Math 284 Honors Differential Equations (Spring 2010)
| Instructor |
Mark Pernarowski |
| Textbook |
Differential Equations (7th ed.) |
|
Nagle, Saff, Snider |
| Office Hours |
Schedule (Wil 2-236) |
| Phone |
994-5356 |
| Classroom |
Wil 1-153 |
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I have the final exams. If you really need them back soon email me.
Otherwise I will keep them for you to pick up in the Fall
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Grading: The course % is determined by:
Midterm 1 M1 100
Midterm 2 M2 100
Final F 100
Quizzes Q 100
_______________________________
400
% = (M1+M2+F+HW)/4
The final is not comprehensive.
Six quizzes each worth 20 points
will be given. Your best 5 quiz
scores determine Q above.
Exam and quizz dates are indicated
on the schedule below. Their content
will be announced in class.
All exams and quizzes are closed
book and no electronic devices
are permitted. With the exception
of the Final, all exams will be
given in class. Final Location - TBA.
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Syllabus: Material covered in text is from:
Chapter 1 Introductory Definitions
Chapter 2 First Order ODE Methods
Chapter 3 First Order Models
Chapter 4 Second Order Linear ODE Methods
Chapter 6 Higher Order Differential Equations
Chapter 7 Laplace Transforms
Chapter 9 Linear Systems
Homework: Suggested homework is listed below.
Although the homework is not graded
but is representative of the kinds of
questions which will be on quizzes
and exams.
Some additional problem sets and/or
handouts will be handed out in class
and/or posted on this site below.
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Suggested Homework and Syllabus: (Continuously Updated)
| 1.1 |
1,3,6,7,10
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Dependent/independent variables, linear ODE |
| 1.2 |
1a,2a,4,6,9,11,21,23,27,29
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Solutions, Existence, Initial Value Problem |
| 1.3 |
not covered
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Direction Fields |
| 1.4 |
not covered |
Euler's Method |
| 2.1 |
none
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Motion of a Falling Body
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| 2.2 |
1,2,3,5,7,8,9,11,17,18,19,23
|
1rst Order Separable |
| 2.3 |
2,3,4,7,9,10,13,15,17,18,19,22
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1rst Order Linear |
| 2.4 |
1,2, 5 (solve as well),11,12,13,22,25,26
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1rst Order Exact |
| 2.5 |
not covered
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1rst Order Special Integrating Factors |
| 2.6 |
5,7,9,11 (implicit),15,23,25
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1rst Order Homogeneous and Bernoulli only |
| 3.1 |
none
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Mathematical Modelling |
| 3.2 |
1,3
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Mixing models (only) |
| 3.3 |
not covered
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Heating and Cooling Problems |
| 3.4 |
1,5,24
|
Newtonian Mechanics |
| 3.5 |
1,2
|
Electrical Circuits |
| 3.6 |
not covered
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Improved Euler Methods |
| 3.7 |
not covered |
Higher Order Numerical Methods |
|
Midterm 1 |
Sections 1.1-3.4 on material HW was assigned. |
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See below for more info and review questions |
| 4.1 |
none
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Introductory 2nd Order Models |
| 4.2 |
1,5,9,13,19,27,31,37(r=1 root), 39 (r=2), 43
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Homogeneous IVP, existence, Real Roots Case |
| 4.3 |
1,3,5,9,11,13,19(r=1),21,25,29b (r=2),29c
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Homogenous, Complex Roots Case |
| 4.4 |
9,11,13,15,17,23 (ugly),25,33
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Nonhomogeneous: Undetermined Coeff. |
| 4.5 |
3,7,17,19,23,25,33,35
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Nonhomogeneous: General solutions |
| 4.6 |
1,3,5,7,11,13,17
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Variation of Parameters |
| 4.7 |
9,11,13,15,17,19, Reduction of Order: 45,47
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Cauchy-Euler equations, Reduction of Order |
| 4.8 |
not covered
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Qualitative theory |
| 4.9 |
1,7
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Mechanical Vibrations |
| 4.10 |
lecture only - no HW |
Mechanical Vibrations: Forced |
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Midterm 2 |
Chapter 4 on HW material assigned |
|
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See below for more info and review questions |
| 5 |
Time permitting at end of course |
Phase Plane, Numerical |
| 6 |
not covered
|
General Theory of Linear Equations |
| 7.2 |
3,5,9,11,13,15,17
|
Laplace Transform Definition |
| 7.3 |
1,3,5,7,9,13,25,31 |
Laplace Transform Properties |
| 7.4 |
1,3,7,9,21,23,25 (last 3 are nastier algebra) |
Laplace Transform Inverse |
| 7.5 |
