Interval of Validity (Existence and Uniqueness)

Tutoring on Interval of Validity (Existence and Uniqueness)

Learning Objectives:

Understand and apply Interval of Validity

Math Tutoring on Interval of Validity (Existence and Uniqueness)

Existence of a Unique Solution for a First Order Differential Equation:

If  and  are continuous on a rectangular region defined by that contains the point , then there exists an Interval centered at  and a Unique Function defined on the Interval that satisfies the Initial Value Problem.

Picard’s Iteration Method:

Given .

The Picard’s Iteration Process consists of constructing a Sequence of Functions that get closer and closer to a solution.

If  for every t, then

.

 

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Hook Questions:

1.    How the Existence of a Unique Solution for a First Order Differential Equation is defined?

2.    What is Picard’s Iteration Method?

 

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