SYSEN 510: Engineering Systems Analysis

Sample Course Syllabus - Students enrolled in SYSEN 510 should access the course syllabus via ANGEL.

Course Description

This 3-credit course provides students with the mathematical foundation for the System Engineering Program. It will address the fundamentals of mathematical tools that are part of the System Engineering Program. The topics covered are both linear and nonlinear differential equations as well as vector and matrix algebra. Students will learn to recognize the types of differential equations and the proper method to use and to solve them. Vector algebra deals with the basics of vector spaces and matrix algebra will cover matrix manipulations.

Specific coverage will include:

  • First order linear and nonlinear differential equations
  • Second and higher order linear differential equations
  • Use of Laplace transforms to solve differential equations
  • Linear algebraic equations and their solution
  • Fundamentals of linear vector spaces
  • Fundamentals of matrix algebra
  • Eigenvalue and Eigenvector problems

Students entering this class are assumed to have had undergraduate calculus (at least 3 classes) and differential equations. Some students may have been out of school for a number of years, and the course is geared to help those individuals reacquire their math skills and to acquire new skills.

Expected Learning Outcomes

Learners who successfully complete this course will be able to:

  • Describe, using real-world examples, the role of differential equations in engineering
  • Recognize the various types of differential equations, and execute the appropriate method to arrive at a solution for each type
  • Determine the analytical solution for each class of differential equations
  • Describe, using real-world examples, the role of linear algebra in engineering
  • Carry through the process of using of linear algebra to perform matrix manipulation

Required Text(s) and Materials

Michael D. Greenberg, Applied Engineering Analysis 2nd Edition, Prentice Hall 1998.
ISBN: 0133214311

The textbook may be purchased through the Penn State University Bookstore, or at any bookstore such as Barnes & Noble or Amazon.

This course is intended to teach students specific forms of mathematics. For this reason, students are not to use software to solve homework or examination problems. You are to show all work. Answers without showing work will not be given any credit.

Instructor & Contact Information

Dr. Maurice J. Smith, Professor of Electrical Engineering

Prior to joining Penn State, Dr. Smith served as a Senior Research Associate with the Big & Bigger Co., Inc. Experimental Station in Anchorage, Alaska. Over a career of 32 years, Dr. Smith was responsible for the development of novel instruments, inspection system, adaptive controllers, and application of expert systems. He holds 5 patents for work in these areas. Most recently, Dr. Smith’s work involved the application of advanced control concepts to chemical problems. He led the New Technology Team to screen and apply new control technology to Big & Bigger’s manufacturing problems. Dr. Smith is recognized for his work in the application of multivariate statistical methods to the problems of monitoring complex systems. Besides his activities with Big & Bigger, Dr. Smith has been an Adjunct Professor of Electrical Engineering at the University of Anchorage for more than 35 years. He was also an Adjunct with Penn State for nearly 20 years prior to joining the faculty full-time.

Dr. Smith received his Bachelor of Electrical Engineering degree from the University of Fairbanks in 1964. He received his MS Electrical Engineering from the University of Arizona in 1965 and his PhD from the University of Virginia in 1969. He is a Registered Professional Engineer in the State of Alaska.

Dr. Smith has been very active in the affairs of the Institute of Electrical and Electronic Engineers for over 30 years. He has served on numerous boards and committees. He has organized and chaired a number of sessions of national meetings. Dr. Smith won the IEEE Control System Society Technology Award for his work on multivariate statistics. Dr. Smith serves as an Associate Technical Editor of the IEEE Control Systems Magazine. He has served as an Associate Technical Editor of the IEEE Transactions on Automatic Control. He is a member of the IEEE Control System Society subcommittee on Process Control. Dr. Smith serves as an Electrical Engineering Program Evaluator for the Accreditation Board for Engineering and Technology (ABET) for approximately, and he has published approximately 50 peer-reviewed articles, and parts of 5 books.


All course-related email should go through ANGEL’s course mail function. Using ANGEL to contact me (your instructor) ensures that I will read you message and respond to you in a timely manner.

Contact through email should be limited to extreme circumstances. If you must use external e-mail to contact me, messages may be sent to Please indicate in the subject line that this is a course related question.

Under normal circumstances, I will respond to ANGEL-based course mail or email within 24 hours, Monday-Friday. If I am unable to do so for some reason, I will notify the entire class. Also, if for some reason, you do not receive a response from me within 24 hours, please try again.

