COLLEGE OF ARTS AND SCIENCES

Department of Mathematics and Physics

§ I: MATH 6611 Matrix Theory and its Applications

Syllabus

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 signiﬁcant applications in engineering and computer science. 3

credits.

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 diﬀerential 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 diﬀerential equations is recommended but not

necessary.

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 ﬁrst, 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

problems;

3. Apply Fourier analysis techniques to solve three important PDEs: heat equation, wave equation and

Laplace equation.

4. Examine basic operations on the ﬁeld of complex numbers, interpret the analytic properties of com-

plex functions, formulate harmonic conjugate using Cauchy-Riemann Equations, and integrate complex

functions using Cauchy’s Integral Theorem.

Required Curriculum Content

This course introduces important mathematical concepts that are useful in engineering sciences, including

ordinary diﬀerent equations (ODEs), partial diﬀerential 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

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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 coeﬃcients

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, Cramer’s 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 Diﬀerentiation

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, Euler’s formula

13.7 Logarithm, general power, principal value

14 Complex Integration

14.1 Complex line integral

14.2 Cauchy’s integral theorem

14.3 Cauchy’s 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 ﬁelds

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 ﬁnal day to drop a course without it appearing on your transcript is Tuesday, December 4, as discussed

at http://www.newhaven.edu/academics/calendar. During the second week of classes, further adjustment

requires the approval of the chair of the department oﬀering the course, as described at http://catalog.

newhaven.edu/content.php?catoid=7&navoid=730#Changes.

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 http://catalog.newhaven.edu/content.php?catoid=12&navoid=881#Academic_

Status_and_Progress, or alternatively in the Student Handbook at http://www.newhaven.edu/studenthandbook

on pp. 48–49,. i.e., at http://viewer.zmags.com/publication/bc83d17d#/bc83d17d/48.

Withdrawal Deadline

Students wishing to withdraw must submit a request for an oﬃcial course withdrawal in writing using the

Course Withdrawal Form available online from http://forms.newhaven.edu/view.php?id=134169. The ﬁ-

nal date to request a withdrawal is Tuesday, October 30 listed in http://www.newhaven.edu/academics/

schedules-registration/academic-calendar-2017-2018.php. This request must be submitted to the Reg-

istrar’s Oﬃce and signed by the International Oﬃce if you are an international student. The grade of W will

be recorded, but the course will not aﬀect the GPA.

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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,

speciﬁcally:

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 Oﬃce of the University Registrar. Students will be notiﬁed via campus email at least two

weeks prior to the change of grade process.

The University policy on incomplete grades is available at http://catalog.newhaven.edu/content.php?catoid=

12&navoid=881#Academic_Status_and_Progress under the heading, Incomplete (INC) Grade Policy.

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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 staﬀ, 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 speciﬁed in the Student Handbook on

pp. 66–73 of http://www.newhaven.edu/studenthandbook, i.e., at http://viewer.zmags.com/publication/

bc83d17d#/bc83d17d/66.

Coursework Expectations

This course will require signiﬁcant 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.

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Coursework expectations are detailed at http://catalog.newhaven.edu/content.php?catoid=12&navoid=

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 Oﬃce of the Dean of Students at 203-932-7432 or

Campus Police at 203-932-7014 or ﬁll out the form at http://www.newhaven.edu/student-life/report-it.

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/staﬀ member,

they must notify our college’s Title IX coordinator about the basic facts of the incident (you may choose to

request conﬁdentiality 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

CKoziatek@newhaven.edu. Further information about Title IX at UNH may be found at http://www.newhaven.

edu/about/title-ix.php/.

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 http://viewer.zmags.com/publication/bc83d17d#/bc83d17d/48.

More information about religious observance policies can be found in the Student Handbook, and there is

also a separate handbook for International students at https://www.newhaven.edu/student-life/international-services/

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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

index.php.

University Support Services

The University recognizes students often can use some help outside of class and oﬀers academic assistance

through several oﬃces. 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

http://www.newhaven.edu/AcademicSuccess, 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)

http://www.newhaven.edu/academics/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

http://www.newhaven.edu/writertowriter/ is a peer-tutoring program inspired by the belief that all writers

struggle and can beneﬁt from talking through their ideas. Tutors are undergraduate students trained to work

with you at any stage in the writing process.

Accessibility Resources Center

http://www.newhaven.edu/student-life/accessibility-resources-center/index.php. Students with dis-

abilities are encouraged to share, in conﬁdence, information about needed speciﬁc 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 ﬂoor in the rear of Sheﬃeld Hall. Sheﬃeld Hall is located in the Residential Quad

area, and can be contacted at 203-932-7332. The ADA/Section 504 Compliance Oﬃcer is Rebecca Johnson,

RJohnson@newhaven.edu, 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