Department of Mathematics and Physics
§ I: MATH 6610 Fundamentals of Calculus Syllabus
Catalog Description
Prerequisite: MATH 1115 (Pre-Calculus mathematics) or equivalent. Review of algebra and trigonometric func-
tions. Topics from calculus include dierentiation and integration methods applied to problems in science,
business, and the social sciences. A review of series. 3 credits.
Required Textbook
Calculus for Scientists and Engineers, Briggs, Cochran, Gillett. Pearson, 2e, ISBN 9780321826718 (2013).
Course Objectives
The course MATH 6610 provides an introduction to the foundations of dierential and integral Calculus em-
phasizing the role of derivatives and integrals in many applications. Aside from providing many dierentiation
and integration methods, the student is introduced to many geometric and physical applications. The course
aims to provide an overview of both dierential and integral Calculus which will include equally weighted
amounts of foundational theory, applications of the tools that we develop, and an understanding of each
problem or concept within general mathematics. In addition, dierential equations, sequences, power series,
and Taylor series will be introduced.
Student Learning Outcomes
Upon successful completion of the course the student will
1. Have a working knowledge of how limits are used to create both derivatives and integrals as mathemat-
ical tools;
2. Be Procient in the calculation of derivatives using a variety of tools;
3. Have knowledge of the many applications of derivatives across several elds of physical science;
4. Be able to Examine the components of a moving object using the denite integral.
5. Calculate areas between curves using denite integrals;
6. Compute volumes of solids generated from curves using denite integrals;
7. Solve physical problems using integration techniques;
8. Solve elementary dierential equations;
9. Create the Taylor Series of basic functions;
10. Assess the convergence and divergence of power series.
Required Curriculum Content
This course introduces important mathematical concepts that are useful in engineering sciences. Topics cov-
ered include: Rules of dierentiation, related rates, applications of the derivative and optimization problems,
methods of integration, applications of the integral, improper integrals, dierential equations, and an intro-
duction to innite series.
All sections of MATH 6610 Fundamentals of Calculus will cover, as a minimum, the material from Calculus
for Scientists and Engineers, Briggs, Cochran, Gillett. Pearson, 2e, ISBN 9780321826718 (2013), as listed:
Chapter Textbook Topic
1.1 Review of functions
Chapter Textbook Topic
1.2 Representing functions
1.3 Trigonometric functions and their inverses
2 Limits
2.1 The idea of limits
2.2 Denitions of limits
2.3 Techniques for computing limits
2.4 Innite limits
2.5 Limits at innity
2.6 Continuity
3 Derivatives
3.1 Introducing the derivative
3.2 Rules of dierentiation
3.3 The product and quotient rules
3.5 Derivatives as rates of change
3.6 The Chain Rule
3.7 Implicit dierentiation
3.8 Derivatives of logarithmic and exponential functions
4 Applications of the Derivative
4.1 Maxima and minima
4.4 Optimization problems
4.5 Linear approximation and dierentials
4.6 Mean Value Theorem
4.9 Antiderivatives
5 Integration
5.2 Denite integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with integrals
5.5 Substitution rule
6 Applications of Integration
6.1 Velocity and net change
6.2 Regions between curves
6.3 Volume by slicing
6.4 Volume by shells
7 Logarithmic and Exponential Functions
7.2 The natural logarithm and exponential functions
7.4 Exponential models
8 Integration Techniques
8.1 Basic approaches
8.2 Integration by parts
8.4 Trigonometric substitutions
8.7 Numerical integration
8.8 Improper integrals
9 Dierential Equations
9.1 Basic ideas
9.3 Separable dierential equations
9.4 Special rst-order dierential equations
9.5 Modeling with dierential equations
Department Syllabus for MATH 6610, Spring 2019 Page 2 of 6 Rev. 1.0, January 28, 2019
Chapter Textbook Topic
10 Sequences and Innite Series
10.2 Sequences
10.3 Innite series
10.6 Alternating series
11 Power Series
11.2 Properties of power series
11.3 Taylor series
11.4 Working with Taylor series
12 Parametric and Polar Curves
12.1 Parametric equations
12.2 Polar coordinates
Common Department Requirements for MATH 6610
While students in each section of MATH 6610 are assessed by the course instructor, there are general guide-
lines that apply to all sections of MATH 6610. These include:
Calculators and other electronic devices are not allowed on any exams.
Department Syllabus for MATH 6610, 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 6610, 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 6610 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 6610, 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 6610, Spring 2019 Page 6 of 6 Rev. 1.0, January 28, 2019