math 310 a1 - MATH 310 Differential Equations Homework...

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Unformatted text preview: MATH 310 Differential Equations Homework Exercises, Set 1 Summer 2011 Quiz on Wednesday, 14 September 2011 Course Information is on WebCT Textbook references are to: Boyce and DiPrima "Elementary Differential Equations and Boundary Value Problems" (9th edition). Notes: Read Section 1.1 carefully to assist you with these exercises. This set of problems is shorter than usual, as the semester is just beginning. . . Reading: Sections 1.1, 1.2; 2.3 (first few pages) Look at Section 1.4 (historical background) for interest Problems to prepare for quiz (no need to hand in): Section 1.1, # 3, 11; 15, 18, 19 Direction fields; long-time behaviour To sketch or identify a direction field, consider for which y values the function y(t) is increasing, and where it is decreasing. The long-time behaviour (as t ) can then be deduced from the direction field. #11: To assist you, you may wish to generate the direction field using Maple or other software; you will have to choose a sensible domain and range. # 21, 22 Formulating differential equation models #21: The fundamental balance is rate of change = rate in - rate out. Carefully consider each term in the DE; ensure that all dimensions agree. Example 1 of Section 2.3 might help. #22: What is the relationship between volume and surface area for a sphere? # 12 Carbon dating (exponential decay) Section 1.1, Section 2.3, 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 1.1, Section 2.3, # 1, 5, 16, 17, 20; 25 Direction fields; writing down DE # 7, 8 Compound interest (see Example 2 of Section 2.3) ...
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