Multivariate Calculus question

Thread starter mckallin
Start date Feb 10, 2009
Tags

Calculus Multivariate Multivariate calculus

Feb 10, 2009

mckallin

Hi, could anyone tell me the steps to solve the following question:

Find the solution of x'=Ax with the initial value

-------1---------2 0 0
x(0)=( 0 ), if A=( 0 1 -1 )
-------1---------1 1 1

Physics news on Phys.org

Scientist returns to microbial roots and discovers potential quantum computing advancement
Physicists achieve record precision in measuring proton-to-electron mass ratio with H₂⁺
Quantum calculations provide a sharper image of subatomic stress

Feb 10, 2009

Dick

Science Advisor

Homework Helper

Don't you want to start by finding the eigenvectors and eigenvalues of A?

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

View full post »

Thread 'Solve this problem that involves induction'

Hello, This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread. Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).

View full post »