Differential Geometry, easy question, weird hint making me doubt myself

In summary, the conversation is about a question regarding a homework problem and the use of a hint. The person asking the question has a good understanding of the concept and was able to solve the problem without using the hint, but questions if there was a specific reason for the hint being given. The response suggests that the hint may just be there as a guide or reminder, and encourages the person to continue checking their work.
  • #1
Stimpon
33
0

Homework Statement



2yuj4fr.png


Homework Equations



From my notes: [tex](\psi_{*}v)_{k}(x)=\sum_{i=1}^{n}v_{i}(x)\frac{{{{{\partial}}}}{\psi_{k}(x)}}{{x_{i}}}[/tex]


The Attempt at a Solution



Okay so i) is fine (ignoring the typo in the question) but I'm a bit confused about ii)

I don't see any need to bore people with the details but I simply computed [itex](\psi_{*}v)(x)[/itex] and then did the same for [itex]w[/itex] from the definition and got exactly what I wanted. My question is, is there something I've missed i.e. is there a good reason for that hint to be there? My problem is that if it's as easy as it looks, then I don't see why he would feel the need to give us a hint and then I don't see how using the hint would help get me the wanted answer.

Bear in mind this is assessed to vagueness is wanted.
 
Last edited:
Physics news on Phys.org
  • #2


Hi there,

It seems like you have a good understanding of the concept. I agree with you that the hint may not be necessary, but it could just be there to guide you in the right direction or to remind you of a key concept. It's always good to double check your work and make sure you haven't missed anything, so it's great that you took the time to do that. Keep up the good work!
 

1. What is Differential Geometry?

Differential Geometry is a branch of mathematics that studies the properties of curved surfaces and higher-dimensional spaces using the techniques of calculus and linear algebra.

2. How is Differential Geometry applied in real life?

Differential Geometry has many applications in physics, engineering, and computer graphics. It is used to model and analyze the shapes of objects in the physical world, such as the curvature of the Earth's surface or the trajectory of a spaceship.

3. Is Differential Geometry difficult to understand?

Like any branch of mathematics, Differential Geometry can be challenging to grasp at first. However, with dedication and practice, it can be understood by anyone with a strong foundation in calculus and linear algebra.

4. What are some common examples of curved surfaces studied in Differential Geometry?

Some common examples of curved surfaces include spheres, cylinders, cones, and tori. These surfaces have different types of curvature, which can be studied using Differential Geometry techniques.

5. Can Differential Geometry be used to solve practical problems?

Yes, Differential Geometry has many practical applications in fields such as physics, engineering, and computer graphics. It can be used to solve problems related to shape optimization, motion planning, and geometric modeling, among others.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
521
  • Calculus and Beyond Homework Help
Replies
2
Views
939
  • Calculus and Beyond Homework Help
Replies
14
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
922
  • Calculus and Beyond Homework Help
Replies
1
Views
3K
Back
Top