1. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Definition :
a partial differential equation is an equation that contains at least one partial derivative.
Dep variables ?? Indep variables

2. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Definition :
order of PDE is the order of the highest partial derivative occurring in the equation.
Find the order of PDE???

3. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Why We Study PDE:
PDE appears in modeling phenomena in the sciences, engineerig, economics, ecology and other areas.
Notations:

4. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Definition :
a solution is of a PDE is any function that satisfies the equation.
One solution of this differential equation is

5. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Verify???
One solution of this differential equation is
Where f can be any differential function of a single variable.

6. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Verify???
Is a solution for any twice differntiable function f and g of a single variable.
For example:

7. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Definition :
A PDE is linear if it is linear in the unknown function and in its partial derivatives. An equation that is not linear is nonlinear

8. Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
Definition :
A PDE is quasi-inear if it is linear in its highest order derivative terms.
Show that :
satisfies Laplace’s equation:
for all pairs (x,y) of real numbers except (x0,y0)

9. HomeWork: Chapter 1:First order Partial Differential Equations
Sec 1.1:preliminary notation and concepts
HomeWork:
Ex1/p3
Ex4/p4
Ex7/p5
Ex8/p5