New Course Proposal – Page 1/11
NEW COURSE PROPOSAL
College:
Engineering and Computer Science ]
[ Department: [ ECE ]
Note: Use this form to request a single course that can be offered independently of any other course, lab or activity.
1. Course information for Catalog Entry
Subject Abbreviation and Number: [ ECE 280 ]
Course Title: [ Applied Differential Equations in Electrical Engineering ]
Units: [ 3 ] units
Course Prerequisites: [ Math 150B ] (if any)
Course Corequisites: [
] (if any)
Recommended Preparatory Courses: [ Math 250 ] (if any)
2. Course Description for Printed Catalog: Notes: If grading is NC/CR only, please state in course description.
If a course
numbered less than 500 is available for graduate credit, please state “Available for graduate credit in the catalog description.”
[ Prerequisite: Math 150B. Recommended Corerequisite or Preparatory: Math 250. Modeling of
systems by ordinary differential equations. Determination of initial conditions using dynamic
behavior of physical systems. Solution of ordinary differential equations by various methods, such
as separation of variables, undetermined coefficients, series, and Laplace Transform. Linear algebra
and solution of systems of differential equations. Numerical methods and use of application
software such as MatLab & Mathematica in solving differential equations and systems of
differential equations. ]
3. Date of Proposed Implementation: (Semester/Year): [ Spring ] / [ 2013 ] Comments
4. Course Level
[ ]Undergraduate Only
[
]Graduate Only
[
]Graduate/Undergraduate
5. Course Abbreviation “Short title” (maximum of 17 characters and spaces)
Short Title: [ A•P•P•L• •D•E•Q• •E•L•E•C• •E•N•G ]
6. Basis of Grading:
[ ]Credit/No Credit Only
[
]Letter Grade Only
[
]CR/NC or Letter Grade
7. Number of times a course may be taken:
[
] May be taken for credit for a total of [1] times, or for a maximum of [3] units
[
] Multiple enrollments are allowed within a semester
8. C-Classification: (e.g., Lecture-discussion (C-4).)
[ 3 ] units @ [C-4] [ ]
9. Replaces Current Experimental Course?
[
] YES
[
] NO
Replaces Course Number/Suffix:[ ECE 296EMA ]
Previously offered [
] times.
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10. Proposed Course Uses: (Check all that apply)
[
]Own Program:
[
]Major
[
]Minor
[
]Masters
[
] Requirement or Elective in another Program
[
] General Elective
[
] General Education, Section [
]
[
] Meets GE Information Competence (IC) Requirement
[
] Meets GE Writing Intensive (WI) Requirement
[
] Community Service Learning (CS)
[
] Cross-listed with: (List courses) [ Math 280 ]
[
]Credential
[
]Other
11. Justification for Request: Course use in program, level, use in General Education, Credential, or other. Include
information on overlap/duplication of courses within and outside of department or program. (Attach)
12. Estimate of Impact on Resources within the Department, for other Departments and the
University. (Attach)
(See Resource List)
13. Course Outline and Syllabus (Attach) Include methods of evaluation, suggested texts, and selected bibliography.
Describe the difference in expectations of graduates and undergraduates for all 400 level courses that are offered to both.
14. Indicate which of the PROGRAM’S measurable Student Learning Outcomes are addressed in
this course. (Attach)
15. Assessment of COURSE objectives (Attach)
A. Identify each of the course objectives and describe how the student performance will be
assessed
(For numbers 14 and 15, see Course Alignment Matrix and the Course Objectives Chart)
16. If this is a General Education course, indicate how the General Education Measurable Student
Learning Outcomes (from the appropriate section) are addressed in this course. (Attach)
17. Methods of Assessment for Measurable Student Learning Outcomes (Attach)
A. Assessment tools
B. Describe the procedure dept/program will use to ensure the faculty teaching the course will be
involved in the assessment process (refer to the university’s policy on assessment.)
18. Record of Consultation: (Normally all consultation should be with a department chair or program coordinator. ) If
more space is needed attach statement and supporting memoranda.
