Engineering Systems Analysis Instructor & Contact Information Dr. John Smith, Professor of Electrical Engineering Course Description This 3­credit 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. Learning Objectives Learners who successfully complete this course will be able to: ● Describe, using real­world 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 real­world 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 Course Policies All course material is available to you on CourseWorks. 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 lesson­by­lesson 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 module on CourseWorks. 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. 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. Exams​
: Two take­home 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. Class Schedule Week/Date
Unit/Lesson Title
s
Unit/Lesson
Assignments Due
Objectives
Week 1
Introduction to
Representation of
Read:
Monday,
Differential
derivatives
Chapters 1.1-1.2,
September
Equations
Solving linear first order
2.1, 2.2-2.2.3, 2.4,
through
Separable and Exact homogeneous differential
and 2.5
Differential
equations
Homework:
Equations
Solving first order
Page 9: Problems
nonhomogeneous
1-a, 1d, 4, 5a, 5e,
differential equations
and 5h
Solve differential
Page 32-33:
equations using
Problems 9 and 11
Separation of Variables
Page 60: Problem 6
Sunday,
September 7
(Sep.1 –
Sep.7)
method
Solve using exact
differenxtial equation
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
Linear Differential
Sep.8 –
Equations of Second independence
Chapters 3.1, 3.2,
Sep.14
Order and Higher
Homogeneous linear
3.3, 3.4., 3.4.2-3.4.5
ordinary differential
Homework:
equation with constant
Page 83: Problems
Linear dependence or
coefficients
Read:
2b, 2f, 2h, 3g, 3h,
Understanding the total
6a, and 6c
solution to linear ordinary
Page 89: Problems
differential equations
Solution to linear ordinary
differential equation with
constant coefficients
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
Method of undetermined
coefficients
System of differential
equations
Read:
Chapters 3.7 – 3.7.2,
3.9, 5.1-5.3
Homework:
∙ Laplace
Page 148: Problems
Transforms
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
Partial Fraction Expansion
Read:
and Differential
Application of Laplace
Chapters 5.4-5.6,
transforms to differential
8.1-8.2, and 8.3.1
Linear Algebraic
equations
Homework:
Equations
Special functions and
Equations
applications
Basics of the solutions to
algebraic equations
Page 266: Problem
1d
Page 267: Problems
1i, 1n, 1t, and 3
Gauss elimination and
Page 274: Problems
Gauss-Jordan elimination
1a, 1e, 2c, and 2d
to solve
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
Read:
of vector spaces
Chapters 9.1-9.6,
Understand the dot
9.7-9.10
product and its properties
Homework:
Cauchy-Schwartz
Page 415: Problem 5
inequality
Page 418: Problem 6
Fundamentals of the
norm, orthogonality and
function spaces
Bases and supspaces
Dependent and
independent vectors
Dimensions of vector
spaces
Page 421: Problems
4a and 4d
Page 428: Problems
1a and 1e
Page 429: Problems
6d and 9b
Page 438: Problems
12c and 12e
Span of vectors
Page 443: Problem
“Best” approximations
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
Understand matrices and
Read:
Equations
basic operations of
Chapters 10.1-10.4,
addition and multiplication
Special Matrices
10.5, 10.6.1 and
10.6. 4
Partitioning transpose and Homework:
determinant of a matrix
Page 479: Problems 1
Matrix rank
and 5
Row and column spaces
Page 480: Problem
Linear equations and
10
matrices
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
The
Read:
Eigenvectors
eigenvalue/eigenvector
Chapters 11.1,
problem
11.2.1, 11.3.1, and
Solving for eigenvalues
11.4
and eigenvectors
Homework:
Eigenspaces
None Assigned
Application to differential
Complete exam 2 and
equations
submit by October
Properties to symmetrical
20, 2008.
matrices
Diagonalizing matrix