Show that Heun's method can be expressed in difference form, similar to that of the Runge-Kutta method of order four, as wo = a, ki = hfUi, Wi), ki = hf ^ Wi + - f 2h 2 \ ki hf f/, + , Wj + -^2 1 . w/+i = Wi + -{k] + 3^3), for each i =0.1,... , N 1

Module 2 Section 2.1: Properties of the Trigonometric Functions Recall the six trigonometric functions; y x y sin( )= , cos ( ) , tan( )= r r x csc( )= r , sec( )= r , cot( )= x y x y If we consider the unit circle then in each of these cases, r =1. Section 5.3 in the textbook does a very thorough job covering the topics: domain/range, period, signs, fundamental identities, finding exact values with identities. So we don't think writing anything here would add anything significant to the topics. Please read pages