Homework assignments Homework is to be turned in in class on the given date at the latest.
for 1/8: (for first edition) Section 1.1:3, 4, 12, Section 1.2: 1, 3. If you do not have the book, the problems can also be found at the bottom of the main course web page.
for 1/15: Section 1.3: 3, 6(Hint: Use chain rule and polar coordinates to find an expression of u_xx + u_yy in terms of the variable r, using invariance under \theta), 9, Section 1.4: 1, 3 (use your physical intuition to guess what the solution should look like for large t), Section 2.1: 2, 5,
for 1/22: Section 2.2: 3, 5 Section 2.3: 3, 4, 8
Hints: For Section 2.3, 3(c) think of the temperature of a rod whose ends are kept at temperature 0 and use parts (a) and (b); for Section 2.3 4, you can use the strong maximum principle, stated below the maximum principle on page 41(first edition)/42(second ed.)). Remark: For Section 2.3, 4(c) and 8 one needs the `energy method' which is described in the "uniqueness" part of chapter 2.3, page 44 (2nd edition); read it or wait until we do it on Wednesday
for 1/29: Section 2.4: 1(try to relate this to the function Q(x,t) in the lecture), 9, 10, 18, Section 2.5: 1 (find a solution of the wave equation which does not have its maximum at t=0)
for 2/5: Section 3.1: 1, 4, 5(a) (only state by which function you have to replace the function f in Problem 4), Section 3.2: 1 (first state the solution in terms of \Phi_even and \Psi_even, and then try to reduce it to formulas only involving the original \Phi and \Psi), 2, Section 3.3: 2 (consider the function V(x,t)=v(x,t)-h(t) as described in the part SOURCE ON A HALF-Line in chapter 3.3). Section 3.4: 2
Midterm on 2/12: The material goes until the homework assignment for 2/5, i.e. until Section 3.4. You are allowed one hand-written cheat sheet, but no calculators or other notes. Below is a practice exam from a previous course (that one was open book - but as you will be allowed a cheat sheet, it should not be too much difference). More information will be posted next week.
for 2/19: Section 4.1: 2, 3, Section 5.1: 2, 8 (Equilibrium solution means that U_t=0) 9 (use the hint; I will explain the formula later), 4
for 2/26: Section 5.2: 11, 12 (also do 8 and 10, which need not be turned in) Section 5.3: 2 (two functions on the interval [a,b] are called orthogonal if the integral \int f(x)g(x) dx from a to b is equal to 0), Section 5.3: 5 (changed from Friday), 12, 13, Section 5.4: 9, 12
for 3/5: Section 4.3: 4 (do what we did in class now for \lambda <0 and/or read Section 4.3: NEGATIVE EIGENVALUE) Section 6.1: 6, 9, Section 6.2: 3
for 3/12: Section 6.3: 3, Section 6.4: 3, 5, 10
Review session on Wednesday, March 10, 4:30-6:30 in APM 5829. I'll post more info about the final later. Below is a practice final from a previous class.
More homework solutions. These are from an earlier course. So instead of 4.3 Problem 4 you find the solution of the more difficult problem 4.3 Problem 8, and also one or two other problems are missing. We may or may not be able to type solutions for the missing problems in time. Please ask if you would like to see the solutions.
Final The final will take place on Wednesday, 11:30-2:30 in the class room. The same rules apply as for the midterm: you are allowed one cheat sheet, normal size, but no calculator, books or other notes. The material will go over what was covered in homework assignments. You need not worry about Bessel functions or other material from section 10.2, unless it was already covered before in other sections. You also need NOT worry about problems concerning the 3-dimensional Laplacian \Delta_xx +\Delta_yy+\Delta_zz.
You should look at the practice final, homework problems and problems similar to homework problems in the book. Homework solutions have been posted for most of the homework problems. Email me and/or come to office hourse if you have further questions.
Office hours in finals week: M2-3, T3-4