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Sergey Orshanskiy |
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Email: |
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Office: |
418 McAllister Building |
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Office hours: |
MW 12:10 – 1:00 |
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MATH 251 Ordinary & Partial
Differential equations |
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Semester: |
Spring 2006 |
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Section: |
003 |
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Meeting: |
MWF 10:10A – 11:00A
123 E.E.East R 10:10A – 11:00A
111 Tyson |
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Textbook: |
Elementary
Differential Equations and Boundary Value Problems by W.E.Boyce –
R.C.DiPrima, 8th Edition, 2004, John Wiley & Sons. ISBN
0-471-43338-1 |
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Course syllabus: |
TBA |
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Yuxi Zheng yzheng@math.psu.edu 229, McAllister
building WRF 10:30 – 11:00 |
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Course Announcements |
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Final exam is over Average grade: B/C
(95.7 = 64% of 150 points) Median grade: B
(102 = 68% of 150 points) (median over all
sections: C+ (89 = 59% of 150 points)) Suggested
interpretation for the grades: A (111-150), B
(95-110), C(75-94), D(50-74), F(1-49) You may find out
how well you are doing by using this table:
Former
exams: here Review
session: May, 2,
Tuesday. 4:15 – 5:30 p.m. 373, Willard bldg. Final
exam: May, 3,
Wednesday. 12:20 – 2:10 p.m. 100, Thomas bldg. Second midterm exam
is over (except for those
who signed up for the makeup exam) Average grade: B
(81.7) Suggested
interpretation for the grades: A (91-100), B
(81-90), C(71-80), D(61-70), F(1-60) You may find out
how well you are doing by using this table:
Sample exam: Exam, Answers,
(some) Solutions Note: answers updated,
answer for 2b corrected! (It is not u(1)=1) Midterm
exam #2: Mar, 29,
Wednesday. 6:30 – 7:45 p.m. 121, Sparks bldg. Review
session: Mar, 27,
Monday. 4:15 – 5:30 p.m. 218, Willard bldg. First midterm exam
is over (except for those
who signed up for the makeup exam) Average grade: B
(83) Suggested
interpretation for the grades: A (90-100), B+
(85-89), B (80-84), B- (75-79), C+ (70-74), D (60-69),
F (1-59) You may find out
how well you are doing by using this table:
Review session: Feb. 20. 4:15 –
5:30 p.m. 203, Willard bldg. You can visit 104D,
McAllister bldg to sign up for the
makeup exams. If nothing changes,
the makeup dates are: Exam #1 – Feb, 28,
exam #2 - Apr, 4. Midterm exams: Exam #1 – Feb, 22.
6:30 - 7:45 p.m. 108, Forum bldg. Exam #2 – Mar, 29.
6:30 – 7:45 p.m. 121, Sparks bldg. January,16 – Martin
Luther King day, no classes |
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Homework |
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Homework #1 is due
Jan, 20 (Friday) Homework #1: 1.1.4,
1.1.6 – 1.1.11, 1.1.13, 1.1.21 – 1.1.23, 1.1.26, 1.1.28, 1.1.31,
1.2.1(a,b,c), 1.2.6 Averages: 1.86,
1.29, 1.88, 1.92, 1.86, 1.88, 1.51, 1.41, 1.84, 1.18, 1.10, 1.20, 0.92, 0.90,
0.71, 0.90, 0.96, 0.98, 0.63 = 24.96 of 38 (66%), 51 people Homework #2 is due
Jan 26 (Thursday) Homework #2: 1.2: 7, 9, 10 1.3: 8, 9, 15, 16,
17 2.2: 3, 4, 7, 8,
10, 15, 23 2.3: 2, 4, 7, 10,
13 Averages: 94%, 91%,
84%, 99%, 94%, %98, 93%, 65%, 98%, 98%, 98%, 90%, 85%, 93%, 90%, 93%, 78%,
41% = 39.15/45 (87%), 49 people Homework #3 is due
Feb 2 (Thursday) Homework #3: 1.3: 2, 3, 5, 6 2.2: 30 2.3: 9, 12, 19 2.5: 1, 2, 3, 4 Averages: 99%,
