Monday 
Wednesday 
Friday 
Mar 28 Introduction to Scalar Hyperbolic Equations:
Derivation
Definition of hyperbolic equations

Mar 30
Linear Advection Equation,
Burger Equation,
Method of Characteristics
Domain of dependence
Range of Influence
Weak Solution

Apr 1
Numerical Method:
1st Order Upwind

Apr 4
Numerical Method:
LaxWendroff
2nd Upwind
for u_t+ a u_x = 0
ENO for u_t + a u_x = 0
LaxFriedrich Scheme

Apr 6
Riemann Problem
Shock speed

Apr 8
Entropy Conditions for Discontinuity

Apr 11
Entropy Condition based on the spreading of characteristics

Apr 13
Manipulating Conservation Laws
Entropy Functions 
Apr 15
Some Scalar Example:
Traffic Flow
Sound Speed

Apr 18
Two Phase Flow
Shallow Water Eqns

Apr 20
Numerical Method for Linear System Equations
Backward Euler, LaxFriedrichs, LaxWendroff, and Upwind

Apr 22
Local Truncation Error
Stability
The Lax Equivalence Theorem

Apr 25 Conservative Methods for Nonlinear Problems 
Apr 27
Consistency

Apr 29
Discrete Conservation

May 2
The LaxWendroff Theorem

May 4
Godunov's Method
 May 6
Discrete entropy condition

May 9
Compactness 
May 11
Total variation stability

May 13
l_1contracting numerical methods 
May 16
Monotone methods 
May 18
Higher Order Scheme 
May 20
flux limiter 
May 23
2D simulation 
May 25
slope limiter 
May 27
slope limiter for nonlinear eqnation 
May 30
Memorial Day: no class 
Jun 1
Central Scheme and Spectral Difference 
Jun 3 ENO, WENO,
Spectral Volume, DG 
Jun 6
Final Presentation: 11:30am1:18pm
Final Exams week 
Jun 8 Final Exams Week 
Jun 10
Final Exams Week



