Math251

Ordinary and partial differenial equations. Section 4.

Instructor
Andrey Gogolev
email: agogolev@math.psu.edu
office: McAllister #20
Syllabus

first midterm -- thursday, march 1, 6:30pm-7:45pm, 101 Thomas
second midterm -- thursday, march 29, 6:30pm-7:45pm, 100 Thomas

Course description can be found here click. I will be following this plan.

Homework is due Mondays. HW1;
HW2: 1.1: problems 3, 4, 12; 1.2: problems 7, 9; 1.3 problems 2, 4, 6; 2.1: 2, 4 , 7, 8, 14, 17; 2.2: problems 3, 4, 7, 25
HW3: 2.2: problems 6, 10, 14; 2.3: problems 2, 4, 7, 9 2.4: problems 1, 3, 6, 21, 24, 25
HW4: 2.5: problems 10, 11
2.6: problems 1, 3, 4, 7, 8, 9, 16; note that M(x,y)dx+N(x,y)dy is just a different notation for M(x,y)+N(x,y)y'
3.1 problems 3, 6, 8, 10, 13, 20
HW5: 3.2: 3, 8, 10, 11, 17, 18, 22, 24
3.3: 1, 5, 9
3.4: 7, 11, 14, 16, 23a, 27
HW6: due Wednesday after spring break 6.1: 21, 22, 23, 24
6.2: 1, 3, 6, 10, 15, 22
6.3: 3, 8, 10, 14
6.4: 1; 6.5: 1 (by hands)
HW6: due Friday April 13 9.1: 13, 15
10.1: 1, 2, 6, 7, 9 (need to recall "guessing technique for particular solutions!)
10.2: 13, 18 (only two but do them well, understanding Fourier dcomposition is crucial for coming stuff)
HW7: due Monday April 23 10.4: 2, 5, 7, 9, 11, 13(optional)
for the funcion in problem 17 find sine series.
10.5: 1, 2, 3, 5, 6, 7, 8 (all very important, something like that will appear on the final)

Sample previous finals can be found here http://www.math.psu.edu/tseng/class/M251samples.html

Sample exams fot the second midterm, but note that the material covered is not completely the same. We will have laplace transfrom and linear systems only: 1 2 3 answers to 3

Sample exams: 1 2 3 4

quiz1 quiz2 quiz3 quiz4 quiz5 quiz6 quiz89 quiz10 quiz11 quiz12 quiz1415 quiz16 quiz17 quiz18 quiz1920

10.6: Everything till "more general problems"
10.7: Everything is extremely important.
10.8: Again everything. The most important is to understand "Dirichlet problem in a rectangle" Suggested reading on PDE
10.2: Read everythng, but example 3. The most important is to understand examples 1 and 2.
10.3: everything
10.4: everything. Crucial to understand:"cosine\sine series" and the paragraph after example 1
10.5: Again everything. Suggested reading for APRIL 1-4
Read thru 9.1
9.2: Read evrything starting from "oscillating pendulum"
9.3 Read and understand introduction and example 1.
Suggested reading March 19- 26
Read thru 7.1. We need to learn how to solve 2 by 2 systems only. sections 7.5-7.9 treat multydimensional case and assume knowledge of linear algebra, don't read them. Here's the handout: click . It will be distributed in class on Monday.
Suggested reading on Laplace transform (till spring break)
6.1: everything is good. Most important are examples which teach you how to compute Laplace transfrom. Paragraph before example 7 is important.
6.2: Read statements of Theorem 6.2.1 and cor. 6.2.2. After that corollary everything is relevant. Need to remember entries 1,2,3,5,6,9,10,11 of the table of transforms.
6.3: Everything, this short section is well written.
6.4: May skip the paragraph after example 1.
6.5: Everything. Example is the most important. First three pages are hard, but well-written, they would give you some flavor of real math
Suggested problems from last sections
Section 3.5: 3, 6, 10
Section 3.6: 3, 6, 8, 15, 17
Section 3.8: 6, 7
Suggested reading for February 12 -19
Section 3.4: 159-161, if hard then understand and accept conclusion in last 5 lines on page 161. Examples 1-2-3 are extremely important. May omit the rest of the section. Section 3.5: Read intro, may skip example 1 and a page after that. What is important is the outcome which is briefly formulated in several lines on page 169 before example 2 (starting with "Since W(y_1....". Example 2 is good. Summary is something that everybody got to remember and understand. May skip "reduction of order".
Suggested reading for February 5 -9 Section 3.1, may omit example 4. Section 3.2: read starting from theorem 3.2.1 till the end of page 145. May skip 146, but starting from 147 everything is important, though not easy. Try to understand clearly what is written in the last paragraph of this section. Section 3.3 (not sure we'd cover it this week)
Suggested reading for January 29-February 3 Monday-Wednesday section 2.4. Most important: understand what theorem 2.4.1 says, example 1 and example 4.
Wednesday-Thursday: pages 78-83 Thursday-Friday: section 2.6, skip the theorem proof and integrating factors.
Suggested reading for January 24-26 example 2 on the page 13 and section 2.3. In this section everything but example 4 is relevant. The most important thing to read is example 1 on page 52.