Learning Objectives:

__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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