数学物理方法Chapt 7, Series solutions of ODE (1).pdfVIP

Chapter 7 Series solution of ODE 课后看书Chapter 16, MMPE Chap 7: Series solution of ODE shi.xq@sustc.edu.cn 1 Introduction • Series solution: to seek solutions of second order linear ODEs with variable coefficients • Such series can be evaluated numerically, and those occurring most commonly are named and tabulated. • There is in fact no distinct borderline between Series solution or solutions in terms of elementary functions (some series occur so frequently that they are given special names such as sin x, cosx or exp x ) Since we shall be concerned principally with second-order linear ODEs in this chapter, we begin with a discussion of these equations, and obtain some general results that will prove useful when we come to discuss series solutions. Chap 7: Series solution of ODE shi.xq@sustc.edu.cn 2 7.1 linear independence 7.1 Linear independence homogeneous second-order linear ODE with variable coefficients general form general form of the solution linearly independent Wronskian Chap 7: Series solution of ODE shi.xq@sustc.edu.cn 3 7.1 linear independence Chap 7: Series solution of ODE shi.xq@sustc.edu.cn 4 7.1 linear independence • 作业7.1 Chap 7: Series solution of ODE shi.xq@sustc.edu.cn 5 7.2 singular points 7.2 Ordinary and singular points of an ODE Broaden our discussion to complex function y(z) of a complex variable z Ordinary and singular points of an ODE: Chap 7: Series soluti