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Unformatted text preview: MATH 310 Differential Equations Homework Exercises, Set 3 Summer 2011 Quiz on Wednesday, 28 September 2011 Course Information is on WebCT Textbook references are to: Boyce and DiPrima "Elementary Differential Equations and Boundary Value Problems" (9th edition). Reading: Sections 2.1, 2.3 Problems to prepare for quiz (no need to hand in): Section 2.1, # 13, 18, 24, 28, 33 Linear first-order equations, integrating factors (Do as many of 120 as needed to be confident of the method) Note the theme of interpreting/working with properties of the solutions # 4, 23(ad) Applications of linear equations: mixing, gravity/air resistance #23: solve for the first 10 sec, and use the results as IC to continue # 23, 24, 25 Theory of linear equations #2325 discuss properties of linear equations that will be important later Section 2.3, Section 2.4, Additional problems 1. Solve the differential equation y - 2ty = t + 1, Write the solution in terms of the error function 2 erf(t) = t 0 y(1) = 2. e-s ds. 2 You are strongly encouraged to look at and work through other problems; the following is a suggested selection of other useful or interesting (optional) exercises: Section 2.1, Section 2.1, Section 2.1, # 1, 5, 8, 14, 19 Linear equations and integrating factors # 27, 31, 34 Solution of linear DEs and interpretation # 38, 39 #3839: We will again encounter the method of variation of parameters developed here in the context of 2nd (and higher) order DEs # 3, 10, 16, 27 Applications: mixing, compound interest, cooling, falling with friction #27: Millikan's oil drop experiment was historically important in measuring the charge on an electron # 26 Theory of linear equations Section 2.3, Section 2.4, ...
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