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Intro Differential Equations M 274-001, Spring 2016

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Intro Differential Equations M 274-001, Spring 2016
Intro Differential Equations
M 274-001, Spring 2016
TR 12:10-1:40, W 11:40-12:40; LA 300
Instructor
Dr. Saroj Aryal
Office: LA 839
Office Hours: TWR: 3:30-5:00
Phone: 406 657 2924
Email: [email protected]
Webpage: http://www.msubillings.edu/mathfaculty/aryal/
Course
Materials
[1] Textbook: Elementary Differential Equations and Boundary Value Problems by Boyce &
DiPrima, 10th Ed., ISBN-13: 9781118157381.
[2] Online Homework System: WebAssign. To sign up in webassign.com, you will need an access
code which you will have to buy in the website itself ($45.95 for homework only and $90.70
for homework and eBook). When you sign up for the course in WebAssign, make sure to use
the correct class key: msubillings 1140 2711.
Course
Description
4 credits. Prerequisite: M 172. This course presents methods for the solution of first and higherorder differential equations including variation of parameters, undetermined coefficients, the
Laplace transform, and power series expansions, and introduces phase plane methods.
Learning
Objectives
Differential equations are useful both in scientific fields and in applied studies from engineering
to the life sciences. This course mostly deals with ordinary differential equations and integral
transforms with an emphasis on construction of mathematical models arising in physical science
and other areas. The main objectives are
[3] to solve ordinary differential equations,
[4] to use integral transforms as techniques to solve differential equations,
[5] to use a computer software packages such as Mathematica and Maple to enhance your
understanding of this subject's relationship to many of the basic concepts of applications you
will meet in current and future courses,
[6] to be able to read and understand mathematics, think critically, and express mathematical
concepts precisely in writing,
[7] to apply the knowledge gained in this course to other situations and disciplines, and
[8] to be prepared to take a wide variety of other upper-division math courses.
Grading
Exam 1
Exam 2
Online (WebAssign) Homework
Written Homework
Class Participation
20%
40%
20%
15%
5%
Scale:
A
A90
Exams
B+
87
B
83
B80
C+
77
C
73
C70
D+
67
D
63
D60
F
50
There is one mid-term and one comprehensive final exam. The midterm exam is held in the
regular meeting time and classroom. The final exam is held at the end of the term and will be
comprehensive. It will be split into two parts: take-home and in-class. You will be allowed a
couple of days to work on the take-home part. In-class part will be administered in the class
during the final exam week. No calculators, note-cards or any form of aid is allowed during the
exams. However, all the necessary formulas will be provided. I will announce more details about
each exam as we get close to it.
If there is an extreme circumstance that prevents you from taking an exam during its designated
time, then you will need to contact me as soon as possible. Depending on the nature of the
situation, I may ask for a documentation from a proper authority, such as a note from a physician
in the case of illness, or from the office of Vice Chancellor for Student Affairs in case of absence
for special events. Please see Montana State University Billings 2013-2015 General Bulletin for
more information. In all absences, the student is responsible for all requirements of the course.
Online
Homework
WebAssign homework problems focus on the understanding, interpretations and manipulations
of the concepts discussed in classroom and textbook. The problem sets closely correspond to the
material covered in the class and will be assigned with deadlines throughout the semester. The
website will provide you immediate feedback as you submit your answers and you can attempt
a number of times before you get it correct. Some problems may take longer than others and
hence I encourage you to start working on the problems well in advance of the due dates. Three
lowest scores will be dropped.
Written
Homework
Problem Sets. Written homework sets will be assigned from time to time. These problems will
be selected from the set of online homework problems.
CAS Projects/Labs. Relevant projects/labs requiring the use of one of the three computer
software packages, Mathematica, Matlab and Maple, will be assigned to enhance your
understanding of this subject's relationship to many of the basic concepts of applications you
will meet in current and future courses. Mathematica and Matlab packages are widely available
on campus at any university node on the MSUBILLINGS domain.
The homework sets and their solutions will be posted online in the course website and/or handed
out in the class. When completing a written homework, show all work, but do not submit your
scratch paper. Be neat and write up carefully with problems in order. Simplify. Staple carefully
in the upper left corner. Any late submission is accepted only if justified and documented, and
only if it is before I have already returned the graded assignments to the rest of the class.
