Chapter 1:First order Partial Differential Equations

1
Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
Dep variables ?? Indep variables
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
Find the order of PDE???
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
Why We Study PDE
PDE appears in modeling phenomena in the
sciences, engineerig, economics, ecology and
other areas.
Notations
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
Definition
a solution is of a PDE is any function that
satisfies the equation.
One solution of this differential equation is
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
Verify???
One solution of this differential equation is
Where f can be any differential function of a
single variable.
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
Verify???
Is a solution for any twice differntiable
function f and g of a single variable.
For example
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary 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
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
Definition
A PDE is quasi-inear if it is linear in its
highest order derivative terms.
Show that
satisfies Laplaces equation
for all pairs (x,y) of real numbers except
(x0,y0)
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Chapter 1First order Partial Differential
Equations
Sec 1.1preliminary notation and concepts
HomeWork
Ex1/p3 Ex4/p4 Ex7/p5 Ex8/p5