Week 1  

Mon 21 Aug  Classification of ODEs Matlab tutorial: getting started with Matlab Matlab primer 
Chapter 1 
Weds 23 Aug  Derivation of the heat
equation, connection to the diffusion equation. 
Section 2.1 
Fri 25 Aug  Harvey 
Section 2.2 
Week 2  
Mon 28 Aug 
Harvey  
Weds 30 Aug 
Harvey  
Fri 1 Sept 
Harvey  
Week 3  
Mon 4 Sept 
LABOR DAYNO CLASS!!! 

Weds 6 Sept 
Finite differences
for the steady heat equation, begin order of approximation. Texts on order Matlab demo code 
Section 7.5.1 
Fri 8 Sept 
Order of approximation and finite differences continues  Section 7.5.1 
Week 4  
Mon 11 Sept 
Vector spaces,
Vector subspaces,
linear operators, PDEs as operator equations. Begin existence and uniqueness of solutions to operator equations. Range and Null Space. Basis and Dimension. 
Sections 3.1,3.2,3.3 
Weds 13 Sept 
Conclude basis and Dimension. Begin discussion of inner products and inner product spaces.  Sections 3.3, 3.4 
Fri 15 Sept 
Continue with inner products and inner product spaces. Introduced generalized orthogonality of vectors.  Section 3.4 
Week 5  
Mon 18 Sept 
Introduce the L2 inner product and begin the projection theorem.  Sections 3.4.1, 3.4.2 
Weds 20 Sept 
Projection theorem, the Gram matrix and examples Gram matrix example 
Section 3.4.2 
Fri 22 Sept 
Eigenvalues and eigenvectors for general matrices 

Week 6  
Mon 25 Sept 
Relationship between the matrix transpose and
dot product. Eigenvalue properties of symmetric matrices. 
Section 3.5.1, 3.5.2 
Weds 27 Sept 
Spectral method for symmetric linear systems Example of using null space to find eigenvectors 
Section 3.5.3 
Thurs 28 Sept 
Exam 1: 6:309:30pm in Herzstein Hall 210
Fall 2016 exam 1 Solutions NOTE: Big O and little o are new topics. Problem 4 is material for Exam 2. Fall 2017 Exam 1 Solutions 

Fri 29 Sept 
Relationship between Boundary value problems and linear algebraic systems  Section 5.1 
Week 7  
Mon 2 Oct 
Symmetric linear differential operators and eigenpairs,  Section 5.2.1, 5.2.2 
Weds 4 Oct 
Eigenfunctions with different boundary conditions Fourier examples code 
Section 5.2.3 
Fri 6 Oct 
A stepbystep breakdown the stages of the
spectral method for linear BVPs 
Section 5.3.15.3.3 
Week 8  
Mon 9 Oct 
FALL RECESS NO CLASS!!! 

Weds 11 Oct 
A stepbystep breakdown the stages of the
spectral method for linear BVPs Spectral method with inhomogeneous boundary conditions e^x fourier series 
Section 5.3.4 
Fri 13 Oct 
Start Finite Element method for BVPs FEM with sine series basis 
Section 5.4 
Week 9  
Mon 16 Oct 
Bilinear form and consistency of
solutions for two formulations. Notes 
Section 5.5 
Weds 18 Oct  The energy norm, the discrete problem, and solve some examples, The piecewise polynomial space  Beginning of Section 5.6 
Fri 20 Oct  Steady heat equation with nonconstant diffusivity using finite elements  Section 5.6.1 
Week 10  
Mon 23 Oct 
FEM continued 

Weds 25 Oct  Inhomogeneous Dirichlet boundary conditions with
piecewise finite elements Notes 
Section 5.6.2 
Fri 27 Oct  FEM example Example 

Week 11  
Mon 30 Oct 
Solution of timedependent equations: the heat equation. Start solving heat via spectral  Section 4.3.1 
Weds 1 Nov  Solution of homogeneous heat equation (Dirichlet conditions) using the spectral method  Section 6.1 
Thur 2 Nov   
Fri 3 Nov  Continue the timedependent spectral
method 

Week 12  
Mon 6 Nov 
Timedependent spectral method applied to special cases of f(t,x) = C and dealing with inhomogeneous Dirichlet boundary conditions using `shifting the data'  
Weds 8 Nov  Timedependent spectral method applied to Neumann
Boundary conditions. 
Section 6.2 
Fri 10 Nov  Finite element methods for the heat equation. 
Section 6.4 
Week 13  
Mon 13 Nov 
Solving time dependent problems using Forward and
Backward Euler + stability 

Weds 15 Nov  Sample Euler time stepping code  
Fri 17 Nov  Sample code (Check for bugs!)  
Week 14  
Mon 20 Nov 
Stability of ODE, and the CFL condition for PDE 

Weds 22 Nov  Stability and CFL continued, Worked examples, open
discussion 

Fri 24 Nov  Thanksgiving break!  
Week 15  
Mon 28 Nov 


Weds 30 Nov  

Thurs 30 Nov 