week4 - Week 4 Material to be covered: 3.5 Homework to be...

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Week 4 Material to be covered: 3.5 Homework to be handed Sept. 28 Problems: Sec 3.4: 23, 24 Sec 3.5: 2, 3, 9, 10 Prepare, but do not hand in, Playbook entries for: a) Reduction of order, b) Super- position in non-homogeneous equations, c) Undetermined coefficients. This week, we will start the study of non-homogeneous linear second order differential equations. The main result are Theorem 3.5.1 (a superposition principle) and its consequence Theorem 3.5.2 (a formula for the general solution) of the equations. These results show that the general solution of the non-homogeneous equation is obtained by adding to the homogeneous equation a particular solution. Last, week, of course, we became experts in finding solutions of the homogeneous equation. So, this week (and the next) we will concentrate on finding particular solutions of non-homogeneous equations. This week, we will study the method of undetermined coefficients, which applies to constant coefficient equations with a special forcing term. The book presents several
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