Lecture 9 Notes

Introduction to systems of equations geometric

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Unformatted text preview: Ax ￿ • Think of the unknown functions as coordinates (x(t), y (t)) of an object in the plane. • Ax gives the velocity vector of the object located at ￿￿ 2 x= 1 x. Introduction to systems of equations • Geometric interpretation - direction fields. ￿￿ ￿ ￿￿ ￿ dx 11 x = 41 y dt y or x = Ax ￿ • Think of the unknown functions as coordinates (x(t), y (t)) of an object in the plane. • Ax gives the velocity vector of the object located at ￿￿ 2 x= 1 ￿ ￿￿ ￿ ￿ ￿ 11 2 3 Ax = = 41 1 9 x. Introduction to systems of equations • Geometric interpretation - direction fields. ￿￿ ￿ ￿￿ ￿ dx 11 x = 41 y dt y or x = Ax ￿ • Think of the unknown functions as coordinates (x(t), y (t)) of an object in the plane. • Ax gives the velocity vector of the object located at ￿￿ 2 x= 1 ￿ ￿￿ ￿ ￿ ￿ 11 2 3 Ax = = 41 1 9 x. Introduction to systems of equations • Geometric interpretation - direction fields. ￿￿ ￿ ￿￿ ￿ dx 11 x = 41 y dt y or x = Ax ￿ • Think of the unknown functions as coordinates (x(t), y (t)) of an object in the plane. • Ax gives the velocity vector of the object located at ￿￿ 1 x= 1 x. Introduction to systems of equations • Geometric interpretation - direction fields. ￿￿ ￿ ￿￿ ￿ dx 11 x = 41 y dt y or x = Ax ￿ • Think of the unknown functions as coordinates (x(t), y (t)) of an object in the plane. • Ax gives the velocity vector of the object located at ￿￿ 1 x= 1 ￿ ￿￿ ￿ ￿ ￿ 11 1 2 Ax = = 41 1 5 x. Introduction to systems of equations • Geometric interpretation - direction fields. ￿￿ ￿ ￿￿ ￿ dx 11 x = 41 y dt y or x = Ax ￿ • Think of the unknown functions as coordinates (x(t), y (t)) of an object in the plane. • Ax gives the velocity vector of the object located at ￿￿ 1 x= 1 ￿ ￿￿ ￿ ￿ ￿ 11 1 2 Ax = = 41 1 5 x. Introduction to systems of equations • Geometric interpretation - direction fields. ￿￿ ￿ ￿￿ ￿ dx 11 x = 41 y dt y or x = Ax ￿ • Think of the unknown functions as coordinat...
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