Monday 
Wednesday 
Friday 
Mar 30 Introduction to Scalar Hyperbolic Equations:
Derivation
Definition of hyperbolic equations

Apr 1
Linear Advection Equation,
Burger Equation,
Method of Characteristics
Domain of dependence
Range of Influence
Weak Solution

Apr 3
Numerical Method:
1st Order Upwind

Apr 6
Numerical Method:
LaxWendroff
2nd Upwind
for u_t+ a u_x = 0
ENO for u_t + a u_x = 0
LaxFriedrich Scheme
HW1

Apr 8
Riemann Problem
Shock speed

Apr 10
Entropy Conditions for Discontinuity

Apr 13
Entropy Condition based on the spreading of characteristics
HW2 
Apr 15
Manipulating Conservation Laws
Entropy Functions 
Apr 17
Some Scalar Example:
Traffic Flow
Sound Speed

Apr 20
Two Phase Flow
Shallow Water Eqns
HW3 
Apr 22
Numerical Method for Linear System Equations
Backward Euler, LaxFriedrichs, LaxWendroff, and Upwind

Apr 24
Local Truncation Error
Stability
The Lax Equivalence Theorem

Apr 27 Conservative Methods for Nonlinear Problems 
Apr 29
Consistency
HW4

May 1
Discrete Conservation

May 4
The LaxWendroff Theorem

May 6
Godunov's Method
HW5 
May 8
Discrete entropy condition

May 11
Compactness 
May 13
Total variation stability
HW6 
May 15
l_1contracting numerical methods 
May 18
Monotone methods 
May 20
Higher Order Scheme HW7 
May 22
flux limiter 
May 25
Memorial Day: no class 
May 27
slope limiter 
May 29
slope limiter for nonlinear eqnationHW8 
Jun 1
2D simulation 
Jun 3
Central Scheme and Spectral Difference 
Jun 5 ENO, WENO,
Spectral Volume, DG 
Jun 8
Final Presentation: 11:30pm1:18pm
Final Exams week 
Jun 10 Final Exams Week 
Jun 12
Final Exams Week



