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MTL102 - Coggle Diagram
MTL102
PDE
Quasi Linear PDE and corresponding Initial value problem
General Ideas involved
Vector field ,Solution Surface , Normal and tangent , Tangent planes
Parameterization of curves
Parameterizations of the surface
Inverse Function Theorem
Jacobian
What is a curve?
What is a parameter ?
Initial condition in from of curve
What is Quasi Linear PDEs ?
Specific Ideas
Characteristic and Non Characteristic Curve
Solving QL PDEs Core Idea
Equivalent to finding the solution surface
Found by converting the problem into a system of ODEs
Side Note GPolya create an auxiliary problem or equivalent problem
ODEs as PDEs ?? Go back to the definations of ODEs and PDEs and See and Clear DOUBTs
Existence and Uniqueness of the solutions of PDEs