PF Random Thoughts

dkin

On page 95
w = e^z or z = logw

On page 96

First he uses w^z = e^zlogw
In this case he replaces the z he had been using previously with logw and introduces a new z

On page 97
he returns to the definition he was using before the previous paragraph except this time with log to the base b
w = b^z


on page 98 he returns to the z used on page 96 briefly and then introduces the zth root of a complex number (w^1/z).


Ridiculous.

Jimmy Snyder

Ah, now I see what you mean. However, it starts much earlier than page 95. If you look on page 25, Fig. 2.1, you will see the letters a and b used for the sides of a right triangle. Then in Fig 2.8 on page 30 he shows a completely different triangle, not even a right triangle and yet he uses the same letters a and b for the sides. Then on page 52 he uses a and b, not for sides of a triangle, but for integers. He shouldn't reuse letters like that, it's very confusing.

Astronuc

but z is any complex number, e.g., z = x + iy in Cartesian coordinates, or z = r e^iθ = r (cos θ + i sin θ), and w = f(z) = u(x,y) + i v(x,y), where u and v are any real-valued functions.

However, if one is a EE, the i = j, and i is something else like current.

For some reason, I enjoyed complex analysis.

Astronuc

My office mate was out last night, and eventually noticed that he was doing facetime with someone. He quickly checked to find out the he was doing facetime with a client, and the guy had been watching him (an alternating view of his face and the ceiling) for some time. He stopped the facetime and sent a message apologizing for unintentionally broadcasting himself.

Fortunately, he wasn't doing anything for which he would be ashamed.

nazarbaz

There is no legitimate foundation to "power" : the best it could do is to be guided toward the achievement of reasonable goals.
Who and what is "reasonable" in the world we live in ? Well, certainly not me... Are you "reasonable" ?

Borek

I have looked through the window at the feeder and told Marzena chickadees eat seeds as if the world was going to end soon.

Then I started to think - do they know something we don't know?

xunxine

When child actors grow up, do they become adult actors?

turbo

Chickadees are little pigs at seed-feeders. At least they are not wasteful, like the goldfinches. Goldfinches will take a sunflower seed out of the feeder, then drop it on the ground. They do this over and over again. A flock of goldfinches can clean out my seed feeder in no time, and most of the seeds end up in a pile on the patio.

Jimmy Snyder

I just got back from watching the movie Anna Karenina. The movie is flighty, the story is fragmented, Levin's religious awakening is absent, and Vronsky is effeminate. Amid this sinking ship, Knightley managed to portray Anna's disintegration much as the book presents it, as did Jude Law portray Karenin's cold behavior towards his wife.

Ivan Seeking

That reminds me of an episode of Gilligan's Island...

Jimmy Snyder

Tonight's the night. Hapi Hanikinaka.

Evo

Hapi Hapi Jimmy and family!!!

Gad

People want me to go to this party, but I've hiked for 6 hours today and I feel sooo tired -_-''

dlgoff

Go for it. You'll get a second wind.

lisab

Aw c'mon, you can't fool me - pigs don't fly.

lisab

Chappy Chanukah!

Borek

That's what chickadees do here. They sit on the feeder and throw seeds away till they find one they like.

I haven't seen European goldfinch in my yard, they are not very common.