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Unformatted text preview: MA366 Sathaye Chapter 1 Summary 1. Notations. We may use the following variations of the usual Calculus notations: dy dx = d dx ( y ) = D x ( y ) = y = ˙ y. The notation y is used when the independent variable is known (and it need not be x .) The notation ˙ y is typically used when the independent variable is t which stands for time. 2. Higher order derivatives are denoted as: d n y dx n = D n x = y ( n ) . 3. A differential equation is an equation of the form F ( x,y,y (2) , · · · ,y ( n ) ) = 0 or something which reduces to such a form. The equation is said to have order n if the highest derivative present is y ( n ) . 4. A differential equation is linear if it is linear in y,y , · · · ,y ( n ) . Note that it is not required to be linear in the independent variable. 5. For an equation y = f ( x,y ) of order one, we consider its direction field as a display of vectors in the plane such that at each displayed point ( a,b ) we have a short vector displayed having slope f ( a,b ).)....
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This note was uploaded on 01/18/2012 for the course MATH 366 taught by Professor Edraygoins during the Fall '09 term at Purdue.
- Fall '09