12240/Homework Assignment 7

This assignment is due at the tutorials on Thursday November 22. Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.
Task 1. Read sections 2.4, 3.1 and 3.2 in our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, preread sections 2.5 and 3.33.4, just to get a feel for the future.
Task 2. Solve problems 1, 2, 3a, and 3b on pages 9697, problems 1, 2, 4 and 9 on pages 106107, problems 1, 2, and 9 on pages 151152, and problems 1, 2aceg, 2bdf, 7, 19, and 21 on pages 165168, yet submit only your solutions of the underlined problems.
Just for fun. Assume the Earth is flat. We want to fly a virtual video camera from a mile above the Kansas State University campus (so that the whole thing is in sight) to a kilometer above the University of Toronto campus (so that the whole thing is in sight) in 10 seconds or less, so that the resulting movie will have the least blur. Clearly, we shouldn't fly at a constant elevation, for a camera moving so fast so close to the ground will suffer immense motion blur. Instead, we should fly up and thus zoom out, then move sideways fast but while we're far, and then zoom back in again. But what's the precise optimal path? And what should our speed be at any point along that path?