Lecture-2 - AMS 361: Applied Calculus IV (DE & BVP)...

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Outline for Lecture 2 1 st order Differential Equations 2. Sources of Differential Equations (DE): 2.1 Mathematical Manipulations e.g. 1. If A and B are constants and We can see Thus, Therefore, we can say DE has a solution e.g.2. General DE The most general form of n-th order DE with independent variable x and unknown function y(x) and dependent variable x where F is specific real-valued function with (n+2) variables: x, y, y’, y’’, … Solution to a DE: A function u(x) is a solution of the above DE on interval “I” provided that all derivatives, exist on “I” and for all x in “I”.
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e.g.3. Ordinary DE and Partial DE Ordinary DE ’s unknown function has ONLY ONE independent variable. In the above equation, “y” is the unknown function with one independent variable “x”. Partial DE ’s unknown function has two or more independent variables. In the above equation, “y” is the unknown function with two independent variables x1 and x2. 2.2 Practical Applications
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Lecture-2 - AMS 361: Applied Calculus IV (DE & BVP)...

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