1. Chapter 1:First order Partial Differential Equations
Sec 1.4: The Quasi-Linear Equation
Consider the first-order quasi-linear PDE:
Passes through the curve 1
characteristics: 2
Solve for the charac and write in parametric form 3
Parametrize the curve and write in: 4
at t=0: set
find the constants 5
write the carach in parametric form (no constants) 6
Eliminate t and s : and write solution

2. Chapter 1:First order Partial Differential Equations
Sec 1.4: The Quasi-Linear Equation
Consider:
Find a solution satisfying
Two solutions:
on the curve
General solution:

3. Chapter 1:First order Partial Differential Equations
Sec 1.4: The Quasi-Linear Equation 1
Find a solution satisfying
on the curve 2 3
characteristics: 1 2
Solve for the charac and write in parametric form 5 4 3
Parametrize the curve
at t=0: set 4
find the constants 5
write the carach in parametric form (no constants) 6
Eliminate t and s : and write solution 6

4. Chapter 1:First order Partial Differential Equations
Sec 1.4: The Quasi-Linear Equation
Cauchy
Problem
Given PDE