notes1

notes1 - MA366 Sathaye Chapter 1 Summary 1 Notations We may...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ).)....
View Full Document

This note was uploaded on 01/18/2012 for the course MATH 366 taught by Professor Edraygoins during the Fall '09 term at Purdue.

Page1 / 3

notes1 - MA366 Sathaye Chapter 1 Summary 1 Notations We may...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online