Lecture Notes for MATH 365 - Ordinary Differential Equation with Buchanan at Millersville (MILL)

Notes Information

Material Type:Class Note
Class:MATH 365 - Ordinary Differential Equation
University:Millersville University of Pennsylvania
Term: 2009
  • Robert Buchanan
  • Series Solutions
  • Provided That
  • Substituting
  • Continued...
  • Convergence
  • Differentiate
  • Differentiation
  • Homogeneous
  • Singular Points
Login / Sign Up to View Document
Preview Page 1Preview Page 2Preview Page 3Preview Page 4Preview Page 5Preview Page 6

Sample Document Text

Series Solutions Near an Ordinary Point MATH 365 Ordinary Differential Equations J. Robert Buchanan Department of Mathematics Summer 2009 J. Robert Buchanan Series Solutions Near an Ordinary Point Ordinary Points (1 of 2) Consider the second order linear homogeneous ODE: P(t)y'' + Q(t)y' + R(t)y = 0 where P, Q, and R are polynomials. Definition A point t0 such that P(t0) negationslash= 0 is called an ordinary point. If P(t0) = 0 then t0 is called a singular point. J. Robert Buchanan Series Solutions Near an Ordinary Point Ordinary Points (2 of 2) P(t)y'' + Q(t)y' + R(t)y = 0 If t0 is an ordinary point, then by continuity there exists an interval (a, b) containing t0 on which P(t) negationslash= 0 for all t ? (a, b). Thus the functions p(t) = Q(t)P(t) and q(t) = R(t)P(t) are defined and continuous on (a, b) and the ODE can be written as y'' + p(t)y' + q(t)y = 0. If the initial conditions are y(t0) = y0 and y'(t0) = y'0 then there exists a unique solution to the ODE satisfying the initial ...

Related Documents

Power Series Exam
Singular Points Exam
Singular Points Exam
Important Result Notes
Singular Points Exam
Power Series Method Exam
Singular Points Notes
Provided That Notes
General Formula Exam
Catastrophe Notes
Entertaining Notes
Series Solutions Exam
Homogeneous Problem Exam
Matrix Equation Exam
Matrix Equation Exam
Singular Points Exam
155, "/var/app/current/tmp/"