Syllabus for M535: (various file formats)
syllabus.dvi
syllabus.pdf
Syllabus for M536: (various file formats)
syllabus2.dvi
syllabus2.pdf
Link to Class Diary Fall
Link to Class Diary Spring
Some prereq' material:
(various file formats)
cppk.ps
cppk.pdf
This material will contain very elementary stuff (like SV calc) you are long
familiar with. But I want it there so I can refer back to it. It will also
contain hints at material that goes beyond the course and will not be asked
from you (like manifolds and differential geometry). I want this to be there
because it helps build your geometric intuition even in the case of plain
(i.e., plane) vector analysis. In between, there is a quick review and
introduction to the basic vector calculus stuff you need a lot in PDEs, both
conceptually and calculationally.
On the Gamma and Beta functions and volume of n-balls:
(various file formats)
gammabetaball.dvi
gammabetaball.pdf
This stuff is good to know in practice, even though it's not PDEs. But some
calculations explained here have been used without proof in Ch.~2 of Evans' book.
Overview before exam 1:
(various file formats)
overview.dvi
overview.pdf
Homework Problems 535:
#1,2 from book p. 85 #1,2 -- on transport eqn / rotation invariance of Laplace
#3,4 are the last two on p 11 of calc notes handed out. -- Laplace and coord trf.
#5 posted here -- simple example for weak sols of
transport eqn;
#6: from book p 86 pblm 4
#7-10 posted here --
theoretical problems about harmonic functions and Poisson's equation
#11-16 posted here --
heat eqn; #16 reflection of harmonic functions
#17-20 posted here --
heat equation; Fourier series; complex FS
#21-24 posted here --
EVPs, practical heat eqn via FS
#25-27 posted here --
Wave eqn
Homework Solutions 535:
(these links are only accessible within domain .utk.edu)
Sols #1-4 (pdf)
Sol #5 (pdf)
Sol #6 (pdf)
Sols #7-10 (pdf)
Sols #11-16 (pdf)
Sols #17-20 (pdf)
Sols #21-24 (pdf) ---
Sols #21-24 (ps)
Sols 25-27 see M536
Homework Problems 536:
#28-31 posted here --
1st order PDEs via characteristics
#32-33 posted here --
Burgers, inviscid and viscous
#34-35 are numbers 2 and 9 from Evans' book Ch.~4.7
#36-38 posted here --
classification and normal form for 2nd order
#39-41 posted here --
Banach FPT
#42-47 posted here --
42: rearrangement, and a geometric lemma; 43-47: weak derivatives
Homework Solutions 536:
(these links are only accessible within domain .utk.edu)
Sols #25-27 (pdf)
Sols #28-31 (pdf) ---
Sols #28-31 (ps)
Sols #32-33 (pdf)
Sols #34-38 (pdf) ---
Sols #34-38 (ps)
Sols #39-41 (pdf)
Sols #42-47 (pdf) ---
Sols #42-47 (ps)