Recent content by explorer58

Homework Statement Two reservoirs are connected. Water drains from one reservoir to the other, governed by the following ODE: dh/dt= -k1*(h)^0.5 -k2*(h-H)^0.5 , H<0, k1,k2>0 Does an equilibrium exist? What happens in terms of Picard's Existence Theorem? Draw a phase diagram of possible h*...

Gah, the first part was just a slip of the tongue. It was supposed to say cannot be expressed.

Ah, that makes sense. I thought it was right because in my head i was doing examples in my head in R3, so for example (1,1,1) is the sum of its projections on the standard basis. But then I realized that didn't work in reverse. Thanks!

So then the first one is bad? Also, would I need to do it for all vectors? Or would it suffice to show it for just one? Thanks.

Forgive me ahead of time, I don't really know how to use LaTeX, (it's on my to do list). Homework Statement Given the vector space C([0,pi]) of continuous, real valued functions on the given interval, as well as the inner product <f,g>=integral(f(t)*g(t))dt from 0 to pi: a) Prove the set...

Homework Statement Captain Ralph is in trouble near the sunny side of Mercury. The temperature of the ship's hull when he is at location (x; y; z) will be given by T=e^(-x²-2y²-3z²). He is currently at (1,1,1). a)In which direction should Ralph go to cool the fastest? b) If the ship can...