## Partial Differential Equations Math 110, Winter 2010:

under construction

Office hours: M3-4, W2-3 and by appointment (just talk to me after class or send me an email)

Office: APM 5256, tel. 534-2734

Email: hwenzl@ucsd.edu

Course book: Walter A. Strauss: Partial Differential Equations, Wiley & Sons, 2nd edition. The first edition is still available and should be helpful for the course as well. The main possible nuisance from using the first copy (besides the fact that the second one does have some improvements in presentation) may come from different homework numbers. I will try to avoid any confusion by double checking with the first edition (so far the numbers have always been the same), but may not always be able to do so. If in doubt, check with a friend. I also put a copy on reserve at the science library.

Computation of grade: (tentative) The grade is computed from your scores in the final (50%), 1 midterm (30%) and homework (20%). Although homework counts comparatively little, it is extremely important that you do it, as most of the exam problems will be very similar to homework problems. It is OK to compare homework notes or to discuss problems with other students; just copying someone else's homework, however, will not count.

Dates of exams: No make-up exams!

Midterm: 2/12 in class; for further information click at link for homework below

Homework assignments Homework is to be turned in in class on the given date at the latest. The TA also made a drop box. In order to make it easier for you to print out the assigments, I put the newer assignments on a new page. Please click below for new assignments:

for 1/8: Section 1.1:3, 4, 12, Section 1.2: 1, 3. If you do not have the book, can also find the problems at the bottom of this web page.

other homework assignments can be found under the link above

First homework assignment, due 1/8: As the book is not available yet in reserve, here are the homework problems. Observe that u_x means `u sub x' and x^2 means `x squared'. If in doubt, ask the TA or me.

Section 1.1, Prob. 3: For each of the following equations, state the order and whether it is nonlinear, linear inhomogeneous (i.e. of the form L(u)=g, g not equal to 0, with L linear), or linear inhomogeneous; provide reasons.

(a) u_t - u_xx +1 = 0

(b) u_t - u_xx +xu = 0

(c) u_t - u_xx + uu_x = 0

(d) u_tt - u_xxt + uu_x = 0

(e) iu_t - u_xx + u/x = 0

(f) u_x(1+(u_x)^2)^{-1/2} + u_y(1 + (u_y)^2)^{-1/2} = 0

(a^{-1/2} means 1 over the square root of a)

(g) u_x + e^yu_y = 0

(h) u_t + u_xxxx + square root{ 1 + u} = 0

Section 1.1, prob. 4: Show that the difference of two solutions of an inhomogeneous linear equation Lu=g with the same g is a solution of the homogeneous equation Lu=0.

Section 1.1, prob. 12. Verify by direct substitution that u(x,y)= sin(nx)sinh(ny) is a solution of u_xx + u_yy = 0 for every n>0. <\p>

Section 1.2, prob. 1: Solve the first-order equation 2u_t + 3u_x = 0 with the auxiliary condition u(x,0)= sin(x); here u depends on variables x and t.

Section 1.2, prob. 3: Solve the linear equation (1+x^2)u_x+u_y=0 (here x^2 = x squared, u_x = u sub x). Sketch some of the characteristic curves.