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Unformatted text preview: 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 multistep (four or more) conceptual calculations. To achieve excellence (A) you must be able to synthesize and interpret the information provided from multistep calculations in order to reach meaningful analytical conclusions. So, do every answered part of the first 3 problems of: Chapter 2 sections 25, Chapter 3 sections 28, Chapter 8 sections 23, Chapter 9 sections 210, Chapter 10 sections 26, Chapter 11 sections 25. 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 dont have answers in the back. Topics (1) Chapters 13: ODEs (a) Classification: nth order, (non)linear, (non)homogeneous, (non)constant co ecients, separable equations, exact equations, CauchyEuler equation, sys tems of ODEs . (b) Solution techniques: exact equations (for certain firstorder ODEs), separation of variables , (for first order separable equations), variation of parameters (for first or second order, nonhomogeneous linear ODEs), reduction of order , secondorder linear homogeneous ODEs with constant coecients (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 difference 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 coecients...
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 Spring '08
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 Math

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