Solving Basic Index Dilemma Maths Problem

  • Thread starter latentcorpse
  • Start date
  • Tags
    Index
In summary, it seems like the mistake made was not applying the product rule when taking the derivative of the first term in the equation. Remember to always check your work and take a break if you've been doing too much math!
  • #1
latentcorpse
1,444
0
I just can't see what's going wrong here

[itex]\nabla^2 p . (x-y) = p^2[/itex] where [itex]p,x,y[/itex] are all 4 vectors.

so it's obvious from looking at it but i decided to try and show it

[itex]\partial_i \partial_i (p_j r_j)[/itex] where i used r to denote x-y

[itex]= \partial_i \left( \left( \partial_i p_j \right) r_j + p_j \delta_{ij} \right)[/itex]
[itex]= \partial_i \left( \left( \partial_i p_j \right) r_j + p_i \right)[/itex]
[itex]= \left( \partial_i \partial_i p_j \right) r_j + \partial_i p_j \delta_{ij} + p_i[/itex]
[itex]= \left( \partial_i \partial_i p_j \right) r_j + \partial_i p_i + p_i[/itex]

what on Earth has gone wrong? i think I've just done to much maths today!
 
Physics news on Phys.org
  • #2
It looks like you may have forgotten to apply the product rule when taking the partial derivative of the first term. The product rule states that when taking the derivative of a product, you need to take the derivative of each factor and multiply them together. In this case, you need to take the derivative of both p⃗ and r⃗ with respect to i and then multiply them together.The correct expression should be: \partial_i \left( \left( \partial_i p_j \right) r_j + p_j r_i \right)= \left( \partial_i \partial_i p_j \right) r_j + \left( \partial_i p_j \right) r_i + \left( \partial_i r_j \right) p_j + p_j r_i
 

1. What is an index in math?

An index in math is a number or symbol used to indicate the power or exponent to which another number or expression is raised. It is typically written as a small number to the upper right of the base number or expression.

2. How do I solve a basic index dilemma math problem?

To solve a basic index dilemma math problem, you must first identify the base number or expression and the index. Then, you can use the laws of exponents to simplify the expression, such as multiplying or dividing the base numbers and adding or subtracting the indices.

3. What are the laws of exponents?

The laws of exponents are rules that govern how to manipulate and simplify expressions with indices. They include the product rule, quotient rule, power rule, and zero and negative exponent rules.

4. Can I use a calculator to solve index problems?

Yes, most calculators have a function for solving index problems. However, it is important to understand the concepts and laws of exponents to verify the accuracy of the calculator's answer.

5. What are some common mistakes to avoid when solving index problems?

Some common mistakes to avoid when solving index problems include forgetting to simplify the base numbers before applying the laws of exponents, incorrectly distributing an exponent over a sum or difference, and forgetting to apply the power rule when raising a power to another power.

Similar threads

Replies
27
Views
2K
  • Advanced Physics Homework Help
Replies
9
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
7
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
19
Views
2K
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Linear and Abstract Algebra
2
Replies
41
Views
2K
Back
Top