Final Prep
18.03 R05 Spring 2009
The following problems are suggested extra work that will help you be ready for the final. It is a good idea for everyone to go through them, but especially for people who haven't performed that well on the hour exams or that feel shaky about any parts of the material. If you have trouble with a specific topic, let me know and we can meet and discuss it. The due dates are for the people who want to make sure they go over the whole material before the final. There will be no credit given for solving these exercises!
UNIT I: First order ODE
Due Thursday 5/7 (but I recommend you try to finish it by Tuesday 5/5)
I prepared a handout about first order ODE that might help with the material for this unit. And here are the problems.
From the textbook (EP)
section 1.1: #32-26, 45, 46
section 1.2: 3 problems out of #1-10; another 2 out of #11-18; 20, 27, 29
section 1.3: 3 out of #1-10; 3 out of #11-20; 26
section 1.4: 5 out of #1-18; 5 out of #19-28; 29, 30, 33-35, 37, 40, 43, 54, 67
section 1.5: 8 out of #1-25; 26-28, 36, 38, 39
section 1.6: 5 out of #1-30; 5 out of #43-54; 15, 59, 60
section 1.7: #9, 12, 13, 16, 20
section 6.1: 3 out of #1-10
section 6.2: 1 out of #1-10
section 7.1: 5 out of #1-12
From the notes
1A-4, 5
1B-3, 9, 12 (10 of the 26)
1C-1, 2, 3
1D-1, 2
1E-1
2E-1, 2, 4, 7, 9, 10, 14, 15, 18
UNIT II: Second order linear ODE
Due Tuesday 5/12 (but I recommend you try to finish it by Saturday 5/9)
I tried to put together the most essential notions from this unit in this file.
From the textbook (EP)
section 2.1: 3 out of #1-16; 17, 20-26, 43-50
section 2.3: #7, 18, 20, 21-26, 38, 43(b,c)
section 2.4: #1-4, 8, 13, 14
section 2.5: 5 out of #1-20; 29, 3 out of #31-40; 44-46
section 2.6: #1-4, 7-10, 15-20
section 2.7: #11, 13, 15, 18, 20-22
From the notes
2A-2, 3
2B-1, 2, 3, 4
2C-1, 8
2F-1, 2, 3, 4, 6
From the exams and practice exams on the 18.03 website
UNIT III: Fourier series, delta, Laplace transform
Due Thursday 5/14 (but I recommend you try to finish it by Tuesday 5/12)
Please use the exam 3 review handout for this section.
From the textbook (EP)
section 4.1: #5, 7-10, 5 out of #11-22; all #23-32
section 4.2: 5 problems out of #1-15; 16, 17-24
section 4.3: #1-10, 15 -17, 20, 21, 5 out of #27-38
section 4.4: #1-6, 9, 14, 17, 19, 22, 29, 31, 36-38
section 4.5: #1-10
section 4.6: #1-8
section 8.1: #1-10, 15-17, 20-23, 25, 26
section 8.2: #2, 4, 11, 13
section 8.3: #1, 4, 5, 10, 11, 13-15, 19
section 8.4: #2, 4, 6, 7, 9, 11, 15
From the notes
2H-1, 3
3A-3, 6, 10
3B-1
3C-1, 2, 4, 5
3D-1, 2, 4
7A-1, 2
7B-1, 2
7C-1, 2, 3
UNIT IV: First order systems
Due Friday 5/15
A recap of linear systems. Nonlinear systems coming later.
From the textbook (EP)
section 5.1: 3 out of #1-10; 3 out of # 11-20; 21, 22
section 5.2: #1-6, 9-12, 39, 46
section 5.3: #1, 3, 5 out of #11-20
section 5.4: 5 out of #1-16 (at least 2 IVPs); 3 out of # 17-25; 26 -32, 38-41
section 5.5: #2, 4, 5, 8, 12, 13, 17
section 5.6: #2, 7-11, 32
section 5.7: 3 out of #1-8; 3 out of #9-20; 21-24, 3 out of #25-30; 35-40
section 5.8: 5 out of #17-34
section 7.1: #
section 7.2: #
section 7.3: #
section 7.4: #
section 7.5: #
From the notes
4A-3, 5, 6
4B-all of them
4C-1, 2, 3, 5, 6, 7
4D-1, 2, 3
4G-1, 2, 3
4H-1, 2, 3, 6, 7
4I-1, 2a
5A-
5B-1, 2, 3, 4
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