Differential equations is a subject of wide applicability, and knowledge of dif­ Differential equations is a subject of wide applicability, and knowledge of dif­ ferential ferential equations equations topics topics permeates permeates all all areas areas of of study study in in engineering engineering and and applied applied mathematics. mathematics. Some Some differential differential equations equations are are susceptible susceptible to to analytic analytic means means of of so­ so­ lution, lution, while while others others require require the the generation generation of of numerical numerical solution solution trajectories trajectories to to see see the the behavior behavior of of the the system system under under study. study. For For both both situations, situations, the the software software package package Maple Maple can can be be used used to to advantage. advantage. To To the the student student Making Making effective effective use use of of differential differential equations equations requires requires facility facility in in recognizing recognizing and and solving solving standard standard "tractable" "tractable" problems, problems, as as well well as as having having the the background background in in the the subject subject to to make make use use of of tools tools for for dealing dealing with with situations situations that that are are not not amenable amenable to to simple simple analytic analytic approaches. approaches.

I Maple Use and Programming.- 1 Introduction to Maple.- II Differential Equations.- 2 Introduction to Differential Equations.- 3 First Order Equations.- 4 Introduction to Numerical Methods.- 5 Higher Order Differential Equations.- 6 Laplace Transform Methods.- 7 Systems of Equations.- 8 Stability.- 9 Periodic Problems.- 10 Impedances and Differential Equations.- 11 Partial Differential Equations.- III Maple Application Topics.- 12 Introduction to Maple Applications.- 13 Plotting With Maple.- 14 Maple and Laplace Transforms.- 15 Maple Linear Algebra Applications.- 16 Runge-Kutta Designs.- 17 Maple Packages.- IV Appendices.- A Review Problems.- B Laplace Transform Table.- References.