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3f-fall2010-exam_3_review

# 3f-fall2010-exam_3_review - c 1[series c 2[series If the...

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Math 3F — Exam #3 Review Sheet Laney College, Fall 2010 Fred Bourgoin The exam will cover sections 5.2 and 5.3, and chapter 6. You are responsible for all of the material presented in lecture and/or included in homework assignments from these chapters. To help you review, I have made a list of all the things you should know and all the skills you should have. One of the things you should do to get ready for the exam is review your homework. Chapter 5: Series Solutions of Second-Order Linear Equations Know the basics of power series: center, radius and interval of convergence, differentiation, integration, index shifting. Solve homogeneous first- and second-order equations using power series. (There will be non nonhomogeneous equations.) Solve first- and second-order initial-value problems using power series. I do not expect you to know the Maclaurin series for common functions. When the recurrence relation can be found, I expect an answer of the form:
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Unformatted text preview: c 1 [series] + c 2 [series]. If the recurrence relation is too diﬃcult to ﬁnd, I may ask you to ﬁnd the ﬁrst few non-zero terms of each series. Chapter 6: The Laplace Transform • You need to remember how to integrate functions using u-substitution, inte-gration by parts, and partial fractions. • Compute the Laplace transform of a function from the deﬁnition. • Find the inverse Laplace transform of an expression. The table of Laplace transforms will be provided to you. • Solve initial-value problems using the theorems on the Laplace transform. • Solve initial-value problems with discontinuous forcing functions. • Solve initial-value problems with impulse functions. • Compute the convolution of two functions. • Use the convolution theorem to ﬁnd the inverse Laplace transform of a func-tion....
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