AMATH 351: Introduction to
Differential Equations and Applications
SLN 10210, MWF
10:30-11:20, Benson Hall 117
(Prerequisites: MATH 126 or MATH 136)
Instructor: |
Zhang, Yun (Claire) W 4:00 – 5:00 pm Location: Guggenheim 406 |
TA: |
Lai, Su-Miao Office hours: T 12:00 – 1:00
pm Th 2:00 – 3:00 pm Location: Guggenheim 406 |
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Course
Description
Introductory
survey of ordinary differential equations. Linear and nonlinear equations.
Textbook and Notes
Boyce and
DiPrima, Elementary Differential Equations and Boundary Value Problems 8th
Edition.
ISBN-10: 0471433381 ISBN-13: 978-0471433385
Chapter 1-7 of the book deal with ODE while
the left deals with PDE, we will cover Chapter 1-7 only.
Notes written by Professor Bernard Deconinck. We refer to
this notes mainly except series solutions and
I
can’t emphasize more that please READ
READ READ the materials before you come to class. Having a preview of the
materials prepares you a big picture of what we are going to talk each time,
which helps you follow me fluently and saves a lot of time doing homework.
Syllabus
(1)
First-Order Equations
Separable equations
Integrating factor
Existence and Uniqueness
Exact Equation
Introduction to
modeling
Substitution of variables
Direction
fields.
(2) Second-Order Equations
Constant coefficient equations
Linear independence and Wronskian
Complex roots and repeated roots
Undetermined coefficient
Variation of Parameters
Mechanical Vibrations -- Harmonic oscillators, Sinusoidal forcing, undamped
forcing and resonance.
(3) Linear
Systems
Review of linear
algebra
Homogeneous linear systems with constant
coefficients
Solutions
involving real and complex eigenvalues
Phase plane
analysis and the trace-determinant plane
Nonhomogeneous systems.
Decoupled systems and writing second
order equations as systems.
(4) Series Solutions
Review of power series
Series solutions around Ordinary
Point
Series solutions around a Regular
Singular Point
Euler’s Equation and Bessel’s equation.
(6)
Basic functions
Step functions
Impulse functions
Convolution integral.
Learning Objectives and Instructor Expectations
AMATH 351 aims at
familiarizing the students with different types of differential equations,
introducing basic skills of solving some of the differential equations that can
be solved exactly and letting the students get a sense of how odes are applied
in some physical and biological situations. Most of our
efforts will be focused on ordinary differential equations. Since there are
tons of readings and exercises in the book, only attending lectures and
finishing the homework is far from enough for you to establish a solid
foundation. I am expecting you to spend at least 10 hours out of class on it.
You are always welcome to ask any questions.
Schedule and Homework
Follow links in
the table below to obtain a copy of the homework in PostScript (.ps)
or 
Adobe Acrobat (.pdf) format. You may also obtain here solutions
to some of the homework and exam problems. An item shown below in plain text is
not yet available. For additional information regarding viewing and printing
the homework and solution sets, click
here.
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Week |
Homework and Exams |
Homework Due Date |
Homework Problem Sets |
Homework Solutions |
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1 |
First day of class |
Wednesday, Sep 30 |
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Homework#1 |
Friday, Oct 9 |
1.1, 1.3, 2.2 |
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2 |
Homework#2 |
Friday, Oct 16 |
2.1, 2.3, 2.4,
2.5, 2.6, 2.8 |
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3 |
Homework#3 |
Friday, Oct 23 |
3.1, 3.3, 3.5,
3.4, 3.2 |
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4 |
Homework#4 |
Friday, Oct 30 |
3.6, 3.7, 3.8, 3.9 |
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5 |
No
Homework |
Review for midterm exam. |
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6 |
Midterm Exam |
Monday, Nov 2 |
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Homework#5 |
Friday, Nov 13 |
7.1, 7.2, 7.3, 7.4, 7.5 |
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7 |
Veterans Day (No Class) |
Wednesday, Nov 11 |
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Homework#6 |
Friday, Nov 20 |
Key |
7.6,
7.7, 7.8, 7.9 |
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8 |
Thanksgiving (No Class) |
Thursday, Nov 26 Friday, Nov 27 |
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Homework#7 |
Monday, Nov 30 |
Download and Sec 7.9 Problem 1, 7 |
Key |
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9 |
Homework#8 |
Friday, Dec 4 |
Download |
Key |
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10 |
Homework#9 |
Friday, Dec 11 |
Download |
Key |
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11 |
No
Homework |
Review
for final exam. |
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12 |
Final
Exam |
Monday, Dec 14 (tentatively) 8:30 – 10:20 AM BNS 117 |
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Grading
There will be one mid-term, one
final exam and weekly homework assignments except midterm and final weeks. Your
final grades will be determined as follows:
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Homework |
40% |
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Mid-term (50 minutes, full
class time) |
20% |
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Final (110 minutes) |
40% |
Exams will test your basic
understanding of the material covered in class as well as solving problems
based on the class materials.
In the exams, calculator IS allowed. You can bring one 8.5 x 11
(letter-sized, two-sided) hand-written note sheet and you will have to turn in
your note sheet with your exam.
Homework is normally due every
Friday starting from the 2nd week. You need to show your work in
full detail. Partial credits will be deducted if you just give me a number of
equations without any mathematical reasoning or word explanation. And please
also arrange your homework as clear and neat as possible. You may also get
points off if I can’t understand you handwriting. Late homework is not accepted and there are no make-ups! Lowest
homework grade will be dropped when calculating final grade.
Other
Resources
Here is a good tool on the
website: Phase Plane Drawing
Tool by John Polking and others.
There’s also a good Matlab file pplane7, try it out in your Matlab
command window.
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Wed Sep 9 09:06:34 PDT 2009 |