School of Arts and Sciences
MA315: Linear Algebra and Intro to Numerical Methods
Course Syllabus
Mission Statement: “Daniel Webster College educates purposeful men and women for entry,
advancement and advanced studies in professional fields through programs which emphasize the
integration of theory and practice through interactive teaching and learning in professional and liberal
studies.”
Course Number/Section:
Course Title:
Semester/Term Dates:
Class Meeting Time:
Class Location:
Prerequisites:
Co-requisites:
Credits:
MA315-A
Linear Algebra and Intro to Numerical Methods
Fall 2013
Tuesday and Thursday, 9:00 – 10:50
DWH 216
MA205
None
4.0
Instructor Contact Information
Instructor:
Office Location:
Office Hours:
Email:
Phone:
Timothy D. Kostar
DWH 109 G
Monday, Wednesday, Friday, 9:00 – 11:00 am
kostar_timothy@dwc.edu
603-577-6064
Course Description
This course develops mathematical modeling skills, with an emphasis on both analytical and numerical
solution methods. The first component of the course covers linear algebra, the study of systems of linear
algebraic equations, and eigenvalue problems. The second component delves into the derivation of
differential equations and their numerical solution. The third component covers Fourier series, Fourier
transforms, and Discrete Fourier Transforms. In support of all the above, there is a programming and
computer utilization component to the course involving implementation of covered solution methods.
Daniel Webster College Catalog
Course Textbook Information
Erwin Kreyszig, “Advanced Engineering Mathematics”, 10th ed, John Wiley and Sons, Inc., New York
(2011), ISBN 978-0-470-45836-5
Daniel Webster College
1
Course Objective
The objective of this course is to provide a working knowledge of analytical and numerical solution
methods to common mathematical models resulting from analysis of a physical system, process, or data.
Course Outcomes (measurements in parentheses)
The student should demonstrate the ability to;
1) derive systems of linear algebraic equations, based on analysis of a physical system, and obtain their
solution through Gauss elimination and Cramer’s rule (HW#3, HW#4, Exam#1, Final Exam,
Programming Assignment#1).
2) obtain the Eigen values and Eigen vectors of matrices and apply this to solutions of related problems
(HW#6, HW#7, Exam#2, Final Exam).
3) derive ordinary and partial differential equations based on conservation principles and obtain their
solution through numerical methods (HW#8, HW#9, HW#10, HW#11, Exam#2, Programming
Assignment#2).
4) represent an arbitrary function as a Fourier series and, coupled with superposition, apply to the
solution of a differential equation (HW#12, Exam#3, Final Exam).
5) perform Fourier transforms and their inverse as applied to the solution of a differential equation
(HW#13, HW#14, Exam#3, Final Exam).
6) implement both analytical and numerical solution methods through coding and utilization of commercial
software (Programming Assigment#1, Programming Assignment#2).
General Education Competencies
The General Education category that this course supports is critical thinking. Specifically, the following
competencies are addressed:
Communication Competencies:
- None.
Critical Thinking Competencies:
- Demonstrate the ability to describe and evaluate the logic of an argument or analysis.
- Apply quantitative reasoning skills to solve problems.
Cultural and Community Engagement Competencies:
- None.
Students with Disabilities
Daniel Webster College is committed to compliance with Section 504 of the Rehabilitation Act of 1973 and
its regulations. The school does not discriminate on the basis of disability in admission or access to, or
treatment or employment in, its programs and activities.
In accordance with the Americans with Disabilities Act, any student who has a documented physical,
learning, or emotional disability* will be provided with reasonable accommodations designed to meet his
or her needs. Before any such assistance can occur, it is the responsibility of the student to see that
documentation is on file with the ADA Coordinator and that a Reasonable Accommodation Plan has been
developed. Once this is in place the student may request a copy of the plan go to all or some of his/her
instructors so that they may provide the agreed upon accommodations. Students with a disability may
request an accommodation by contacting ADA Coordinator Dr. Kathy Hipp, Associate Dean of Arts and
Sciences, at 603-577-6659 or hipp@dwc.edu.
*Documentation cannot be more than three years old.
Academic Honesty
Intellectual curiosity is at the heart of the academic enterprise. Students, faculty and administration at
Daniel Webster College
2
Daniel Webster College consider such violations as cheating and plagiarism to be so unethical as to call
into question whether the violator should continue as a member of the College community.
Transcripts that misrepresent academic performance not only endanger students’ chances for success in
their careers but also damage the integrity and reputation of the institution.
Student Honor Pledge
Daniel Webster College believes that all students have the right to learn in an academic community that
insures fair competition, and respects truth and honesty. Academic dishonesty is not tolerated at Daniel
Webster College. The Student Honor Pledge is intended to create a community of fairness, respect and
responsibility in the pursuit of academic enterprise. All students are expected to abide by the Student
Honor Pledge.
