Mathematical description and modeling of mechanical and electrical systems through linear differential equations and in the frequency domain with the help of the Laplace and Fourier transforms.
Prerequisites: ENGR 2170 (Electrical Circuits) or instructor's consent.

Class schedule Fall 2015:



What is a system? In one book, a system was defined as an assemblage of things that performs some sepcified function. A system can be anything from a water tank to a car suspension to an aeroplane. In the context of this class, a system has a defined state (e.g., the water level of a tank, the compression of the spring in a car suspension, the attitude of an aeroplane). We interpret this state as the output of the system, and we stipulate that the output is quantifiable and measurable. In addition, the system must have an input. A control signal (for example, electrical or mechanical) applied to the input changes the output of the system in a predictable way.

A linear, time-invariant system is a system that has several defined properties. Strictly, linear systems do not exist. However, within limits, many electrical and mechanical systems can be adequately described with the linear system model.

In this course, we will examine systems and learn to describe them with mathematical models. With the help of a model, the behvior of the system can be predicted. By association, we will also examine signals, that is, the inputs and outputs of a system. We will learn how to measure and analyze signals to obtain meaningful information that allows us to describe a system. Specifically,

  1. We will learn how to describe and characterize a linear system
  2. We will learn how to measure and interpret signals
  3. We will use time-domain methods (differential equations) and frequency-domain methods (Fourier analysis, Laplace transform) to effectively model linear systems and predict their dynamic and steady-state behavior
  4. We will also use computer simulations to help us analyze a system and support the purely mathematical model.

This course provides you with the mathematical tools to analyze and describe systems. Notably, in the second class (Feedback Control Systems), we will then learn how to design a system, that is, modify a system that has a given, but undesirable behavior, into a system that meets specific design goals.


Please note that this table is tenatative and will be updated as we go.
Block Topic
1 Signals and Systems
2 Properties of Linear Systems
3 Description of linear systems with differential equations
4 Input and output signals, system response and the convolution
5 Transient and steady-state response
6 The Laplace transform
7 Description of linear systems in the Laplace domain
8 Transfer functions, characteristic equation, poles and zeros
9 State-variable description of linear systems
10 Predicting the system response in the Laplace domain
11 The Fourier transform
12 Frequency-domain analysis methods
Bode diagrams and Nyquist plots
13 Simulation with Scilab
14 Scimulation with Scilab and Xcos
15 Presentation of the semester projects


Suggested primary book: ENGINEERING SIGNALS AND SYSTEMS. By Fawwaz T. Ulaby and Andrew E. Yagle. National Technology and Science Press (2013). ISBN 978-1-934891-16-2.
We will focus on Chapters 1 through 5 (partially), and not use any of the later chapters.

Suggested complementary reading: LINAR FEEDBACK CONTROLS - THE ESSENTIALS. By M. Haidekker. Elsevier Insights series (2013). ISBN: 978-0-124-05875-0
Link to publisher's web site
NEW! Link to the e-resource from our library
Out of this book, Chapters 2, 3, 5, 6, 7, and 11 are of relevance. For those of you who will take Feedback Controls next semester, this book is highly recommended! Many examples that we use in Linear Systems are fully described in this book.


Computer lab 310 has Scilab/Scicos installed. You may login with your UGA password.

Scicos/Scilab is Free Software. You may download and install a copy free of charge and with the right to access the source code.


The grade will be based about equally on short quizzes, the Comprehensive Assignments, the midterm exam, the final exam, and -- if assigned -- the semester project. You will receive score points based on the fill-the-bucket principle, i.e. for each homework assignment and for each test, you accrue score points. Your final grade will be determined from the score you achieved relative to the maximum score achievable. Typically, you receive a maximum of 30-50 points per homework, 100 points for the semester project, a total of 100 pints in quizzes, and 100 points per test, resulting in a maximum score of around 600 points.

We use a fixed grading system. There will be no adjustment based on the overall class performance. To get a passing grade, you will have to achieve an overall score of at least 45%. The following table shows the percentage of your score you need to reach for a specific grade:

GradeMinimum percentage GradeMinimum percentage GradeMinimum percentage
A95% A-90%   
B+85% B80% B-75%
C+70% C65% C-60%
D+50% D45%   


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Office hours: TBD

Queries by e-mail or on the blog: any time. In fact, I strongly encourage you discuss the topics on the Blog site so that everybody can benefit from the discussion.


Quiz assignments

Don't panic. Quizzes are really short problems that you solve at home. You typically get two days to solve a Quiz. Quizzes deal with a limited theoretical or conceptual aspect, and they are closely linked to the lecture material. There are no in-class quizzes or other ugly surprises.

Quiz No. Topic Date assigned Date due Grade due Discussion thread
Quiz 1         Quiz 1 discussion

Comprehensive Homework Assignments

The purpose of the comprehensive homeworks is to allow you to compare the theory to practical linear systems and identify how well the theory actually describes the real-world system. Comprehensive homeworks are teamwork assignments, ideally with teams of three people. Sharing the work is encouraged, but each team member should actually have an overview of the entire project. The score assigned is the same for each team member.

Assignment No. Topic Date assigned Date due Max. score Assignment (pdf) Discussion thread


Here are some interesting links: