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topics - MathEng 351(Fall 2004 Study tips To achieve...

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MathEng 351 (Fall, 2004) Study tips . To achieve minimal competency (C-) you must be able to do, without hesitation, the first 3 problems from the exercises in the book of the sections we covered. To achieve prof- ficiency (B-), you must be able to know how to apply the tools we have explored to problems involving multi-step (four or more) conceptual calculations. To achieve excellence (A-) you must be able to synthesize and interpret the information provided from multi-step calculations in order to reach meaningful analytical conclusions. So, do every answered part of the first 3 problems of: Chapter 2 sections 2-5, Chapter 3 sections 2-8, Chapter 8 sections 2-3, Chapter 9 sections 2-10, Chapter 10 sections 2-6, Chapter 11 sections 2-5. Beyond that, make sure you can do without hesitation all the problems on the midterms. Then review the rest of your homework assignments. Stick to the problems that have answers in the back so you can check your work. I will be available to help with the questions that don’t have answers in the back. Topics (1) Chapters 1-3: ODE’s (a) Classification: n’th order, (non)linear, (non)homogeneous, (non)constant co- e cients, separable equations, exact equations, Cauchy-Euler equation, sys- tems of ODE’s . (b) Solution techniques: exact equations (for certain first-order ODEs), separation of variables , (for first order separable equations), variation of parameters (for first or second order, nonhomogeneous linear ODE’s), reduction of order , second-order linear homogeneous ODE’s with constant coe cients (know what to do with the characteristic polynomial/equation and repeated roots, know what linear independence of general solutions means and how to test for/generate linearly independent solutions, know how many linearly inde- pendent solutions to expect for a general n th order ODE, know the di ff erence between the general solution expressed as a linear combination of n linearly in- dependent functions ( Theorem 3.3.2 ) and an exact solution satisfying given initial/boundary conditions), method of undetermined coe cients

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