Telephone & Fax

I would prefer to handle any course-related question via ANGEL's mail messaging system. If we cannot resolve an issue, you or I may request that we have a phone conversation. Please arrange for a time convenient for both of us through ANGEL mail message. Remember that I am on the East Coast of the United States.

If it is necessary to contact me using the telephone, my office number is (610) XXX-XXXX, and my fax number is (610) XXX -XXXX.

Technical support

World Campus helpdesk, (800) XXX-XXXX, option 4 or (814) XXX-XXXX - Available by phone on weekdays from 8:00 a.m. until Midnight (EST) and on weekends from 10:00 a.m. until 7:00 p.m. (EST).

In-person office hours

I am available for in-person visits on an appointment-only basis. Please contact me to set up an appointment.

Virtual office hours

If necessary, I will establish a synchronous online meeting via Penn State University's Adobe Connect system with individuals, small groups, or the entire class. Given that scheduling synchronous online meetings requires a great deal of effort given the locations and time zones of the students involved, we will use this method only when necessary.

Course Policies

All course material is available to you on ANGEL. I will be posting to the course bulletin board information to remind you what is available and what you should be working on. Material is provided on a lesson-by-lesson basis, and is presented to you as Web pages, Microsoft Word documents (.doc), or Portable Document Format (PDF). Material that you submit for course will be placed in the appropriate drop box on ANGEL, and should be submitted as PDF files (In certain cases I will tell you whether a Microsoft Word document is an appropriate submission format). Work may be handwritten as long as it is legible, scanned to a PDF file, and uploaded to a dropbox. I will not have the ability to read any other file formats, and I appreciate your cooperation with these details of the course.

Class Participation

There will be discussion boards for students to discuss among themselves different aspects of the course, and I will participate in the discussions when it is appropriate. I encourage people to work together on homework assignments. Use the discussion board to post your questions and to read the responses from your classmates. Exams are on an individual basis. Any questions on exams should be directed to me. I will add information to the exams if there many students are experiencing particular problems.

Policy on late/missing assignments

It is important that students maintain the proper pace in this course. For that reason, homework and other assignments are expected to be submitted on time. Homework will be accepted up to one week late with a 50% penalty. Work submitted after one week will not be accepted. Exception may be made for extraordinary circumstances, but these are on an individual basis and must be approved by me in advance of the due date for the homework. Examples of circumstances include illness and family emergencies.

Specifications for writing and submitting assignments

Assignments are accepted in their assigned ANGEL drop-box without penalty if they are received by 5 PM Eastern Time on the due date. No assignments are accepted after 5 PM Eastern Time on its stated due date. No assignments are accepted after 5 PM of the final day of the course.

Netiquette: Internet Etiquette Guidelines

I'm sure that the students in our class will have a range of skill and ability levels related to online learning and Internet usage. Without belaboring the concept of "Netiquette", or etiquette for using the Internet as it pertains to our online learning environment, let me just offer a few basic reminders:

  • It is generally bad form to type your messages IN ALL CAPITAL LETTERS. In addition to proper capitalization (first words of sentences, proper nouns, names, etc.), a majority of online students have reported that complete sentences and punctuation make online text communication easier to read.
  • It is much better to not post inflammatory or accusational remarks than it is to "get it off of your chest". Profanity and personal attacks will have no part of this course. If you discover such remarks, please notify me immediately, and I will personally address the source of those remarks.

Examination policy

There will be two take-home exams. You are free to spend as much time as you wish on completing the exams and to use any material other than software to solve the problems. Examinations are to be taken without collaboration of other students or other individuals. You will have at least two weeks to complete the exams, and each exam is due at 5 PM Eastern Time on the date specified. Your examination responses must be submitted in the specified file format, either PDF or DOC format, and must be placed in the appropriate drop box on ANGEL. Again, students are free write their responses by hand and then scan their papers into a PDF file. Late exams will not be accepted unless there are mitigating circumstances and I have given permission prior to the due date of the exam. When the exam is first made accessible, there will be problems on material that has already been covered and on material that has not yet been covered. I do this so that students can get a head start on the exam. All material on the exam will be covered in time for the students to complete the exam on-time. The last exam will be due on the last official scheduled day of class at 5pm.

