Department of Mathematics and Physics
§ I: MATH 6611 Matrix Theory and its Applications
Catalog Description
Prerequisite: undergraduate linear algebra or permission of instructor. Review of matrix algebra, systems of
linear equations and rank; linear algebra in n-dimensions; inner product spaces and orthogonality; eigenval-
ues and eigenvectors; Hermitian, unitary, and normal matrices; quadratic and Hermitian forms. The course
covers topics in matrix theory needed for signicant applications in engineering and computer science. 3
This course covers a broad range of topics that are relevant to graduate students majored in applied
sciences, including engineering and computer science. It introduces fundamental mathematical concepts
and methods, and encourages students to apply these materials in their major studies. A solid background in
Calculus (IIII) and linear algebra is necessary. Further knowledge in dierential equations is recommended
but not necessary.
Required Textbook
Advanced Engineering Mathematics, E. Kreysig, John Wiley, 10e, ISBN 9781111827052 (2011).
Course Objectives
This course covers a broad range of topics that are relevant to graduate students majored in applied sciences,
including engineering and computer science. It introduces fundamental mathematical concepts and methods,
and encourages students to apply these materials in their major studies. A solid background in Calculus (I
III) and linear algebra is necessary. Further knowledge in dierential equations is recommended but not
Student Learning Outcomes
After successfully completing this course the expectation is that students will be able to:
1. Analyze and apply appropriate methods for of solution of rst, second and higher order linear ODEs,
systems of ODEs and construct series solutions of ODEs with the help of special functions;
2. Categorize concepts of linear algebra, conduct matrix operations, and solve and apply matrix eigenvalue
3. Apply Fourier analysis techniques to solve three important PDEs: heat equation, wave equation and
Laplace equation.
4. Examine basic operations on the eld of complex numbers, interpret the analytic properties of com-
plex functions, formulate harmonic conjugate using Cauchy-Riemann Equations, and integrate complex
functions using Cauchys Integral Theorem.
Required Curriculum Content
This course introduces important mathematical concepts that are useful in engineering sciences, including
ordinary dierent equations (ODEs), partial dierential equations (PDEs), Laplace transforms, Fourier trans-
forms, eigenvalue problems, complex analysis, and linear algebra. Finally, a brief introduction to numerical
linear algebra is given at the end of the course. This course does not focus on the mathematical rigor behind
theories, but emphasizes the applications of mathematical ideas to practical examples in engineering and
computer sciences. Students are expected to apply the course materials in their major studies in the future.
All sections of MATH 6611 Matrix Theory and its Applications will cover, as a minimum, the material from
Advanced Engineering Mathematics, E. Kreysig, John Wiley, 10e, ISBN 9781111827052 (2011), as listed:
Chapter Textbook Topic
1 First-Order ODEs
1.5 Linear ODE
2 Second Order Linear ODEs
2.1 Homogeneous linear ODEs of second order
2.2 Homogeneous linear ODEs with constant coecients
2.7 Non-homogeneous ODEs
2.9 Modeling:Electrical circuits
4 Systems of ODEs
4.1 Systems of ODEs as models in engineering applications
6 Laplace Transform
6.1 Laplace transforms, 1st shifting theorem
6.2 Transforms of derivatives and integrals, ODEs
6.3 Unit step function, 2nd shifting theorem
6.4 Short impulses, Dirac Delta function
6.5 Convolution, Integral equations
7 Linear Algebras
7.1 Addition and scalar multiplication of matrices
7.2 Matrix multiplication
7.3 Linear systems of equations Gauss elimination
7.4 Linear independence, rank, vector space
7.6 Second and 3rd order determinants
7.7 Determinants, Cramers rule
7.8 Inverse of a matrix, Gauss-Jordan elimination
7.9 Vector spaces, Inner product spaces, linear transformation
8 Matrix Algebra and Eigenvalue Problems
8.1 Determining eigenvalues and eigenvectors
8.2 Applications of Eigenvalue problem
8.3 Symmetric, skew symmetric and orthogonal matrices
8.4 Eigenbases, diagonalization, quadratic forms
8.5 Complex matrices and forms
13 Complex Dierentiation
13.1 Complex numbers
13.2 Polar form, powers, roots
13.3 Derivative, analytic function
13.4 Cauchy-Riemann equations, Laplace equation
13.5 Exponential functions
13.6 Trigonometric and hyperbolic functions, Eulers formula
13.7 Logarithm, general power, principal value
14 Complex Integration
14.1 Complex line integral
14.2 Cauchys integral theorem
14.3 Cauchys integral formula
Department Syllabus for MATH 6611, Spring 2019 Page 2 of 6 Rev. 1.0, January 28, 2019
Chapter Textbook Topic
14.4 Derivatives of analytic functions
15 Power Series, Taylor Series
15.2 Power series
15.3 Functions given by power series
15.4 Taylor series
16 Laurent series, residue integration
16.1 Laurent series
16.2 Singularities and zeros
16.3 Residue integration
16.4 Residue integration of real integrals, including Fourier integrals
18 Complex Potential Theory
18.1 Electrostatic elds
20 Numerical Linear Algebra
20.1 Least squares method
Common Department Requirements for MATH 6611
While students in each section of MATH 6611 are assessed by the course instructor, there are general guide-
lines that apply to all sections of MATH 6611. These include:
Calculators and other electronic devices are not allowed on any exams.
