Math 231 - Alexiades - Spring 2022
Assignments (for practice)   sections/pages refer to F: Finan, T: Trench free books

--------------- week 1 --------------
1. T 25 Jan:  Trench §1.2(p.14):  1, 2a,b,c,e,f, 4a,c,h, 5a,d, 7, 8
Trench §1.3:  1
2. R Jan 27:   F: 1.10, 1.11, 1.12, 1.15, 1.18, 1.24 ;
F: 5.3, 5.4, 5.10, 5.12, 5.18   (separable)
-------------- week 2 --------------
3. T Feb 1:   F: 2.9, 2.13 (recognize linear ODEs)
F: 3.2, 3.8, 3.12, 3.21, 3.23 (linear):
4. R Feb 3 :   F: 7.1, 7.5, 7.9 (Bernoulli)
-------------- week 3 --------------
5. T Feb 8:   T §2.4(p.65): 16, 17, 23, 24 (homogeneous-RHS type)
6. R Feb 10 Quiz1
F: 6.2, 6.3, 6.6, 6.7, 6.15, 6.17 (exact)
T §2.5: 4, 8, 12, 29c, 30b, 33, 40 (exact)
-------------- week 4 --------------
7. T Feb 15:   linear operator, Superposition Principle (see review for Exam I)
e.g. L[x]=ax, L[x]=Ax , L[y]=y' , L[y]=ay'+by , L[y]=ay''+by'+cy , L[y]=∫ab y(x)dx
8. R Feb 17 :   linearly independent functions, basis, dimension, Fundamental set for L[y]=0 (see review for Exam I), learn definitions
(parts of) F: chap.11, T: §5.1
-------------- week 5 --------------
9. T Feb 22 :   general solution of linear homogeneous L[y]=0   F: chap.11, T: §5.1 F: 11.1, 11.2, 11.8, 11.16, 11.19;
10. R Feb 24 :   Exam I
-------------- week 6 --------------
11. T Mar 1 :   direction field, Euler scheme   F chap.8: Example 8.1, 8.3; T: §3.1 (look at some examples)
[Trench p.95 says: "Section 3.1 deals with Euler's method, which is really too crude to be of much use"
That's FALSE! it is very much used in practice and may beat fancier methods if the cost of f-evaluation is very high!
In laser ablation modeling, we compared 17 ODE solvers and Forward Euler was the winner!!! ]
12. R Mar 3 :   homogeneous with constant coeffs:
F: Examples 12.1,2,4,5,6; Problems 12.3, 12.6, 12.9, 12.10
F: Examples 13.1. Problems 13.3, 13.8.
F: Examples 14.1, 14.2. Problems 14.2, 14.3, 14.5, 14.7
-------------- week 7 --------------
13. T Mar 8 non-homogeneous L[y]=f: F: Problems: 16.2, 16.3, 16.4 (yp is given)
Undetermined coefficients: T: §5.3: Examples 1, 2 ; Problems 2, 4.   §5.4: Problems 1, 8, 12, 24.
T: §5.5: Examples 1, 2, 3, 5, 6(and remark at the end); Problems 1, 3, 5, 24.
14. R Mar 10 :  Quiz2
Variation of parameters do all these problems!
F: Problems 17.1, 17.2, 17.4
T: §5.7: Example 3 ; Problems 1, 4, 7, 28
-------------- week 8 --------------
15. T Mar 22 Cauchy-Euler equ  F: 17.8;   T §5.6: 3, 31
16. R Mar 24 Reduction of order   T: §5.6: Examples 1, 3 ; Problems 4, 13, 22, 31
nonlinear with missing x or y: problems
Oscillators: T §6.1, 6.2 look at some examples
------------ week 9 ------------
17. T Mar 29 :   Quiz3
Laplace Transform : short LT table (LT tables:   F: p.147-148 ; T: p.399, 463-464 LTransforms.pdf )
F: §18: Example 18.1, 18.5, 18.7 ; Problem 18.9
T: §8.1: Examples 4, 6, 10 ; Problems 2(i)
18. R Mar 31   Inverse Laplace Transform : T: §8.2: Ex 2, 4, 5; Problems 1(h), 2(i), 7(e);   F: Ex 19.2, 19.4; Problems 19.5, 19.7
------------ week 10 ------------
19. T Apr 5 :   Inverse Laplace Transform, solving IVPs :
F: Example 20.2, 20.4, 20.5 ; Problems 20.2, 20.4, 20.9, 20.13
T: §8.3: Example 2, 3 ; Problems 3, 15, 18, 20, 22
20. R Apr 7   Examples, no new problems
------------ week 11 ------------
21. T Apr 12 :   Exam II
------------ week 12 ------------
22. T Apr 19   unit step, jump functions   T: §8.4: Example 2, 3, 7 ; Problems 10, 11, 19.   T: §8.5: Example 2 ; Problems 1, 10
Convolution :   F: Example 22.5, 22.6   T: §8.6: Example 2, 3, 6 ; Problems 3(b), 3(h), 7
23. R Apr 21:   Series review (see your Calculus book...)
------------ week 13 ------------
24. T Apr 26 :   Power Series Review :   T: §7.1: Example 1, 3 ; Problems 1(a),(d),(e)
25. R Apr 28 :   Power Series Solution of ODEs :
T: §7.2: Example 1, 4 ; Problems 1, 4.   T: §7.3: Example 2, 3 ; Problems 5, 10
------------ week 14 ------------
26. T May 3 :   Power Series Solution of ODEs : examples, no new material.
27. R May 5 :   example, idea of Frobenius method
! The End !
I hope you learned a lot !
...and will show it on the Final...
PLEASE fill out the TNVoice evaluation form ASAP
Quizes: Quiz 1:  R Feb 10     Quiz 2:   R Mar 10 (on linearity theory and linear with constant coeffs)
Quiz 3: T Mar.29 (linearity theory; linear non-homog: y=yh+yp, find yh and yp; Cauch-Euler; nonlinear with x or y missing)
Review sheets:   review for Quiz1,     review for Exam I review for Exam II   review for Final
Exams:    I:  R Feb 24       II:  T Apr 12       Final:  Tue May 17, 3:30-5:30
Cvs             Calendar: Spring 2022
January                February                  March
Su Mo Tu We Th Fr Sa    Su Mo Tu We Th Fr Sa    Su Mo Tu We Th Fr Sa
1  2  3  4  5           1  2  3  4  5
6  7  8  9 10 11 12     6  7  8  9 10 11 12
13 14 15 16 17 18 19    13  spring break  19
20 21 22 23 24 25 26    20 21 22 23 24 25 26
25 26 27 28 29    27 28                   27 28 29 30 31
30 31

April                    May
Su Mo Tu We Th Fr Sa    Su Mo Tu We Th Fr Sa
1  2     1  2  3  4  5  6  7
3  4  5  6  7  8  9     8  9 10
10 11 12 13 14 15 16          17
17 18 19 20 21 22 23
24 25 26 27 28 29 30

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