MA483 Instructor: Russell Brown Spring 2001

The following selection of problems will allow us to get acquainted and review facts from calculus. Homework #1. Due Wednesday, 19 January.

• Strauss, §1.2 #1, 6. Hint: In #6, sketch the characteristic curves in the (x, y) plane. Find all curves which pass through the y-axis.

• Additional problem 1. If r = \sqrt{x^{2} + y^{2}} and u(x, y) = f(r), compute and simplify u_{xx} + u_{yy}. Hint: Use the chain rule to write

\frac{∂u}{∂x} = \frac{df}{dr} \frac{∂r}{∂x}.

Repeat to find the second derivative.

• Additional problem 2. Solve the ordinary differential equation

\frac{dy}{dx} = y^{2} y(0) = 2.

Hints: Rewrite as dy/y^{2} = dx. Integrate. Don’t forget +C. Solve to express y in terms of x and find C using that y(0) = 2.

January 11, 2001