Department Syllabus for MATH 6611, Spring 2019 Page 3 of 6 Rev. 1.0, January 28, 2019
Department, College and University Expectations and Policies
It is important that students familiarize themselves with a range of policies and guidelines that have been es-
tablished by the Department of Mathematics and Physics, the College of Arts and Sciences, and the University
of New Haven. These are an integral part of the syllabus for this course.
Adding/Dropping a Class
The nal day to drop a course without it appearing on your transcript is Tuesday, December 4, as discussed
at During the second week of classes, further adjustment
requires the approval of the chair of the department oering the course, as described at http://catalog.
Attendance Regulations
University attendance policy guidelines require that:
All students are expected to attend regularly and promptly all their classes, appointments, and exercises. While
the university recognizes that some absences may occasionally be necessary, these should be held to a minimum.
A maximum of two weeks of absences will be permitted for illness and emergencies. The instructor has the right
to dismiss from class any student who has been absent more than the maximum allowed. After the last date to
drop as published in the academic calendar, a student will receive a failure (F), if failing at that point, or a W, if
passing at the time of dismissal.
Students are to adhere to the policy attendance policy guidelines outlined in the University Catalog under the
heading, Attendance Regulations, at
Status_and_Progress, or alternatively in the Student Handbook at
on pp. 4849,. i.e., at
Withdrawal Deadline
Students wishing to withdraw must submit a request for an ocial course withdrawal in writing using the
Course Withdrawal Form available online from The -
nal date to request a withdrawal is Tuesday, October 30 listed in
schedules-registration/academic-calendar-2017-2018.php. This request must be submitted to the Reg-
istrars Oce and signed by the International Oce if you are an international student. The grade of W will
be recorded, but the course will not aect the GPA.
Incomplete Grades
A grade of Incomplete (INC) is given only in special circumstances and indicates that the student has been
given permission by the instructor to complete required course work (with the same instructor) after the
end of the term. Students need to examine carefully the changed guidelines pertaining to INC grades,
To remove the INC grade, the student must complete all required course work in timely fashion as stipulated
by the instructor but no later than the end of the following term. Fall and intersession course incompletes must
be completed no later than the last day of the spring term. Spring and summer course incompletes must be
completed no later than the last day of the fall term.
If the course work is not submitted within the allotted time, the INC grade will be changed to an F shortly after
the deadline by the Oce of the University Registrar. Students will be notied via campus email at least two
weeks prior to the change of grade process.
The University policy on incomplete grades is available at
12&navoid=881#Academic_Status_and_Progress under the heading, Incomplete (INC) Grade Policy.
Please note that this withdrawal deadline represents a
significant policy change
. It is the responsibility of the student to assure that the required
paperwork and documentation is completed by the deadline.
Department Syllabus for MATH 6611, Spring 2019 Page 4 of 6 Rev. 1.0, January 28, 2019
Academic Integrity Policy
This class fully adheres to the Academic Integrity Policy:
Academic integrity is a core university value that ensures respect for the academic reputation of the University,
its students, faculty and sta, and the degrees it confers. The University expects that students will conduct
themselves in an honest and ethical manner and respect the intellectual work of others. Please be familiar with
the UNH policy on Academic Integrity. Please ask about my expectations regarding permissible or encouraged
forms of student collaboration if they are unclear.
