The following problems are for tutorial and test preparation. These are in addition to webassign and to Kritik assignments, and help prepare for the Tests.
Some are taken from Zill and some from Trench. The ones from Zill are either on webassign or from the book. You should do as much or as little as needed to feel comfortable with the material.
Zill webassign in pdf: practice pb 1, practice pb set #2, ppb#3, practpb4, pracpb5, pracpb6, pracpb7, pracpb8, pracpb9, pracpb10, pracpb11, pracpb12,lastprpb_BVP
Zill webassign assignments: assignment 1, assignment 2, assignment 3, assignment 4, assignment 5, assignment 6 , assignment7, assignment8, assign9, lastassign
Zill Sec 1.1 #39, Sec 1.2 # 27, 31,
Zill Sec 2.1 #39, Sec 2.2 #31, Sec 2.3 # 35
Zill Chap 2 Review # 3,7, 9, Sec 3.2 #5, Chap 3 review #9
Zill Sec 4.1 38, 40, 41, 42
Trench Sec. 2.2, p. 52, # 4, 11, 12, 18, 19, 20, 21
Trench Sec. 2.3, p. 61, #1, 4, 5, 15, 16, 17, 19
Trench Sec. 2.2, p. 53, # 8, 27, 29, 30 [For each, create a Direction Fields or Phase Lines graph (as appropriate) AND solve explicitly.] NOTE: for # 27, assume both a, b>0. Distinguish y0<0; 0<y0<b/a; and y0>b/a.
Trench Sec. 2.1, p. 41, # 6, 7, 8, 16
Trench Sec 5.1 26, 28, 30
Trench Sec 9.1 #15
Trench Sec 5.2 #34 a,b,c
Trench Sec. 5.7, p. 262, # 1, 4, 6, 7, 12 Sec. 6.1, p. 278, # 6, 16 Sec. 6.2, p. 288, # 20
Trench Sec. 7.1, p. 317, # 1ac, 2, 4, 5ab
Note: be careful of units in the Spring/Mass problems! Pounds is a unit of force: an object which weighs 16 lbs contains 16/32=1/2 slugs of mass. In the metric system, Newtons measure force, mass in kg times gravity g=9.8 m/sec^2. Be careful of mixing feet and inches, centimeters and meters!
For Power Series solutions, note that most problems in Zill are a bit disappointing, as most don’t ask for the Recurrence Relations, and don’t ask you to find explicit formulas for a_n when possible. So in addition to the Kritik #4, I recommend that you also do these problems from Trench (solutions are in the Student Solution Manual):
Trench Sec. 7.2, p. 329, # 2, 4, 10a, 16
Here are some other problems from the Trench textbook on singular points: [p0(r) gives the Indicial Equation; don’t worry about p1(r), p2(r), as we haven’t used Trench’s method.
Trench Sec 7.4, p. 347, # 4, 8, 12 Sec 7.5, p. 358, # 2, 4
Trench Sec 8.5 2,4, 8, 10, Sec 8.6 2, 4 Sec 8.7 2, 4, 8, 20