A vector calculus proof question

In summary, the conversation is about a homework problem that involves finding the dot product of grad(∅) with dr, and the solution involves writing out grad(∅) in terms of unit vectors and taking the dot product. The person asking for help initially found the hint confusing, but eventually understands the solution with the help of the expert.
  • #1
physics2000
13
0

Homework Statement



The image contains the problem statement and all relevant equations. I have no idea what to do, this is all very new to me...plus the hint doesn't make sense to me.

[url=http://postimage.org/][PLAIN]http://s13.postimage.org/b0kq27bkn/photo_6.jpg[/url] photo uploader[/PLAIN]
 
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  • #2
physics2000 said:

Homework Statement



The image contains the problem statement and all relevant equations. I have no idea what to do, this is all very new to me...plus the hint doesn't make sense to me.

[url=http://postimage.org/][PLAIN]http://s13.postimage.org/b0kq27bkn/photo_6.jpg[/url] photo uploader[/PLAIN]

I think they just want you to show that the dot product of grad(∅) with dr gives you the expression for d(∅) in the expression for the total derivative in the hint.
 
  • #3
I kind of understand what you mean, but not sure what the first step is:confused:
 
  • #4
physics2000 said:
I kind of understand what you mean, but not sure what the first step is:confused:

You've got dr in terms of the unit vectors with the hats on them. Write out grad(phi) in terms of the unit vectors and take the dot product.
 
  • #5
Dick said:
You've got dr in terms of the unit vectors with the hats on them. Write out grad(phi) in terms of the unit vectors and take the dot product.

is this what you mean?... i think I was overthinking it , thanks for your help!

[url=http://postimage.org/][PLAIN]http://s2.postimage.org/rgazdfeih/photo_7.jpg[/url] online photo storage[/PLAIN]
 
  • #6
Yes, I think that's what they want.
 

1. What is a vector calculus proof question?

A vector calculus proof question is a question that requires the use of vector calculus concepts and principles to prove a given mathematical statement or theorem.

2. What are some common topics in vector calculus proof questions?

Some common topics in vector calculus proof questions include vector fields, line integrals, surface integrals, and the fundamental theorem of calculus for line integrals.

3. How do I approach solving a vector calculus proof question?

To solve a vector calculus proof question, it is important to have a strong understanding of vector calculus concepts and techniques. It is also helpful to break down the question into smaller, more manageable steps and to use visual aids such as diagrams or graphs.

4. Are there any specific strategies or techniques that can help with solving vector calculus proof questions?

Yes, there are several strategies and techniques that can be helpful when solving vector calculus proof questions. These include understanding theorems and their applications, using appropriate notation and terminology, and practicing with a variety of examples and exercises.

5. Can I use software or calculators to solve vector calculus proof questions?

While technology can be helpful in verifying solutions or performing calculations, it is important to have a strong understanding of vector calculus concepts and techniques before relying on software or calculators to solve proof questions. Additionally, some exams or assignments may not allow the use of technology, so it is important to be able to solve proof questions by hand as well.

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