Series and differential equations ib pdf
The aims of this option are to introduce limit theorems and convergence of series, and to use calculus results to solve differential equations. Before beginning any work in this option, it is recommended that you revise Topic 1 and Topic 7 of the core syllabus, as a lot of background knowledge ofIn this section we define ordinary and singular points for a differential equation. We also show who to construct a series solution for a differential equation about an ordinary point. The method illustrated in this section is useful in solving, or at least getting an approximation of the solution, differential equations with coefficients that are not constant. series and differential equations ib pdf
The most important property of power series is the following: Theorem 2. (Radius of convergence) For any power series P a n (x x0) n, there is a number [0, (meaning: 0 and can be innity) such that the power series converges for all x such that x x0.
Adifferential equation is an ordinary differential equation if the unknown function depends on only one independent variable. If the unknown function depends on two or more independent variables, the differential equation is a partial differential equation. In this book we will be concerned solely with ordinary differential equations. A very large class of nonlinear equations can be solved analytically by using the ParkerSochacki method. Since the ParkerSochacki method involves an expansion of the original system of ordinary differential equations through auxiliary equations, it is not simply referred to as the power series method. series and differential equations ib pdf Preface What follows are my lecture notes for a rst course in differential equations, taught at the Hong Kong University of Science and Technology.
Option Calculus IB Maths HL 3. Introduction to power series: Interval of convergence for power series: Introduction to Taylor and Maclaurin series: Another example for Taylor series: An introduction to differential equations: Solving homogenous differential equations using substitute: series and differential equations ib pdf Download Mathematics HL paper 3 TZ2 series and differential equations. pdfRating: 4.54 / Views: 651