Assessment / Grading

Homework: Homework assignments will be given weekly. Due dates will be specified in the course calendar, but are typically due one week later. Homework will constitute 20% of your final grade. Doing the homework promptly and carefully is necessary for learning the material. A reasonable amount of collaboration with fellow students is allowed and encouraged on homework. However, each student must turn in his or her own written work which reflects his or her own understanding of the material. An example of how your homework should generally appear when submitted it is available here [would be linked]. You are not expected to type your homework—write it out by hand, scan it to a PDF file, and upload your PDF file to the assignment's drop box. The filename for your uploaded PDF file should contain your surname (family name) and an indicator of the assignment (for example: surname-homework-lessons091011.pdf).

Exams: Two take-home tests will be given. You will have as a minimum 2 weekends of time to complete the exam. You are expected to work alone on this exam, and are free to use whatever material that you have your disposal. Late exams will not be accepted unless there are mitigating circumstances. Each exam is worth 40% of your grade. You final grade will be determined by following table:

Letter Grade Ranges
92A- 89
87B+  85
84B  80
79B-  75
74C+  70
69C 65
64C-  60
59D  50

Course Schedule & Due Dates

Eastern Standard Time (or EDST in the Spring/Summer) is the timezone by which all times will be specified. The Penn State ANGEL server is set to EST, and all of the lesson availability times and submission deadlines are established according to EST.

Course Schedule
Week/Dates Unit/Lesson Title Unit/Lesson Objectives Assignments Due

Week 1

Monday, September 1


Sunday, September 7

(Sep.1 – Sep.7)

Introduction to Differential Equations

Separable and Exact Differential Equations

Representation of derivatives

Solving linear first order homogeneous differential equations

Solving first order nonhomogeneous differential equations

Solve differential equations using Separation of Variables method

Solve using exact differential equation


Chapters 1.1-1.2, 2.1, 2.2-2.2.3, 2.4, and 2.5


Page 9: Problems 1-a, 1d, 4, 5a, 5e, and 5h

Page 32-33: Problems 9 and 11

Page 60: Problem 6

Page 61: Problem 12

Page 69: Problems 1c, 1f, 1i

Page 70: Problems 5c, 5h

Assignment is due 5PM EST on September 8, 2008.

Week 2

Sep.8 – Sep.14

Linear Differential Equations of Second Order and Higher

Linear dependence or independence

Homogeneous linear ordinary differential equation with constant coefficients

Understanding the total solution to linear ordinary differential equations

Solution to linear ordinary differential equation with constant coefficients


Chapters 3.1, 3.2, 3.3, 3.4., 3.4.2-3.4.5


Page 83: Problems 2b, 2f, 2h, 3g, 3h, 6a, and 6c

Page 89: Problems 1c, 1f, 1i, 2b, and 2e

Page 90: Problem 7

Pages 108-109: Problems 2b, 2n, 2o, 6b, 6c, 8b, and 8f

Page 131: Problems 1c and 1g

Assignment is due 5PM on September 15, 2008.

Week 3
Sep.15 – Sep.21

Non-Homogeneous Differential Equations with Constant Coefficients

Laplace Transforms

Method of undetermined coefficients
System of differential equations


Chapters 3.7 – 3.7.2, 3.9, 5.1-5.3


Page 148: Problems 1a, 1f, 1l, 2a, 2f, and 2q

Page 170: Problems 5a, 5e, 5j, and 8

Page 254: Problems 3, 5, and 9

Page 260: Problems 1b, 1c, 1d (Use partial fraction only), 3a, 3c, and 3f

Homework due 5:00 PM on September 22, 2008

Exam 1 will be available on September 15 and is due 5:00 PM on September 29, 2008