Students are required to adhere to the Academic Integrity Policies specied in the Student Handbook on
pp. 6673 of, i.e., at
Coursework Expectations
This course will require signicant in-class and out-of-class commitment from each student. The University
estimates that a student should expect to spend two hours outside of class for each hour they are in a
class. For example, a three credit course would average six [6] hours of additional work outside of class.
Coursework expectations are detailed at
881#General_Policies under the heading Course Work Expectations.
Please note, that MATH 6611 is a 3-credit course, and as such requires a total of 9 hours per week invested
in study and homework for the average student.
Commitment to Positive Learning Environment
The University of New Haven wants to foster and support a civil, respectful, and open-minded climate so that
all of us can live and work in an environment free of harassment, bias-motivated behaviors, unfair treatment,
and fear. To this end, the university expects all members of our community to refrain from actions or behav-
iors that intimidate, humiliate, or demean persons or groups or that undermine their security or self-esteem
based on traits related to race, ethnicity, country of origin, religion, gender identity/expression, sexual orienta-
tion, age, or physical or mental ability, including learning and/or developmental disabilities and past/present
history of mental disorder or other category protected by state or federal law. If you have witnessed or are
the target of a bias-motivated incident, please contact the Oce of the Dean of Students at 203-932-7432 or
Campus Police at 203-932-7014 or ll out the form at
The University adheres to the philosophy that all community members should enjoy an environment free
of any form of harassment, sexual misconduct, discrimination, or intimate partner violence. If you have been
the victim of sexual misconduct we encourage you to report this. If you report this to a faculty/sta member,
they must notify our colleges Title IX coordinator about the basic facts of the incident (you may choose to
request condentiality from the University). If you encounter sexual harassment, sexual misconduct, sexual
assault, or discrimination based on race, color, religion, age, national origin, ancestry, sex, sexual orientation,
gender identity, or disability please contact the Title IX Coordinator, Caroline Koziatek at (203)-932-7479 or Further information about Title IX at UNH may be found at http://www.newhaven.
Religious Observance Policy for Students
The University of New Haven respects the right of its students to observe religious holidays that may neces-
sitate their absence from class or from other required university-sponsored activities. Students who wish
to observe such holidays should not be penalized for their absence, although in academic courses they are
responsible for making up missed work. More information about religious observance policies can be found
in the Student Handbook on p.48 at
More information about religious observance policies can be found in the Student Handbook, and there is
also a separate handbook for International students at
Please note that study guidelines are important, i.e., there is substantial evidence that shows that the pass rates for students in math courses decrease
dramatically as the time spent on outside study falls below 2 hours of homework per credit per week.
Department Syllabus for MATH 6611, Spring 2019 Page 5 of 6 Rev. 1.0, January 28, 2019
University Support Services
The University recognizes students often can use some help outside of class and oers academic assistance
through several oces. In addition to discussing any academemic issues you may have with your instructor,
advisor, or with the the coures or department coordinator or chair, the University provides these additional
resources for students:
The Academic Success Center, located in Maxcy 208 for help with your academic studies, or
call 203.932.7234 to set up an appointment.
The Center for Learning Resources (CLR) located in Peterson Library, provides academic content support
to the students of the University of New Haven using metacognitive strategies that help students become
aware of and learn to apply optimal learning processes in the pursuit of creating independent learners CLR
tutors focus sessions on discussions of concepts and processes and typically use external examples to help
students grasp and apply the material.
Writer to Writer is a peer-tutoring program inspired by the belief that all writers
struggle and can benet from talking through their ideas. Tutors are undergraduate students trained to work
with you at any stage in the writing process.
Accessibility Resources Center Students with dis-
abilities are encouraged to share, in condence, information about needed specic course accommodations.
The Accessibility Resources Center (ARC) provides comprehensive services and support that serve to promote
educational equity and ensure that students are able to participate in the opportunities available at the Uni-
versity of New Haven. Accommodations cannot be made without written documentation from the ARC. The
ARC is located on the ground oor in the rear of Sheeld Hall. Sheeld Hall is located in the Residential Quad
area, and can be contacted at 203-932-7332. The ADA/Section 504 Compliance Ocer is Rebecca Johnson,, and can be reached by phone at 203-932-7238. Information on the ARC can be
found at
Department Syllabus for MATH 6611, Spring 2019 Page 6 of 6 Rev. 1.0, January 28, 2019