100%, 97%, 98%, 96%, 84%, 70%, 55%, 52%, 18%, 85%, 90%, 90%, 66%, 71%, 80%,
64% = 76.86/100 (77%), 51 people Homework #4 is due
Feb 9 (Thursday) Homework #4: 2.4: 13, 15, 24, 25 2.5: 7, 8 3.1: 5, 6, 12, 15,
17 3.2: 4, 5, 21, 23,
24 Averages: 49%, 44%,
28%, 76%, 47%, 38%, 74%, 81%, 99%, 90%, 86%, 67%, 98%, 100%, 98%, 90%, 85%,
70% = 58.71/80 (73%), 46 people Homework #5 was due
Feb 16 (Thursday) Homework #5: 2.5: 22 3.1: 21, 22 3.2: 27 3.3: 2, 4, 6, 17,
18, 22 3.4: 5, 6, 10, 18 Averages: 50%, 80%,
80%, 82%, 84%, 78%, 79%, 92%, 95%, 74%, 72%, 40%, 88%, 83%, 85%, 71% = 77.45/100
(77%), 45 people Homework #6 was due
Feb 23 (Thursday) Homework #6: 1.3: 22, 24 2.1: 10c, 20 2.3: 8 2.4: 4, 6, 8 2.6: 1, 2, 3, 4 Averages: 97%, 97%,
85%, 84%, 88%, 92%, 89%, 93%, 60%, 77%, 92%, 96%, 94%, 93% = 49.61/56 (89%), 49 people Homework #7 was due
Mar 2 (Thursday) Homework #7: 3.6: 2, 4, 6, 16 4.1: 4 – 13 Averages: 86%, 84%,
85%, 76%, 93%, 64%, 79%, 79%, 76%, 60%, 52%, 82%, 74%, 79% = 65.87/88 (75%), 46 people Homework #8 was due
Mar 16 (Thursday) Homework #8: 4.1: 27 4.2: 1, 2, 11, 14,
18 4.3: 4, 5 5.1: 1, 4 6.1: 2, 4, 6 Average: 42.43/50 =
85%, 45 people Homework #9 was due
Mar 23 (Thursday) Homework #9: 5.1: 10, 11, 12, 13 5.2: 1, 2, 3 6.1: 5abc, 7, 16,
21 6.2: 2, 6, 12, 13,
17 6.3: 6, 7, 8 Averages: 82%, 80%,
87%, 77%, 69%, 64%, 54%, 71%, 63%, 25%, 79%, 38%, 82%, 86%, 38%, 78%, 71%,
55%, 59%, 64%, 77% = 57.73/84 (69%),
51 people Homework #10 was
due Mar 30 (Thursday) (or due Friday
-10%) Homework #10: 6.3: 4, 12, 13 6.4: 1, 6, 11
(without graphs and explanations) 6.5: 1, 4 3.8: 1, 2, 24 3.9: 5 Average: 43.98/48 =
92%, 43 people Homework #11 was
due Apr 6 (Thursday) 7.1: 1, 4, 6, 22a 7.2: 22, 23 7.5: 1, 2, 4 7.6: 1, 12, 13 Extra credit: 7.9.2 Also in all
problems (where applicable) classify the origin as a critial point
(source/sink – node/spiral point, saddle point, center) Averages: 51.03/66
= 77%, 39 people Homework #12 was
due Apr 13 (Thursday) 9.1: 2, 3, 5, 6 9.2: 2, 3, 5a, 6a 9.5: 2 Extra credit:
9.5.12 Averages: 88%, 88%,
70%, 79%, 49%, 63%, 86%, 88%, 46% = 29.98/44 (68%), 41 people Homework #13 is due
Apr 20 (Thursday) 10.1: 1, 5, 6, 10 10.2: 6, 8, 13, 15 10.3: 4 10.4: 1, 7, 17, 18 Extra credit:
10.4.33 Note: each extra
credit problem amounts to +2 to the final score for the homeworks after the
best 10 homeworks added up Averages: 42.97/64
= 67%, 42 people Homework #14 is due
Apr 28 (Friday) 10.5: 1, 3, 5, 7,
22 10.6: 1, 2, 3, 9ad 10.7: 1a, 2a Extra credit:
10.8.1ab Averages: N/A Good news: No more homeworks! |
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Quizzes |
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Quiz #1 – Jan, 12
(Thursday) Averages: 1.75,
2.00, 1.40, 1.40, 1.74 = 8.28 of 10 (83%),
53 people Quiz #2 – Jan, 20
(Friday) Averages: 1.39,
1.08, 1.22, 1.73, 1.65 = 7.08 of 10 (71%),
49 people Quiz #3 – Jan, 27
(Friday) Averages: 1.96 of
4, 1.44, 1.65, 0.90, 1.33=7.27 of 12 (61%),
48 people Quiz #4 took place
– Feb, 3 (Friday) Averages: 2.12 of
4, 2.38 of 4, 1.30, 0.94 = 6.74 of 12 (56%), 50 people Quiz #5 took place
– Feb, 10 (Friday) Averages: 2.83 of
4, 2.29 of 4, 1.19 of 4 = 6.31 of 12 (53%),
48 people Quiz #6 took place
– Feb, 17 (Friday) Averages: 1.07,
0.53, 1.40, 0.76 = 3.76 of 8 (47%),
45 people Quiz #7 took place
– Feb, 22 (Wednesday) It was 30 minutes
long instead of 12-20 Averages: 2.44 of
4, 3.22 of 4, 3.69 of 4 = 9.36 of 12 (78%), 45 people Quiz #8 took place
– Mar, 3 (Friday) Averages: 2.67 of
4, 2.74 of 4, 2.49 of 4 = 7.90 of 4 (66%), 39 people Quiz #9 took place
– Mar, 17 (Friday) Averages: 3.33 of 4,
1.57 of 4, 2.74 of 4 = 7.62 of 12 (64%), 46 people Quiz #10 took place
– Mar, 24 (Friday) Averages: 1.54 of
4, 1.30 of 4, 3.14 of 4 = 5.98 of 12 (50%), 43 people Quiz #11 took place
