Monday 
Wednesday 
Friday 
Mar 26 Scalar Hyperbolic Equations:
Linear Advection Equation,
Burger Equation,
Method of Characteristics

Mar 28 Numerical Method:
1st Order Upwind
LaxWendroff
2nd Upwind
for u_t+ a u_x = 0

Mar 30 ENO for u_t + a u_x = 0
LaxFriedrich Scheme
HW1 
Apr 2
Domain of dependence
Weak Solution

Apr 4
Riemann Problem
Shock speed

Apr 6
Entropy Conditions for Discontinuity
HW2 
Apr 9
Entropy Condition based on the spreading of characteristics

Apr 11
Manipulating Conservation Laws
Entropy Functions 
Apr 13
Some Scalar Example:
Traffic Flow
Sound Speed
HW3 
Apr 16
Two Phase Flow
Shallow Water Eqns

Apr 18
Numerical Method for Linear System Equations
Backward Euler, LaxFriedrichs, LaxWendroff, and Upwind

Apr 20
Local Truncation Error
Stability
The Lax Equivalence Theorem
HW4

Apr 23 Conservative Methods for Nonlinear Problems 
Apr 25
Consistency
Discrete Conservation 
Apr 27
The LaxWendroff Theorem
HW5 
Apr 30
Godunov's Method 
May 2
Discrete entropy condition 
May 4
Discrete entropy condition
HW6 
May 7
Compactness
Total variation stability 
May 9
l_1contracting numerical methods
Monotone methods 
May 11
Higher Order Scheme HW7 
May 14
flux limiter 
May 16
slope limiter 
May 18
slope limiter for nonlinear eqnation HW8 
May 21
Conference 
May 23
Conference 
May 25
Conference 
May 28
Memorial Day (no class) 
May 30
Central Scheme and Spectral Difference 
Jun 1 ENO, WENO,
Spectral Volume, DG 
Jun 4 Final Exams Week 
Jun 6 Final Exams Week 
Jun 8 Final Exams Week



