
3K