Math 2280 - 1 Schedule and Homework Problems Aug. 15, 2005
Treibergs
Turn in the starred problems only. Your solutions must be self-contained and
complete to receive full credit. For now, homework from each week (M,T,W,F)
is due the following Wednesday. (This may change after discussing the schedule
with the grader.) Homework which is more than one week late but not more than
two weeks late receives half credit. Homework which is more than two weeks late
will receive zero credit.
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The problems listed here correspond to the THIRD EDITION of the text,
~~~~~~~~~~~~~
by Edwards & Pinney, "Differential Equations and Boundary Value Problems,
Computing & Modelling, 3nd ed.
The corresponding problems for the second edition can be found on the homework
listing from my M2280 class of Fall 2003:
http://www.math.utah.edu/~treiberg/M2281hw.txt
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Third Edition
Day, Sec. TOPIC Page[ Numbers ]
W, Aug. 24 1.1 Models 8[7,12,16*,29*,35,39]
F 26 1.2 Integrating DE 16[5,10*,17,30*,37]
M 29 1.3 Slope Fields 25[(A = see below)*,16,29]
T 30 1.4 Separable Eqns. 40[3,11,19,36*,
55(refers to 54),58*],
W 31 LAB
F, Sept. 2 1.5 Linear 1st order 54[9,15,33*,39]
M 5 LABOR DAY HOLIDAY
T 6 1.6 Exact 71[5*,18,34*,63]
W 7 2.1 Population Models 86[7,13*,30]
F 9 2.2 Stability 96[9*,21,23]
M 12 2.3 Acceleratiion 106[2,11*,21*,24]
T 13 2.4-5 Euler Polygons 119[6*],129[7*]
W 14 LAB
F 16 2.6 Runge-Kutta 139[4*]
M 19 3.1-2 2nd order linear 155[5,9*,12*,25,38*,46],
167[4,10*,15,23,27*]
T 20 Review
W 21 FIRST MIDTERM EXAM
F 23 3.3 Homog., const. coef. 180[9*,10,15,24*,28,35*,40,46]
M 26 3.3 Complex roots
T 27 3.4 Vibrations 192[3*,10,13,18*,35-38]
W 28 LAB
F 30 3.5 Undetermined coef.'s 207[1,3*,5,7,9,18*,
34*,37,41,45,53*,60*]
M, Oct. 3 3.6 Resonance 218[4,10*,17,23,28*]
T 4 3.7 Circuits 228[2*,3*,8,14,19*]
W 5 4.1-2 Systems 251[2,17*,24*,26*,27],
262[8,15*,34]
F 7 FALL BREAK
M 10 4.3 Systems numerically 274[6*,10,17]
T 11 5.1 Eigenvectors 297[32*,38*],
W 12 5.2 Eigenvalue method 312[9*,19*,30*,32,36,39*]
F 14 5.3 Mechanical systems 324[3,9*,14*,16,19]
M 17 5.4 Multiple EV's 341[(B=see below) 5*,12,22*,
25,35]
T 18 Review
W 19 SECOND MIDSEMESTER EXAM
F 21 5.5 Matrix exponential 356[3,7*,15,23,27*]
M 24 Solving Systems
T 25 5.6 Nonhomogeneous sys 364[5*,16,22*,31]
W 26 LAB
F 28 6.1 Phase plane 375[11*,20,24*]
M 31 6.2 Stability 389[8*,15,27,33*,37]
T, Nov. 1 6.3 Predator / Prey 402[(C = see below)*,3*,5,8-10,
13,17,21*]
W 2 Competition
F 4 6.4 Nonlinear mech. sys. 418[4*,12]
M 7 6.5 Chaos
T 8 7.1 Laplace Transform 444[2*,4,15,25,29*,
33,35,36,39*,41]
W 9 LAB
F 11 7.2 Laplace properties 455[3*,14*,19,24,29*,33*,35]
M 14 7.3 Partial Fractions 465[3,7,10*,13,19*,30*,39*]
T 15 Review
W 16 THIRD MIDSEMESTER EXAM
F 18 7.4 Convolutions 474[3,11*,14,17,20*,
23,26,31*,36*]
M 21 7.5 Tansforming Periodic 484[5,14,25*,33]
T 22 7.6 Delta functions 495[3*,10*,15,17,21]
W 23 LAB
F 25 THANKSGIVNG HOLIDAY
M 28 9.1-2 Fourier Series 580[15*,23,27], 586[13*,17,
24a*]
T 29 9.3 Sine series 598[4,9,11*,20,22*]
W 30 9.4 Applying F. S. 606[3*,8,15,18]
F, Dec. 2 9.5 Sep. Var. 618[3,10*,14,15*,17,18*,19]
M 5 9.6 Wave Equation 630[3,6,11,13,14,15,16,17,19]
T 6 9.7 Laplace's Equation 642[5,9,11]
W 7 Review
F 16 FINAL EXAM 8:00 10:00 AM
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
A. Identify the isoclines of the given differential equation. Draw a sketch
showing several of the isoclines, each marked with short line segments
having the appropriate slope.
dy / dx = x^2 - y^2
B. The instructions should be "Find the general solution."
C. Separate variables in the system
dx / dt = ax - pxy, dy / dt = -by + qxy
to derive the general solution
a ln y + b ln x - qx - py = C
If an implicit function plotter is available, choose fixed positive values
of a, b, p, and q, then plot contour curves through selected initial
points near the critical point (b / p, a / p ). (Sketching by hand is OK!)
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