I pledge on my honor, as a student at Daniel Webster College, that I have neither given nor
received any unauthorized aid on this assignment/examination.
For more information regarding Daniel Webster College’s ethical standards, please refer to the current
college catalog.
Grading Scale
The following scale is used to assign letter grades:
A = 93+
C+= 76-79
A- = 90-92
C = 70-75
B+= 87-89
D = 65-69
B = 83-86
F = Below 65
B- = 80-82
Expectations
Homework problems from the text, and potentially other sources, will be assigned on a regular basis and
are subject to change. It is expected that the interested student will endeavor to solve these problems.
Remember that you cannot adequately learn this material without practicing the methods.
Talk to me in advance if you have reasonable reason(s) for not being able to turn in your homework or
any assignment on time. To be fair to all students, late homework or other assignments are given a 33%
reduction in points per day that the homework or assignment is late. A “day” is defined as 24 hours,
beginning at the start of class time.
In addition, there will be two (2) computer programming assignments which you will work on
independently outside of class time (Gauss Elimination and the Finite Difference Method). Finally, in
support of the student evaluation process, there will be three (3) in-term exams, and one (1)
comprehensive final exam. No make-ups for exams will be given unless satisfactory advanced
notice and reason is supplied to the instructor. The grades will not be curved. The grades will be
assigned based on the absolute grade scale shown above.
Active class participation is expected. In this course you will be expected to act in a professional
manner. Among other things, this includes showing up on time prepared for the task at hand. This shall
include not just being on time for class, but also for any and all additional outside meetings you will have
with group work. You will be expected to read assigned chapters/tutorials before coming to class
and be ready to actively participate. Classroom activities such as chatting, use of computer, ipod, cell
phone and other electronics are not allowed. Students may ask questions of one another when working
on out-of-class assignments. However, each student must do their own work. A first occurrence of
academic dishonesty will result in a zero for that assignment for all who are involved. A second
occurrence will result in an F for the course. Note that all such occurrences must be reported in writing
Daniel Webster College
3
to the Chief Academic Officer who may prescribe additional penalties.
Course Evaluation
Homework
15%
Programming Assignment #1
5%
Programming Assignment #2
5%
Exam #1
15%
Exam #2
15%
Exam #3
15%
Final Exam
30%
________________________________________
Total
100%
Daniel Webster College
4
Planned Schedule of Activities
Schedule may be modified, with announcements posted on-line.
Week
1
2
3
4
5
6
7
8
9
10
09/02
09/06
No
Monday
Class
09/09
09/13
09/16
09/20
09/23
09/27
09/30
10/04
10/07
10/11
10/14
10/18
No Mon.
meets
Tues.
10/21
10/25
10/28
11/01
11/04
11/08
Reading
Topics
Assignments
Course Overview: Syllabus walk-thru, administrative policies,
expectations, course overview.
Lecture Topics: Intro to matrices.
7.1, 7.2, 7.4
7.5, 7.3
7.6, 7.7, 20.1,
Notes
7.9
Lecture Topics: Matrices and matrix algebra. Linear algebraic equations
as matrices. Rank and Linear Independence.
Lecture Topics: Conditions for solution per Rank, Gauss elimination.
Lecture Topics: Determinants and Cramer’s rule, Conditions for solution
per determinants. Modeling, derivation of linear equation system, and
solution procedure per Gauss.
HW #1 (Short Research
paper on Matrices)
HW #2
HW #3
HW #4
Gauss elimination
programming assignment.
Average of Standard and
Rubric Grading.
Lecture Topics: Vector space, orthogonal vectors, and matrix mappings.
HW #5
8.2
Thursday: Exam #1
Lecture Topics: Eigen values and Eigen vectors (definition and concept),
Principle values and directions per Eigen. Diagonalization per Eigen
values.
Lecture Topics: Population models and steady state distributions per
Eigen.
1.2, notes
Lecture Topics: Derivation of non-linear ODE’s and the Finite Difference
Method per simple numerical integration via Euler. Intro to PDE’s.
HW #8
Lecture Topics: Derivations of standard PDE’s and comments on
analytical solution methods.
Lecture Topics: the FDM and first order partials.
HW #9
8.1, 8.3, 8.4,
notes
notes
notes
HW #6
HW #7
HW #10
Thursday: Exam #2
11
12
13
14
15
16
11/11
11/15
11/18
11/22
11/25
11/29
Only
Mon.
and
Tues.
12/02
12/06
12/09
12/13
12/14
12/18
notes
11.1, 11.2,
11.3, 11.5,
notes
11.7, 11.8,
notes
11.9, notes
HW #11
Lecture Topics: the FDM and second order partials, Laplace and Diffusion
eqns in FDM form, Crank-Nicolson method.
Lecture Topics: Fourier series of an arbitrary periodic function, even and
odd functions, Euler Formula and orthogonal functions, Fourier series
representation of a periodic function, superposition and applications
FDM programming
assignment
HW #12
Lecture Topics: Fourier cosine and sine transforms, complex variable
form, the FT and its Inverse.