1,3,7(nasty),11 (set y(t)=w(t-2)),15,17,19,35 |
Laplace Transform Initial Value Problems |
| 7.6 |
not covered |
Laplace Transform Discontinuous Functions |
| 7.7 |
1,2,3,5,7,9,13 |
Laplace Transform Convolution Theorem |
| 7.8 |
not covered |
Laplace Transform - delta function |
| 7.9 |
not covered |
Laplace Transform - Systems of Equations |
| 8 |
not covered
|
Series Approximations and Solutions |
| 9.1 |
1,3,5,8,11 |
Differential Equations as Systems |
| 9.2 |
none |
Gaussian Elimination
|
| 9.3 |
1,3,5,7b,7c,8,9,17,21,27,31,33,35,37,39 |
Matrix algebra and Calculus |
| 9.4 |
1,3,5,9,13,15,19, 28!! |
Linear Systems - Normal Form |
| 9.5 |
1,3,5,7,11,19,21,31!! |
Linear Systems - Constant Coefficient (Real Case) |
| 9.6 |
1, 3 (given lamba=1),5,13a |
Linear Systems - Constant Coefficient (Complex Case) |
| 9.7 |
11,13,21a |
Linear Systems - Variation of Parameters |
| 9.8 |
Class notes and review problems
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Linear Systems - Repeated eigenvalues. |
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Final
|
Chapter 7 and 9 |
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See below for more info and review questions |
Exam, Quiz and Holiday Schedule:
| Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| Jan 11 |
12 |
13 |
14 |
15 |
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Lectures Begin
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| 18 |
19 |
20 |
21 |
22 |
| MLK Holiday |
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Quiz 1
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| 25 |
26 |
27 |
28 |
29 |
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| Feb 1 |
2 |
3 |
4 |
5 |
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Quiz 2 |
| 8 |
9 |
10 |
11 |
12 |
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Midterm 1 |
| 15 |
16 |
17 |
18 |
19 |
Pres Holiday
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| 22 |
23 |
24 |
25 |
26 |
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Quiz 3 |
| March 1 |
2 |
3 |
4 |
5 |
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| 8 |
9 |
10 |
11 |
12 |
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Quiz 4
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| 15 |
16 |
17 |
18 |
19 |
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Spring
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Break |
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| 22 |
23 |
24 |
25 |
26 |
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Midterm 2 |
| 29 |
30 |
31 |
April 1 |
2 |
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Univ. Day |
| 5 |
6 |
7 |
8 |
9 |
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Quiz 5 |
| 12 |
13 |
14 |
15 |
16 |
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| 19 |
20 |
21 |
22 |
23 |
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Quiz 6 |
| 26 |
27 |
28 |
29 |
30 |
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Classes End |
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| May 3 |
4 |
5 |
6 |
7 |
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Final |
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6:00-7:50pm |
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FINAL EXAM: Thursday, May 6 from 6-7:50pm (Wil 1-153)
Review and Handouts:
- Midterm 1:
- (Practice Problems)
- Definitions: explicit, implicit solns; order, linear, dependent and independent variables
- Existence and uniqueness
- Initial Value Problems versus general solutions
- First Order Methods: Separable, Linear, Exact, Homogenous, Bernoulli
- Mixing Problems: equations for equal and unequal flow rates.
- Falling body with friction: equations of motion for velocity.
- Rocket problem: equations of motion.
- Midterm 2 (4.2-4.7, 4.9)
- (Practice Problems)
- Constant Coefficient 2nd Order (all cases)
- Initial Value Problems, Wronskian for independence
- Cauchy Euler 2nd Order (all cases)
- Undetermined Coefficients Method for yp(t)
- Variation of Parameter Method for yp(t)
- Reduction of order method for homogeneous solutions
- Mechanical Vibrations: Amplitude Phase Form for unforced case
- Laplace Transform Table that you will be allowed to use on quizzes and tests
- Repeated Eigenvalues Notes ( in 9.8 of text)
- Final (7.2-7.5,7.7,9.1,9.3-9.8)
- Thursday, May 6 (6:00-7:50pm) Wil 1-153
- Practice Problems - On Laplace Transform and On Systems of ODEs
- Laplace - Definition
- Laplace - Taking transforms using tables and properties
- Laplace - Inversion via Partial Fraction, Completing square
- Laplace - Solving initial value problems
- Laplace - Convolution Theorem: computing, using to invert
- Systems - Matrix operations and inverse of a 2 by 2 matrix
- Systems - Converting scalar equations to systems
- Systems - Independence, Wronskian, Fundamental matrix
- Systems - Real Distinct eigenvalues (2 by 2 case)
- Systems - Complex eigenvalues (2 by 2 case)
- Systems - Real Repeated eigenvalues (2 by 2 case)
- Systems - Using Fundamental matrix to solve IVP
- Systems - Variation of Parameters
- Systems -
Solutions for simple 3 by 3 cases (non-complex).
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