Test 1 
Thu, Feb 28,
in class 
Test 2 
Tue, Apr 30,
9:00am (location TBA) 
Date 
Material
Covered 
Suggested HW problems 
Assignments  Remarks 
Tue Jan 8 
Introduction
and examples of important PDEs. 
1.2 of chapter 1. 

Thu Jan 10 
Basic concepts
(sec. 1.1, 1.2, 1.4, 1.5). Solutions of the heat equation by separation of variables (sec. 5.1, 5.2). 
1.7 of chapter 1. 
These
problems. Due: Jan 18. 

Tue Jan15 
More on the
heat equation (sec. 5.2). Solutions of 1d wave equation by separation of variables (sec. 5.3) 
5.1 to 5.6 of chapter 5. 
Problems 5.1, 5.3, 5.4, and 5.5 of
chpter 5. Due: Jan 28. 

Thu Jan 17 
Solutions of the wave equation by separation of variables (sec. 5.3 and a little of 5.4).  5.14 of chaper 5.  

Tue Jan 22 
More on
separation of variables. The energy method for the wave equation (sec 5.5). Discussion on nonuniqueness of solutions. 
5.17, 5.18 and 5.19 of chapter 5. 
These
problems. Due: Feb 7. 
It is useful here to review the
results about existence and uniqueness of solutions for
ODEs. 
Thu Jan 24 
Function
spaces and linear operatos. Discussion on differentiability of functions. 
Do the extra credit assignment 1.  Extra
credit assignment. Due: Feb 7. 

Tue Jan 29 
Dirichlet and
Neuman problem for the Laplacian (sec. 7.1 and 7.2). Maximum principle (sec. 7.3). 
7.1, 7.2, 7.5, 7.7, 7.9, 7.13 of
chapter 7. 
7.1, 7.2, 7.5, 7.7(a) of chapter
7. Due: Feb 14th. 
For the problems in polar
coordinates, you can check your multivariable calculus
book or some other PDE textbook. 
Thu Jan 31 
Maximum principle (sec. 7.3).  
Tue Feb 5 
Review of
multivariable calculus. Green's identities (sec. 7.4). 
Integration by parts in more than
one dimension, Green's identities and the chain rule for
functions of several variables are very important here.
Review these topics thoroughly if necessary. 

Thu Feb 7 
Green's
function for the Dirichlet problem (sec. 8.2). 
8.4, 8.8, 8.9, 8.10, 8.11 of
chapter 8. 
8.4(a), 8.8, 8.11 of chapter
8. Due: Feb 28th. 

Tue Feb 12 
Green's function for the Dirichlet problem (sec. 8.2).  
Thu Feb 14 
Final remarks
on the Green's function. 

Tue Feb 19 
Optimization
problems and calculus of variation: the minimal surface
equation (sec. 10.1). 
We are going to do many
calculations similar to the ones done in class. Make sure
you understand them. Also, read section 10.1 of the
textbook. 

Thu Feb 21 
More on
calculus of variations. 
Problems from chapter 10 

Tue Feb 26 
No class:
extended office hours during the time of the class in
light of the midterm. 

Thu Feb 28 
Test 1 

Tue Mar 5 
Spring Break 

Thu Mar 7 
Spring Break 

Tue Mar 12 
Finite
propagation speed for the wave equation (sec. 4.4). General comments on elliptic, parabolic and hyperbolic equations. 
Problmes 10.1, 10.2, 10.3 and 10.5
of chpater 10. Due: March 28th. Extra credit: problems 4.2, 4.3 and 4.5 of chapter 4. Due: March 28th. 
Some of the terminology in these
problems is different than what we used in class (although
the concepts are the same). Make sure to check the
textbook for the meaning of those. 

Thu Mar 14 
Generalities
on the heat equation. 
Derivation
of the heat equation (Nithin's presentation). 

Tue Mar 19 
Numerical
methods: finite difference (sec. 11.1 and 11.2). 

Thu Mar 21 
More on finite
difference (sec. 11.3). 

Tue Mar 26 
Stability and
consistency of a numerical scheme (sec. 11.3). 
Numerical
solutions with Mathematica  Mathematica code 
right click to download file (Clayton's presentation). More details. 

Thu Mar 28 
Convergence of
a numerical scheme. 

Tue Apr 2 
Finite
difference for Laplace's equation. Maximum principle. 

Thu Apr 4 
Finite
diference for the wave equation. 
Problems 11.1, 11.2, 11.6 , 11.10,
11.11 of chapter 11. Note: for 11.6, see the definition on page 317; the parts of the problems where you are asked to use a computer are optional. 

Tue Apr 9 
Rudiments of
the finite element method. 

Thu Apr 11 

Tue Apr 16 
Student's
presentations. 
Curvature
and PDE (Parker's presentation). 

Thu Apr 18 

Tue Apr 30 
Test 2, 9:00am (location
TBA) 