Attendance
Attendance is the main component of class participation. You are expected to attend every class,
listen to lectures, take notes, ask and answer questions, and participate in classroom discussions.
You are expected to avoid any behaviors that would be disruptive in class. I reserve the right to
ask you to leave or to put away any devices that are not helpful should I deem it necessary.
Persistence in such behavior may get you dropped from the course. Please see the document
entitled Code of Student Conduct produced by the MSUB for more information.
Getting Help You are always welcome to contact me whenever you have any question. However, before seek
any help you should have made a several attempts to solve your problem.
If you live nearby MSU-Billings, the Academic Support Center, located in the Student Union,
offers free tutoring in many areas of mathematics, statistics, languages, sciences and more. See
http://www.msubillings.edu/asc/ for more information.
Academic
Integrity
Montana State University Billings is built upon a strong foundation of integrity, respect and trust.
All members of the university community have a responsibility to be honest and the right to
expect honesty from others. Any form of academic dishonesty is unacceptable to our community
and will not be tolerated. As college students you should be very familiar with the requirements
for academic integrity. Any student found to have engaged in academic dishonesty of any form
will meet with disciplinary action, including, but not limited to, a failing grade in the course. For
further information, consult the MSUB Student Policies & Procedures Handbook available online
at the university home page.
Disability
Statement
If you have a physical, learning, or psychological disability and require accommodations, please
let me know as soon as possible. You have the responsibility to identify yourself, request
appropriate accommodations and reasonable modifications. You are encouraged to contact
Disability Support Services in College of Education Room 135, (406) 657-2283 (Phone), (406)
545-2518 (Video Phone).
M 274-001 Spring 2016 Syllabus
Tentative
Schedule
Week
Chapter/Section
Jan 18
Sep 9 Classes Begin
1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
2.1 Linear Equations; Method of Integrating Factors
2.2 Separable Equations
2.3 Modeling with First Order Equations
2.4 Differences Between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
2.6 Exact Equations and Integrating Factor
2.7 Numerical Approximations: Euler’s Method
2.8 The Existence and Uniqueness Theorem
2.9 First Order Difference Equations
3.1 Homogenous Equations with Constant Coefficients
3.2 Solutions of Linear Homogenous Equations; the Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots; Reduction of Order
3.5 Non-homogenous Equations; Method of Undetermined Coefficients
3.6 Variation of Parameters
Review for Midterm Exam
Mar 3 Midterm Exam covering 1.1 – 3.6
Spring Break: No Classes
4.1 General Theory of nth Order Differential Equations
4.2 Homogenous Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problem
6.3 Step Functions
Mar 24-25 Mini Spring Break: No classes
6.4 Differential Equations with Discontinuous Forcing Functions
6.5 Impulse Functions
6.6 The Convolution Integral
7.1 Introduction
7.2 Review of Matrices
7.3 Systems of Linear Algebraic Equations
7.4 Basic Theory of System of First Order Linear Equations
7.5 Homogenous Linear Systems with Constant Coefficients
7.6 Complex Eigenvalues
7.7 Fundamental Matrices
7.8 Repeated Eigenvalues
7.9 Non-homogenous Linear Systems
Apr 28 Last day of classes
Jan 25
Feb 1
Feb 8
Feb 15
Feb 22
Feb 29
Mar 7
Mar 14
Mar 21
Mar 28
Apr 4
Apr 11
Apr 18
Apr 25
May 2
WeAssign Due
Jan 25
Jan 25
Jan 25
Feb 1
Feb 1
Feb 1
Feb 8
Feb 8
Feb 8
Feb 15
Feb 15
Feb 15
Feb 22
Feb 22
Feb 22
Feb 29
Feb 29
Feb 29
Mar 21
Mar 21
Mar 21
Mar 21
Mar 28
Mar 28
Mar 28
Apr 4
Apr 4
Apr 4
Apr 11
Apr 11
Apr 18
Apr 18
Apr 25
Apr 25
Apr 25
May 2
May 2
May 3 10:30-12:00 Final Exam
The policies in this syllabus are subject to change. Substantive changes shall be communicated in writing.
M 274-001 Spring 2016 Syllabus
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