HW #13
Lecture Topics: Linearity and transforms of derivatives, the frequency
spectrum of a continuous function. The DFT and FFT. Applications to
digital signal processing.
HW #14
Tuesday: Exam #3
Final Exams
Week
Comprehensive Final Exam
Daniel Webster College
5
Relationship of Course to Program Outcomes
Mechanical Engineering
(slight, moderate, substantial)
Outcome
Level of
contribution
Outcome
Level of
contribution
Outcome
a
b
c
d
e
f
g
h
i
j
k
l
m
a
b
substantial
slight
h
i
moderate
c
d
e
f
slight
j
g
moderate
k
l
m
moderate
moderate
slight
Description of Outcome
an ability to apply knowledge of mathematics, science, and engineering
an ability to design and conduct experiments, as well as to analyze and interpret data
an ability to design a system, component, or process to meet desired needs within realistic
constraints …
an ability to function on multi-disciplinary teams
an ability to identify, formulate, and solve engineering problems
an understanding of professional and ethical responsibility
an ability to communicate effectively
the broad education necessary to understand the impact of engineering solutions in a
global, etc., societal context
a recognition of the need for, and the ability to engage in life-long learning
a knowledge of contemporary issues
an ability to use the techniques, skills, and modern engineering tools needed for
engineering practice
an ability to apply principles of engineering, basic science, and mathematics (including
multivariate calculus and differential equations) to model, analyze, design, and realize
physical systems, components or processes.
an ability to work professionally in both thermal and mechanical systems areas.
Daniel Webster College
6
Relationship of Course to Program Outcomes
Aeronautical Engineering
(slight, moderate, substantial)
Outcome
Level of
contribution
Outcome
Level of
contribution
Outcome
a
b
c
d
e
f
g
h
i
j
k
l
m
n
a
b
substantial
slight
h
i
moderate
c
d
e
f
slight
j
g
moderate
k
l
m
moderate
moderate
slight
Description of Outcome
an ability to apply knowledge of mathematics, science, and engineering
an ability to design and conduct experiments, as well as to analyze and interpret data
an ability to design a system, component, or process to meet desired needs within realistic
constraints …
an ability to function on multi-disciplinary teams
an ability to identify, formulate, and solve engineering problems
an understanding of professional and ethical responsibility
an ability to communicate effectively
the broad education necessary to understand the impact of engineering solutions in a
global, etc., societal context
a recognition of the need for, and the ability to engage in life-long learning
a knowledge of contemporary issues
an ability to use the techniques, skills, and modern engineering tools needed for
engineering practice
a knowledge of aerodynamics, aerospace materials, structures, propulsion, flight
mechanics, and stability and control
design competence that includes integration of aeronautical topics
an ability to develop flight test plans and conduct in-flight experiments, as well as to
analyze, etc., the resulting data
Daniel Webster College
7
MA315 Programming Assignment Assessment Rubric
The following Rubric will be utilized to assess your first programming assignment. An average of the
standard grade and the rubric grade will be assigned as your assignment grade. The primary intent of
the Rubric is for the student to clearly and succinctly see what aspects of the assignment are crucial, and
to help the student evaluate and revise their work before final submittal.
The evaluation will be in 0.5 increments (0.0, 0.5, 1.0, …, 3.5, 4.0)
Performance
Indicator
Report Content
30% weighting
Report Clarity
and Flow
20% weighting
Programming
40% weighting
Program
Documentation
10% weighting
Criteria
Eval.
Beginning (1)
Developing (2)
Accomplished (3)
Exemplary (4)
The report contains
very little of the
content it should.
The report contains
some of the
content it should.
The report contains all
of the content it should.
The report contains all
of the content it
should and
demonstrates writer
insight into the nature
of the problem and
the solution.
It was often not
clear what the writer
was intending to
communicate and
paragraphs and
sections often did
not seem to have a
logical flow.
It was sometimes
not clear what the
writer was
intending to
communicate and
paragraphs and
sections
sometimes did not
seem to have a
logical flow.
It was clear what the
writer was intending to
communicate and
paragraphs and
sections had a logical
flow.
It was extremely
clear what the writer
was intending to
communicate and
paragraphs and
sections had a very
fluid logical flow.
The program is
producing incorrect
results.
The program
produces correct
results but does not
display them
correctly.
The program works
and produces the
correct results and
displays them correctly.
The program works
and produces the
correct results and
displays them
correctly and is
efficiently written.
The documentation
is simple comments
embedded in the
code and does not
help the reader
understand the
code.
The documentation
is simple
comments
embedded in the
code with some
simple header
comments
separating
routines.
The documentation
consists of embedded
comments and some
simple header
documentation that is
useful in understanding
the code.
The documentation is
extremely well written
and clearly explains
what the code is
accomplishing and
how.
Total
Daniel Webster College
8