Department Chair/ Program
Concur
Date:
Dept/College:
Coordinator
(Y/N)
[ 9/29/2011 ]
[ ECE/CECS ]
[ Dept. Vote: Ali Amini ]
[Y]
[ 10/20/2011
[ ME/CECS ]
[ Hamid Johari ]
[Y]
]
[ 10/14/2011
[ CS/CECS ]
[ Steven Stepanek ]
[Y]
]
[ 10/28/11 ]
[ MSEM/CECS ]
[ Ileana Costea ]
[Y]
[ 10/28/2011
[ CEAM/CECS ]
[ Nazaret Dermendjian ]
[Y]
]
[ 9/30/11 ]
[ Math/CSM ]
[ Werner Horn ]
[Y]
Consultation with the Oviatt Library is needed to ensure the availability of appropriate resources to
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support proposed course curriculum.
Collection Development Coordinator, Mary Woodley
Please send an email to: collection.development@csun.edu
Date
[ 10/7/11
]
19. Approvals:
Department Chair/Program Coordinator:
Date:
College (Dean or Associate Dean):
Date:
Educational Policies Committee:
Date:
Graduate Studies Committee:
Date:
Provost:
Date:
[ 10/14/2011 ]
[
]
[
]
[
]
[
]
Attachments
11. Justification for Request:
This course is designed to enhance the students’ understanding of modeling of electrical systems by
ordinary differential equations and determining the system initial conditions. Solution of ordinary
differential equations as applied to Electrical Engineering using various methods such as; separation of
variables, undetermined coefficients, series, Laplace Transform and Linear Algebra are discussed in
detail. Numerical solutions of ordinary differential equations are emphasized in this course. This includes
the extensive use of MATLAB and Mathematica. Electrical and Computer Engineering Majors will be
allowed to substitute this course for Math 280.
12. Estimate of Impact on Resources within the Department, for other Departments and the
University:
This course requires the use MATLAB and Mathematica which are already available. Hence the same
computers and application software that are used for some ECE courses such as ECE350, ECE351,
ECE450, ECE455 and ECE480 would be used for this course. System modeling and solution of system
problems is an important part of Electrical & Computer Engineering Curriculum. Majority of ECE faculty
are well capable of teaching this course.
13a. Course Outline and Syllabus:
 Writing the differential equations of engineering systems including required initial conditions.
Understanding practically where initial conditions come from and how to evaluate them.
 Becoming familiar with linear or nonlinear, constant parameter or time varying parameter,
instantaneous or dynamic, causal or noncausal, lumped parameter or distributed parameter as
applied to differential equations and systems in general.
 Modeling multiple input-multiple output engineering system by a system of differential equations.
 Solving a first order differential equation.
 Solving an n-th order linear differential equations with constant coefficients.
 Having complete familiarity with Laplace Transform and Inverse Laplace Transform.
 Applying Laplace Transform in solving ordinary differential equations.
 Solving differential equations using power series solution.
 Applying numerical and application software such as MATLAB and Mathematica, in solving
differential equations, linear or nonlinear.
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
Fundamental understanding of linear algebra and applications of linear algebra to differential
equations.
 Solving engineering problems described by a differential equation or systems of differential
equations.
 Applying numerical and application software such as MATLAB and Mathematica, in solving
systems of differential equations.
 Understanding the fundamental difference between ordinary and partial differential equations from
physical point of view. Be able to solve simple partial differential equation problems.
(SYLLABUS ATTACHED)
13b. Methods of Evaluation for Measurable Student Learning Outcomes:
Assessment will be made on the basis of two mid-term exams, one comprehensive final examination and
weekly assigned homework problems. Homework problems include analytical as well as those using
MATLAB and Mathematica. A written report must be submitted at the end of the semester showing the
proficiency of use of MATLAB and Mathematica in solving differential equations.
13c. Suggested Text:


A First Course in Differential Equations with Modeling Applications, Dennis G. Zill. Ninth
Edition, Thompson (Brooks/Cole 2009).
Advanced Engineering Mathematics with Mathematical and MATLAB(volumes 1 & 2), Reza
Malek-Madani (Addison Wesley 1998).
13d. Selected Bibliography:
 Elementary Differential Equations, Earl D. Rainville, Phillip E. Bedient, Richard E. Bedient. Eight
Edition, (Prentice Hall 1996).
 Fundamental of Differential Equations and Boundary Value, Nagle, Saff and Snider. Sixth Edition,
(Addison/Wesley 2011).
 Elementary Differential Equations, William E. Boyce, Richard C. DiPrima. Ninth Edition,
(Wiley 2009).
13e. Grade Replacement Policy:
 Grade replacement is allowed between Math 280 and ECE280.
14. Indicate which of the Program’s Measurable Student Learning Objectives are addressed in this
course.
The table below shows applicability of the objectives of this course against those of the program.
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2. Become familiar with linear or
nonlinear, constant parameter or time
varying parameter, instantaneous or
dynamic, causal or noncausal, lumped
parameter or distributed parameter as
applied to differential equations and
systems.
3. Model multiple input-multiple
output engineering system by a system
of differential equations.
4. Solve a first order differential
equation.
5. Solve an n-th order linear
differential equations with constant
coefficients.
6. Evaluate Laplace Transform and
Inverse Laplace Transform. Apply
properties of Laplace Transform.
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N. Knowledge of math including differential equations, linear algebra, complex
variables and discrete math.
M. An ability to analyze and design complex devices and systems containing
hardware and software components.
L. Knowledge of probability and statistics.
I
K. An ability to use modern engineering techniques for analysis and design.
I
J. A broad education and knowledge of contemporary issues.
I. A recognition of the need for and an ability to engage in life-long learning.
G. An ability to communicate effectively through written reports and oral
presentations.
F. An understanding of ethical and professional responsibility.
E. An ability to identify, formulate, and solve electrical engineering problems.
D. An ability to function in multidisciplinary teams.
C. An ability to design systems which include hardware and/or software components.
H. An understanding of the impact of engineering in a social context.
1. Write the differential equations of
engineering systems including required
initial conditions. Understand
practically where initial conditions
come from and how to evaluate them.
B. An ability to design and conduct scientific and engineering experiments, as well
as to analyze and interpret data.
Course Objectives
A. An ability to apply knowledge of math, science, and engineering to the analysis of
electrical and computer engineering problems.
COURSE ALIGNMENT MATRIX
Directions: Assess the how well ECE280 (course) contributes to the program’s student learning outcomes by rating each course objective
for that course with an I, P or D.
I=introduced (basic level of proficiency is expected)
P=practiced (proficient/intermediate level of proficiency is expected)
D=demonstrated (highest level/most advanced level of proficiency is expected)
P
P
P
P
I
I
I
P
P
P
P
P
P
P
I
P
I
I
I
P
P
New Course Proposal – Page 5/11
7. Apply Laplace Transform in solving
ordinary differential equations.
8. Solve differential equations using
power series solution.
9. Apply numerical and application
software such as MATLAB and
Mathematica, in solving differential
equations, linear or nonlinear.
10. Learn the fundamentals of linear
algebra and apply them to differential
equations.
11. Solve engineering problems
described by a differential equation or
systems of differential equations.
12. Apply numerical and application
software such as MATLAB and
Mathematica, in solving systems of
differential equations.
13. Understand the fundamental
difference between ordinary and partial
differential equations from physical
point of view. Solve simple partial
differential equation problems.
I
I
I
I
I
I
I
I
I
I
I
P
I
I
I
I
I
I
I
P
P
P
I
I
P
P
I
I
15. Methods of Assessment for Measuring Student Learning Outcomes
Homework assignments, examinations, and a written report submitted at the end of the semester showing
the proficiency of use of MATLAB and Mathematica in solving differential equations will be used to
evaluate and measure students learning outcomes.
ECE 280 is an undergraduate course and as such will be assessed like any other ECE undergraduate
course. Furthermore due to ABET requirements, this course will be evaluated in detail in terms of
Measuring Students Outcomes using appropriate tables, feedback and consultation with appropriate
groups such as Industrial Advisory Committee.
NC – 9/29/05
P
P
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Course Objectives
1. Write the differential equations of engineering systems
including required initial conditions. Understand
practically where initial conditions come from and how
to evaluate them.
2. Become familiar with linear or nonlinear, constant
parameter or time varying parameter, instantaneous or
dynamic, causal or noncausal, lumped parameter or
distributed parameter as applied to differential equations
and systems.
3. Model multiple input-multiple output engineering system
by a system of differential equations.
4. Solve a first order differential equation.
5. Solve an n-th order linear differential equations with
constant coefficients.
6. Evaluate Laplace Transform and Inverse Laplace
Transform. Apply properties of Laplace Transform.
7. Apply Laplace Transform in solving ordinary differential
equations.
8. Solve differential equations using power series solution.
9. Apply numerical and application software such as
MATLAB and Mathematica, in solving differential
equations, linear or nonlinear.
10. Learn the fundamentals of linear algebra and apply them
to differential equations.
11. Solve engineering problems described by a differential
equation or systems of differential equations.
12. Apply numerical and application software such as
MATLAB and Mathematica, in solving systems of
differential equations.
13. Understand the fundamental difference between ordinary
and partial differential equations from physical point of
view. Solve simple partial differential equation problems.
Assessments of Student
Performance
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLA/Mathematica.B
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
Homework and Use of
MATLAB/Mathematica.
Homework, Exams, and Use of
MATLAB/Mathematica.
17. Methods of Assessment for SLO’s
Once every three years the ECE Department generates assessment tables showing average student
achievement on each of the SLO’s. The tabulated scores are obtained mostly from embedded test
questions, lab reports and occasionally from projects. All faculty members submit assessment tables for
every course that they teach (during the data-gathering semesters). For this particular course, the faculty
members will assess student performance on student learning outcomes a, e, k and n.
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California State University, Northridge - Spring 2013
College of Engineering & Computer Science
Department of Electrical & Computer Engineering
ECE 280 – Applied Differential Equations in Electrical Engineering
Course Units: 3.00
Design Units: 00
Professor:
Ali Amini
Office:
JD 4509/JD 3523
Office Phone:
(818) 677-2190
ECE Fax:
(818) 677-7062
EMAIL:
aamini@csun.edu
Class Schedule:
MW 5:30 pm – 6:45 pm, JD1590
Office Hours:
MW 4:30 pm – 5:30 pm, JD4509
And By Appointment
I - COURSE DESCRIPTION
Modeling of systems by ordinary differential equations. Determination of initial conditions using dynamic
behavior of physical systems. Solution of ordinary differential equations by various methods, such as;
separation of variables, undetermined coefficients, series, and Laplace Transform. Linear algebra and
solution of systems of differential equations. Numerical methods and use of application software such as
MATLAB in solving differential equations and systems of differential equations.
II - TEXTBOOK (Recommended)
Recommended Text:
A First Course in Differential Equations with Modeling Applications, Dennis G. Zill.
Ninth Edition, Thompson (Brooks/Cole, 2009). ISBN-13:978-0-495-10824-5.
Advanced Engineering Mathematics with Mathematical and MATLAB(volumes 1 & 2), Reza MalekMadani, (Addison Wesley 1998).
Additional Reference:
Elementary Differential Equations, Earl D. Rainville, Phillip E. Bedient, Richard E. Bedient. Eight
Edition , (Prentice Hall 1996).
Fundamental of Differential Equations and Boundary Value, Nagle, Saff and Snider. Sixth Edition,
(Addison/Wesley 2011).
III – SOFTWARE
MATLAB & Mathematica.
Internet Resources:
http://hpme12.me.edu/matlab/hml/
IV - PREREQUISITE
Prerequisite: Math 150B – Calculus II.
