Math
274 Differential Equations (Spring 2012)
| Instructor |
Mark
Pernarowski |
| Textbook |
Differential
Equations (8th ed.) |
|
Nagle, Saff, Snider |
| Office
Hours |
Schedule
(Wil 2-236) |
| Phone |
994-5356 |
| Classroom |
ROBH
301 |
|
MTRF
11am |
|
 |
The course grades will be available on-line through MyInfo after noon
on May 7
I have posted the grades on my door by student number.
I am in my office between 9-11am on Wednesday if you want your final
exam back
Otherwise try again Thursday between 1-2pm.
Final
Exam: Monday, April 30 at
10-11:15am (1 hour 15 min) in REID
103
Content:
summarized at bottom of
website along with
practice problems
You
may
have ONE two sided sheet of notes. No electronic devices.
People
who have three exams on Monday or have another exam at
exactly
the same time will have their exam times rescheduled by me.
There
are no other exceptions.
| |
|
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. All exams including
the Final will be given in class:
Wil 1-144
|
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
it 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.
|
Suggested
Homework and Syllabus:
Subject to change
| 1.1 |
1,3,6,7,10
|
Dependent/independent
variables, linear ODE |
| 1.2 |
1a,2a,4,6,9,11,21,23,27,29
|
Solutions,
Existence, Initial Value Problem |
| 1.3 |
not
covered
|
Direction
Fields |
| 1.4 |
not
covered |
Euler's
Method |
| 2.1 |
none
|
Motion
of a Falling Body
|
| 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
|
1rst
Order Linear |
| 2.4 |
1,2,
5 (solve as well),11,12,13,22,25,26
|
1rst
Order Exact |
| 2.5 |
not
covered |
1rst
Order Special Integrating Factors |
| 2.6 |
5,7,9,11
(implicit),15,23,25
|
1rst
Order Homogeneous and Bernoulli only |
| 3.1 |
none
|
Mathematical
Modelling |
| 3.2 |
1,3
|
Mixing
models (only) |
| 3.3 |
not
covered
|
Heating
and Cooling Problems |
| 3.4 |
1,5,24
|
Newtonian
Mechanics |
| 3.5 |
1,2
not covered
|
Electrical
Circuits |
| 3.6 |
not
covered |
Improved
Euler Methods |
| 3.7 |
not
covered |
Higher
Order Numerical Methods |
|
Midterm 1 |
Content Summary Below |
|
|
Review Problems |
| 4.1 |
none
|
Introductory
2nd Order Models |
| 4.2 |
1,5,9,13,19,27,31,37(r=1
root), 39 (r=2), 43
|
Homogeneous
IVP, existence, Real Roots Case |
| 4.3 |
1,3,5,9,11,13,19(r=1),21,25,29b
(r=2),29c
|
Homogenous,
Complex Roots Case |
| 4.4 |
9,11,13,15,17,23
(ugly),25,33
|
Nonhomogeneous:
Undetermined Coeff. |
| 4.5 |
3,7,17,19,23,25,33,35
|
Nonhomogeneous:
General solutions |
| 4.6 |
1,3,5,7,11,13,17
|
Variation
of Parameters |
| 4.7 |
9,11,13,15,17,19,
Reduction of Order: 45,47
|
Cauchy-Euler
equations, Reduction of Order |
| 4.8 |
not
covered |
Qualitative
theory |
| 4.9 |
1,7
|
Mechanical
Vibrations |
| 4.10 |
Not
on exam |
Mechanical
Vibrations: Forced |
|
Midterm 2 |
Chapter 4 on
HW material
assigned |
|
|
Outline and some Review
questions |
| 5 |
Time
permitting at end of course |
Phase
Plane, Numerical |
| 6 |
not
covered
|
General
Theory of Linear Equations |
|
Laplace
Transform Table |
May
be used on quizzes and
final exam |
| 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
|
Linear
Systems - Repeated eigenvalues. |
|
Final |
Chapter
7 and 9 |
|
Monday April 30,
10-11:50am, REID 103 |
Review
questions: Laplace Transforms
and Systems |
Previous
Exams
and Quizzes: Here
Exam,
Quiz and Holiday Schedule:
| Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| Jan
9 |
10 |
11 |
12 |
13 |
| |
|
Lectures
Begin |
|
|
| 16 |
17 |
18 |
19 |
20 |
| MLK
Holiday |
|
|
|
Quiz 1
|
| 23 |
24 |
25 |
26 |
27 |
|
|
|
|
|
| 30 |
31 |
Feb
1 |
2 |
3 |
|
|
|
|
|
Quiz 2 |
| 6 |
7 |
8 |
9 |
10 |
| |
|
|
|
Midterm 1 |
| 13 |
14 |
15 |
16 |
17 |
|
|
|
|
|
| 20 |
21 |
22 |
23 |
24 |
|
Pres Holiday |
|
|
|
Quiz 3 |
| 27 |
28 |
29 |
March
1 |
2 |
| |
|
|
|
|
| 5 |
6 |
7 |
8 |
9 |
|
|
|
Quiz
4
|
|
|
12 |
13 |
14 |
15 |
16 |
|
Spring
|
|
Break |
|
| 19 |
20 |
21 |
22 |
23 |
| |
|
|
|
Midterm
2 |
| 26 |
27 |
28 |
29 |
30 |
| |
|
|
|
|
| April
2 |
3 |
4 |
5 |
6 |
| |
|
|
Quiz
5 |
University Day |
| 9 |
10 |
11 |
12 |
13 |
| |
|
|
|
|
| 16 |
17 |
18 |
19 |
20 |
| |
|
|
|
Quiz
6 |
| 23 |
24 |
25 |
26 |
27 |
|
|
|
|
Last
Class |
|
30 |
May
1 |
2
|
3 |
4 |
Final 10-11:50
Reid 103 |
|
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|
|
Review and Handouts:
Midterm 1 Review:
Sample
Problems
- Section
1.1 ODE definitions and
theory
- Section
1.2 IVP explicit/implicit
solutions, existence uniqueness
- Section
2.2 Separable Equations
- Section
2.3 Linear Equations
- Section
2.4 Exact Equations
- Section
2.6 Homogeneous Equations,
Bernoulli Equations
- Section
3.2 Mixing Problems (no
population problems)
- Section
3.4 Newtonian Mechanics -
falling bodies, friction, rockets
Midterm 2 Review:
- (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
Final
Review:
- Practice
Problems: Laplace Transforms
and Systems
- Laplace:
Definition, using to calculate
F(s)
- Laplace:
Taking transforms using tables
and properties
- Laplace:
Inversion via partial fractions
- Laplace:
Solving Initial Value Problems
- Laplace:
Convolutions, convolution theorem
- Systems:
Matrix inverse (2x2) and
calculus, i.e. (AX)'=AX'+A'X
- Systems:
Converting scalar equations to
systems
- Systems:
Independence, Wronskian,
Fundamental Matrix X(t)
- Systems:
General Solution for
homogeneous/nonhomogeneous systems
- Systems:
Solving Initial Value Problems
using X(t)
- Systems:
Constant A (2x2): real distinct
eigenvalues
- Systems:
Constant A (2x2): real repeated
eigenvalue
- Systems:
Constant A (2x2): complex
eigenvalue
- Systems:
Variation of Parameters
Laplace Transform
Table:
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