Mathematics & Science
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Numerical Methods for Solving Differential EquationsEuler's MethodUsing the Method with Mathematica(continued from last page...) Instructions for the ExercisesOnce again it's time to have you attempt to do some work on your own. The examples that we've already done together should have sufficiently prepared you to tackle these problems. As you work through them, don't cheat yourself by first skipping forward and looking at the solutions. After all, you are supposed to be doing these exercises to enhance your learning, and to prepare yourself for the laboratory exam that you'll take later. Some of these exercises may be solved exactly using the techniques that you have already learned in the lecture component of this course. If you're feeling ambitious, you might attempt to find the exact solutions to the exercises, where this is possible, and then use these solutions to help you gauge how good the corresponding numerical solutions are, just as we did back in the Introduction. Use the euler program:
euler[f_,{x_,x0_,xn_},{y_,y0_},steps_]:= that you entered into Mathematica earlier, to solve each of the initial value problems given in the table below. For each exercise, do the following:
ExercisesIf you've finished the above exercises, then you may either return to the beginning of this laboratory, jump to the Table of Contents of all of the differential equations laboratories, or simply quit. |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker ©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |