4. Course Level [ ]Undergraduate Only [ ]Graduate Only [ ]Graduate/Undergraduate

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1 New Course Proposal Page 1/11 NEW COURSE PROPOSAL College: [ Department: [ ECE ] Engineering and Computer Science ] 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 ] [C-4] [ ] 9. Replaces Current Experimental Course? [ ] YES [ ] NO Replaces Course Number/Suffix:[ ECE 296EMA ] Previously offered [ ] times.

2 New Course Proposal Page 2/ Proposed Course Uses: (Check all that apply) [ ]Own Program: [ ]Major [ ]Minor [ ]Masters [ ]Credential [ ]Other [ ] 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 ] 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. Date: Dept/College: Department Chair/ Program Coordinator Concur (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

3 New Course Proposal Page 2/11 support proposed course curriculum. Collection Development Coordinator, Mary Woodley Date Please send an to: [ 10/7/11 ] 19. Approvals: Department Chair/Program Coordinator: Date: [ 10/14/2011 ] College (Dean or Associate Dean): Date: [ ] Educational Policies Committee: Date: [ ] Graduate Studies Committee: Date: [ ] Provost: Date: [ ] 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 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.

4 New Course Proposal Page 3/11 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 ECE 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.

5 New Course Proposal Page 4/11 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) Course Objectives A. An ability to apply knowledge of math, science, and engineering to the analysis of electrical and computer engineering problems. B. An ability to design and conduct scientific and engineering experiments, as well as to analyze and interpret data. C. An ability to design systems which include hardware and/or software components. D. An ability to function in multidisciplinary teams. E. An ability to identify, formulate, and solve electrical engineering problems. F. An understanding of ethical and professional responsibility. G. An ability to communicate effectively through written reports and oral presentations. H. An understanding of the impact of engineering in a social context. I. A recognition of the need for and an ability to engage in life-long learning. J. A broad education and knowledge of contemporary issues. K. An ability to use modern engineering techniques for analysis and design. L. Knowledge of probability and statistics. M. An ability to analyze and design complex devices and systems containing hardware and software components. N. Knowledge of math including differential equations, linear algebra, complex variables and discrete math. 1. Write the differential equations of engineering systems including required initial conditions. Understand practically where initial conditions come from and how to evaluate them. P P I I P 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. P I P I I I I P P P P P P P P I I P

6 7. Apply Laplace Transform in solving ordinary differential equations. New Course Proposal Page 5/11 I I I P 8. Solve differential equations using power series solution. I I P 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. I I I I I I I I P I P P P 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 P I I I P 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.

7 New Course Proposal Page 6/11 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. Assessments of Student Performance 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. MATLA/Mathematica.B 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 Homework and Use of 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. Homework and Use of 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.

8 New Course Proposal Page 7/11 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) ECE Fax: (818) aamini@csun.edu Class Schedule: Office Hours: MW 5:30 pm 6:45 pm, JD1590 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: Advanced Engineering Mathematics with Mathematical and MATLAB(volumes 1 & 2), Reza Malek- Madani, (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: IV - PREREQUISITE Prerequisite: Math 150B Calculus II. Recommended Co-requisite: Math 250 Calculus III.

9 New Course Proposal Page 8/11 V - GRADING POLICY Homework 15% + / - Grading is used in this course Exam 1 25% Exam 2 25% Final 35% 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 ed 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.

10 New Course Proposal Page 9/11 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

11 New Course Proposal Page 10/ 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