MATH 231-DIFFERENTIAL EQUATIONS-FALL 2022- A. FREIRE

Syllabus

DATES (28 lectures):

First Day:  Thursday Aug. 25
Midterm I:  Tuesday Oct 4 (likely)
Fall Break: Thursday Oct 6
Midterm II: Thursday Nov. 10 (likely)
Thanksgiving: Thursday, Nov. 24
Last Day:  Tuesday, Dec. 6
Final Exam: Tuesday, Dec. 13, 1:00-3:15

COURSE LOG

8/25 Th Section 1.2 initial-value problem, E/U theorem
HW: (Sect 1.2) 18, 23-28, 29, 31

8/30  Tu Linear equations (2.3) Implicit solutions (1.2)
HW (1.2) 9 to 12 (2.3) 7--12, 17-20

9/1 Th (Zoom) Phase line (1.2) Project B--HW problems (d)(e)(f)
Problem session
Notes (scan, 5 pages)

9/6 Tu  Separable equations (2.2) exact equations (2.4)--start
HW (2.2) 7--11, 17--19 (2.4) 1--3, 9--11, 21--23

9/8  Th Exact equations: examples, integrating factors (2.4, 2.5)/ QUIZ 1
HW (2.5) 7, 9, 11 (int. factors are powers of x or of y)

9/13 Tu: special techniques: integrating factors, homog. equations, functions of linear forms
HW (2.6) 9, 11, 13, 17

9/15 Th Special techniques: Bernouilli equations, linear differentials/ QUIZ 2
HW (2.6)19, 23, 25, 27, also the following;
(-3x+y)dx+(x+y) dy=0
(2x-y) dx+(4x+y) dy=0

9/20 Tu Models involving 1st order DE: exponential and logistic growth, radioactive decay
HW (3.2) 9, 19, 21, 22, 23, 24, 25

9/22 Th  Problems on applications: mechanics with velocity-dependent forces
Review (3.4) 9, 10, 12, 13, 25
QUIZ 3

9/27 Tu Heating/cooling
Review (3.3) 1, 6, 7, 8, 9

9/29  Th  REVIEW SESSION
Midterm I: Tuesday, Oct 4 Material: sections covered from 8/25 to 9/29 (see above)

10/4 Tu: Midterm 1
Midterm1: solutions

10/6 Th FALL BREAK (no lecture)

10/11 Tu: Chapter 4, Second Order equations (start)
4.2 3, 17  4.3 21, 25, 23

10/13 Th Nonhomogeneous equations: undetermined coefficients
4.4 13, 15, 17, 27, 31
4.5 25, 31, 35

10/18 Nonhomogeneous equations: variation of parameters, convolution integrals
4.6 5, 11, 15, 23, 24

10/20 4.7 variable-coefficient equations
HW (4.7) 11, 19, 22, 24d, 37
QUIZ 4

10/25 Tu  reduction of order, energy approach to NL equations (4.8)
HW (4.7) 44, 45, 46 (4.8) 5(a), 6, 10

10/27 Th  (4.9) free oscillationsHW: 3, 7, 11
QUIZ 5

11/1 Tu  (4.10) forced oscillations HW 12, 13, 15

11/3 Th REVIEW SESSION
Review problems (updated 11/8)

11/8 Tu Review/Q&A(cont.)8.2 Power series (not on Midterm II)
(8.2) HW: 1, 5, 17, 21, 31, 34, 35

11/10 Th MIDTERM II: material from 10/11 to 11/3
Midterm 2
Midterm 2: Solutions

11/15 Tu (8.3) Power series solutions to linear DE
(8.3) HW: 15, 17, 25, 27, 32

11/17 Th (8.4) Equations with analytic coefficients
QUIZ 6
(8.4) HW 1, 3, 6, 7, 9, 14, 21, 24

11/22 Tu Laplace transforms
(HW) 7.2 15, 17, 29
(HW) 7.3 7, 9, 11, 13, 33, 35

11/24 Th Thanksgiving

11/29 Tu Laplace transforms

12/1  Th  Laplace transforms
QUIZ 7 (HW from 11/15, 11/17)

12/6 Tu Laplace transforms (last day)