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Unformatted text preview: Page 1 - 4 ENGR 232: Homework 1 Name _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Due Week 2 at 6PM Sharp! Part A: Review of Integration: In freshman calculus, you learned how to integrate elementary functions. Every integration problem can be recast as a differential equation as shown in the example below. Example: Find all anti-derivatives of the function f ( x ) = 3 x 2 . In freshman year, you noted there was an infinite number of solutions all differing by a constant. y = f ( x ) dx = x 3 + c = F ( x ) + c Recasting integration as a differential equation. Suppose we know the indefinite integral y = f ( x ) dx = F ( x ) + c That is, F ( x ) is an anti-derivative (or integral) of f ( x ). Then f ( x ) is the derivative of F ( x ). Thus every integration problem can be recast as the differential equation: dy dx = f ( x ) If F ( x ) is an anti-derivative of f ( x ), then the solutions of the differential equation are: y = F ( x ) + c All the solutions are obtained as vertical...
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- Spring '08