Week 4
Sep.22 – Sep.28

Laplace Transforms and Differential Equations

Linear Algebraic Equations

Partial Fraction Expansion

Application of Laplace transforms to differential equations

Special functions and applications

Basics of the solutions to algebraic equations

Gauss elimination and Gauss-Jordan elimination to solve


Chapters 5.4-5.6, 8.1-8.2, and 8.3.1


Page 266: Problem 1d

Page 267: Problems 1i, 1n, 1t, and 3

Page 274: Problems 1a, 1e, 2c, and 2d

Page 275: Problems 5a and 5e

Page 280: Problems 1a, 1c, 1j, 2a, and 2c

Page 407: Problems 1m and 1p

Page 408: Problems 6a, 6c, and 8

Homework is due by 5PM on September 29, 2008

Week 5
Sep.29 – Oct.5

Vector Spaces

Understand fundamentals of vector spaces

Understand the dot product and its properties

Cauchy-Schwartz inequality

Fundamentals of the norm, orthogonality and function spaces

Bases and supspaces

Dependent and independent vectors

Dimensions of vector spaces

Span of vectors

“Best” approximations


Chapters 9.1-9.6, 9.7-9.10


Page 415: Problem 5

Page 418: Problem 6

Page 421: Problems 4a and 4d

Page 428: Problems 1a and 1e

Page 429: Problems 6d and 9b

Page 438: Problems 12c and 12e

Page 443: Problem 1b, 1c, and 3

Page 447: Problem 2a, 2c, 3b, 3f and 3n

Page 456: Problems 1c, 1f, 1i, 2c, and 4e

Page 462: Problem 4b

Homework is due by 5PM on October 6, 2008

Week 6
Oct.6 – Oct.12

Matrices and Linear Equations

Understand matrices and basic operations of addition and multiplication

Special Matrices

Partitioning transpose and determinant of a matrix

Matrix rank

Row and column spaces

Linear equations and matrices


Chapters 10.1-10.4, 10.5, 10.6.1 and 10.6. 4


Page 479: Problems 1 and 5

Page 480: Problem 10

Page 486: Problem 6

Page 493: Problems 6a and 6c

Page 506: Problems 1c and 1d

Page 507: Problem 11

Page 522: Problems 1c and 1h

Page 523: Problems 5b and 5c

Homework due October 13, 2008

Exam 2 handed out October 6 and due October 20, 2008.

Week 7
Oct.13 – Oct.19

Eigenvalues and Eigenvectors

The eigenvalue/eigenvector problem

Solving for eigenvalues and eigenvectors


Application to differential equations

Properties to symmetrical matrices

Diagonalizing an matrix


Chapters 11.1, 11.2.1, 11.3.1, and 11.4


None Assigned

Complete exam 2 and submit by October 20, 2008.

REMINDER:  Each "week" of the course begins on Monday and ends on the following Sunday at 11:59 PM EST.  Assignments for the each week must be submitted to the appropriate drop box before 5:00 PM EST on the following Monday (see table above for exact dates) for the submission to be considered "on-time".


PSU Policies

Academic Integrity

Academic integrity is a basic guiding principle for all academic activity at Penn State University, allowing the pursuit of scholarly activity in an open, honest, and responsible manner. In according with the University's Code of Conduct, you must not engage in or tolerate academic dishonesty. This includes, but is not limited to cheating, plagiarism, fabrication of information or citations, facilitating acts of academic dishonesty by others, unauthorized possession of examinations, submitting work of another person, or work previously used without informing the instructor, or tampering with the academic work of other students. Any violation of academic integrity will be investigated, and where warranted, punitive action will be taken. For every incident when a penalty of any kind is assessed, a report must be filed. This form is used for both undergraduate and graduate courses. This report must be signed by both the instructor and the student, and then submitted to the Senior Associate Dean.

Disability Statement

The Pennsylvania State University encourages qualified persons with disabilities to participate in its programs and activities. If you anticipate needing any type of accommodation or have questions about the physical access provided, please contact Kathy Mingioni at 610-648-3315 in advance of your participation.

Systems Engineering Online Technical Requirements

Operating System

Windows 2000, XP, or Vista
Mac OS X (10.3 or higher)


1 GHz or higher


256 MB of RAM or more

Hard Drive Space

2 GB free disk space or more


Mac OS X: Firefox 2.0 or higher
Windows: Firefox 2.0 or higher

Note: Cookies, Java, and Java Script must be enabled.
Pop-up blockers should be configured to permit new windows from Penn State web sites.

Due to nonstandard handling of CSS, JavaScript and caching, we do not recommend using Internet Explorer 6 as your browser.


Adobe Flash Player, Apple Quicktime, Adobe Connect Plug-in (provided upon first usage),

Additional Software

Microsoft Office (Word, Excel, PowerPoint), E-mail, PDF document creation software (i.e. Adobe Acrobat Standard/Professional or similar), PDF viewing software, Apple iTunes/QuickTime

Some courses will require specialized software like Matlab or Simulink

Internet Connection

broadband (cable or DSL) connection required


Ready and convenient access to a scanner is required for some courses (owning a scanner may not be necessary if student has regular access to one)


graphics-capable printer



Sound Card, Microphone, and Speakers (or Headphones)



15-inch or larger (minimum 1024 x 768 resolution)


Notice Regarding Sample Syllabus

This sample syllabus is dated 17 July 2008, and is for orientation and promotion purposes only. Students currently enrolled in SYSEN 510 should NOT use this syllabus to guide their progress through the course. Enrolled students should log into SYSEN 510 via ANGEL, and access the most current syllabus from there.


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