Recommended Co-requisite: Math 250 – Calculus III.
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V - GRADING POLICY
Homework
15%
Exam 1
25%
Exam 2
25%
Final
35%
+ / - Grading is used in this course
VI – CLASS POLICIES AND PROCEDURES
Attendance:
Each student is required to attend every lecture. Students are responsible for arriving before class begins,
and remaining for the duration of the course meeting. If a student misses a class, it is his or her
responsibility to find out what was discussed in class, any homework assigned or exam scheduled.
Make-Up Exam And Homework:
No late homework is accepted, and no examination can be made up.
Homework:
Homework will be assigned on a regular basis and it will be due one week after it is assigned. Homework
must be turned in on 8.5"X11" paper written on one side with the necessary information such as ID#,
Course #, Homework # and date on top left hand corner of the first page.
Distance Learning students must turn in the homework on the day it is due. If a student is out of town, the
homework can be faxed to the number shown above or emailed to me via ece@csun.edu. Distance
Learning students are required to come on campus to take the exams.
MatLab will be used to enhance the understanding of Differential Equations and become familiar
with this important software package.
Examinations:
Midterm I will be administered during week 5 or 6.
Midterm II will be administered during week 10 or 11.
Final Examination: As Scheduled By The University.
All Exams are closed book, closed notes. One 3”x5” card (both sides) allowed on exams 1 & 2. Two
3”x5” cards (both sides) allowed on the final exam.
Academic Integrity:
Ideas and learning form the core of the academic community. In all centers of education, learning is
valued and honored. No learning institution can thrive if its members counterfeit their achievement and
seek to establish an unfair advantage over their fellow students. The Academic Integrity is designed to
foster a fair and impartial set of standards. All students are required to adhere to these standards. Any
dishonest act such as copying, plagiarism, lying, unauthorized collaboration, alteration of records, bribery,
and misrepresentation for the purpose of enhancing one’s academic standing results in a failing grade for
the entire course and will be reported to the College as well as the Dean of Students.
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VII - COURSE MATERIAL
Week
Material
1.0 week
Chapter 1 – Introduction To Differential Equations
1.1
Definitions & Terminology
1.2
Initial Value Problems
1.3
Differential Equations as Mathematical Models
2.0 weeks
Chapter 2 – First Order Differential Equations
2.1
Solution Curves
2.2
Separable Variables
2.3
Linear Equations
2.4
Exact Equations
2.5
Solution by Substitution
1.0 week
Chapter 3 – Modeling With First-Order Differential Equations
3.1
Linear Models
3.3
Modeling With Systems of First-Order Des
4.0 weeks
Chapter 4 – Higher-Order Differential Equations
4.1
Preliminary Theory-Linear Equations
4.2
Reduction of Order
4.3
Homogeneous Linear Equations with Constant Coefficients
4.4
Undetermined Coefficients – Superposition Approach
4.5
Undetermined Coefficients – Annihilator Approach
4.6
Variation of Parameters
4.7
Cauchy-Euler Equations
4.8
Solving Systems of Linear DEs by Elimination
1.0 week
Chapter 5 – Modeling With Higher-Order Differential Equations
5.1
Linear Models: Initial Value Problems
2.5 weeks
Chapter 7 – The Laplace Transform
7.1
Definition of Laplace Transform
7.2
Inverse Transforms and Transforms Derivatives
7.3
Operational Properties I
7.4
Operational Properties II
7.5
The Dirac Delta Function
7.6
Systems of Linear Differential Equations
2.5 weeks
Chapter 8 – Systems of Linear First-Order Differential Equations
8.1
Preliminary Theory
8.2
Homogeneous Linear Systems
8.3
Non-Homogeneous Liners Systems
8.4
Matrix Exponential
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1.0 week
Chapter 6 – Series Solutions Of Liner Equations
6.1
Solutions About Ordinary Points
6.2
Solutions About Singular Points
The Content of the Course Syllabus is Subject to Change with Appropriate Notice to the Students
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