1.1 (3rd): 4, 6,12, 18;
1.2 (3rd): 5, 10, 25, 31,34; 1.2 (4th): 43 (compare solution of "linear friction" w. "quadratic friction"); Plot solutions for all problems
Handout problems: 1) Decay with source #2; 2) Problem from handout on US-population
1.3 (3rd):12,14, 20, 24;
1.4 (3rd): 14; 1.5: 13,18 (plot solutions);
1.6 (3rd): 1(write Lineraized problem and its solutions at 2 equilibria); 2+14 (phaseline + several IV solutions);30+32,
Handout problems: financing #1; mixing #4
1.6: 42 (consider cases: a>0; a<0; a=0); 1.7: 3,19;22
1.8: 8,10, 26 (plot solutions for all); 1.9: 3,10,27
Handout Problem #2 (drug delivery) from Undetermined coefficients;
Optional (extra credit): Other techniques (#1); Rocket science (Problems 1-2);
HW4: solutions
2) Logistic "sandwitch" Other techniques (#2)
Optional (Extra credit):
1) Solve (by separation) DE: dy/dx = (c*x-d)*y/((a-b*y)*x), with constant a,b,c,d
2.1: 2+3+4 (3 questions make up 1 hw problem); 9+10+11 (same); 24; 30
2.2: 10, 12, 16, 19, 21
2.3 (3rd: problems Ch 2.3-4): 7+9+11; 13+14; 16;
2.4 (3rd): 1, 4
Extra credit (optional): 1) Pendulum-spring problem in Duffing oscillator.
HW6: Solution
SIR 2.7 (4th): 4,6
2.5 (3rd) or 2.8 (4th): 4 (plot solution functions x[t],y[t]), 5.
3.1 (same 3rd 4th): 10, 16,19; 24 (solve LDS directly, sketch phase plane)
3.2 (same 3rd 4th): 7, 8 ; 13 (phase-plane, solution curves)
Extra credit (optional): 1) Problem in SIR-model; 2) 2.4 (3rd): 16
3.2: 16+17 (extra: show eigenvestors {X1,X2} of 17 are orthogonal) ; 22 ( phase portrait)
3.4: 3+9,4+10, 5, 23
3.5: 4+8; 11.
3.7: 4,5,
Problems 1,2,4 in handout Applications.
Extra: 3.7: 8
HW8 (same numbers in 3rd and 4th; use computer, when appropriate) Solutions (nb)
3.8: 6,17; 3.6: 7;17+25 (compare "matrix solutions" to "char. polynomial method"; plot them), 38;
4.1: 10,22, 41; 4.2: 8, 19 (plot solutions);
4.3: 5 (plot solutions),21(use qualitative analysis: no algebra, no technology); 4.4:6+7
Extra credit: 4.3: ,23; Heat-diffusion problems 1,2,3; Problems in Coupled oscillators; Problems 1,2 in Population
HW9: Solutions
Ch.5 (most problems require computer)
5.1: 6, 22, 26; 5.3: 1, 15, 18;
5.4: 2 (Hint: damped oscillator with f(x)=x^2-x; L = "energy function"; explain the effect of damping on equilibria and energy), 18;
1) Problem from handout Analysis of competition
2) Find which value(s) {a} make v.f. F=(y^3/3+2*x, a*y) - Hamiltonian, compute hamiltonian f-n, sketch phase-plot and equilibriua, verify equilibrium type by Jacobian
HW 10
6.1: 9-12-13 (3-problem set); 15;20; 6.2: 10,14;
6.3: 16-18 (2-set); 27, 31
6.4:3,9
Additional Laplace problems:
1. Solve 2nd order DE: y''+2*y'+5*y=cos(2*t); y(0)=0; y'(0)=0; by Laplace transform, plot solutions. Compare to undetermined coefficients.
2. Find and plot fundamental solutions of the following DEs (with zero initial data), write source solutions as convolution integrals.
1. y'+3y=f(t)
2. y''+3y=f(t)
3. y''+2*y'+5*y=f(t)
1. Review 1. Sample problems: problem set w. solutions; spring 07
2. Review 2. Samples problems: spring 02; fall 02; spring 08
3. Final review-notes. Review problems
4. Final samples: Fall01; Fall02; Spring 07
1. Test1: solution
2. Test2: solution
Final: solution
E-mail: dxg5@case.edu Phone: (216) 368-2857