– Mar, 29 (Wednesday) Averages: 3.66 of
5, 3.52 of 5 = 7.12 of 10 (72%), 44 people Quiz #12 took place
– Apr, 7 (Friday) Averages: 1.07 of
4, 1.70 of 4 = 2.77 of 8 (35%), 43 people Quiz #13 took place
– Apr, 24 (Monday) Averages: 3.31 of
8, 0.167 of 2 = 3.48 of 10 (35%), 42 people Quiz #14 took place
– Apr, 28 (Friday) Averages: 1.39 of
4, 1.61 of 4 = 3.00 of 8 (38%), 38 people No more quizzes! |
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Topics (being) covered Paragraph: 10.7 (as of Apr, 28) |
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Main questions covered What is a differential equation? Examples of differential equations. What is a solution of an equation? Check whether some function solves (is a
solution of) some particular equation. What is a direction field? (for an equation of the type dy/dt = f(t,y)) Sketch a direction field for some equation. Sketch the solutions on a direction field. The equilibrium solution(s) of an equation. Find the equilibrium solutions for a
particular equation. (if there’re any) Solve an equation of the kind dy/dt = ay-b Solve an initial value problem of the kind
dy/dt = ay-b, y(x0) = y0 Correct applications of the chain rule Recognize first order differential equations Recognize first order linear differential
equations Recognize and solve some separable equations
and the corresponding initial value problems Determine the order of an equation Recognize whether the equation is linear or
not Recognize autonomous equations For autonomous equations: draw graph f(y)
versus y, find critical points, describe them in terms of stability, draw the
phase line, sketch several solutions in the ty-plane Convert a wordy problem statement into a
differential equation Set up an initial value problem Find simple limits, derivatives and integrals Second order linear differential equations Same with constant coefficients;
characteristic equation Fundamental set of solutions The Wronskian determinant Initial value problem (two initial
conditions) Linear (in)dependence, relation to the
Wronskian Solve a differential equation and an initial
value problem – when the equation is with constant coefficients (three cases –
pagrapaphs 3.1, 3.4, 3.5) Review of complex arithmetic Basic trigonometric formulae Reduction of order Classification of PDE’s Some more on linear ODE’s (Existence &
Uniqueness theorem etc) Theorems for linear and nonlinear first order
differential equations Exact equations Nonhomogeneous linear second order equation Method of undetermined coefficients General solution + particular solution Series, convergence, absolute convergence Solution of simple ODEs using series Laplace transform, definition, transforms of
various functions Initial value problems (nonhomogeneous linear
ODEs with constant coefficients) Heaviside step function, Dirac delta
function, their transform Initial value problems with functions with
discontinuities Modelling with 2nd order equations: mass on a
string, electric circuit Free systems without damping, systems with
damping, critical damping |
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Examination and grading policy |
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There will be regular homework assignments throughout
the course. There will be regular quizzes throughout the
course. Only 10 best homeworks and 10 best quizzes
will be counted. Grading: two midterm exams – 100 points each. Final exam – 150 points. Homeworks – 100 points. Quizzes – 100 points. Total: 550 points. 90% correspond to an A, 60% correspond to a
D. No cellphones, computers etc. on quizzes
& exams. No communication with other students during
quizzes & exams. No makeup quizzes. |