COLLEGE OF ARTS AND SCIENCES

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 diﬀerentiation 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 diﬀerential and integral Calculus em-

phasizing the role of derivatives and integrals in many applications. Aside from providing many diﬀerentiation

and integration methods, the student is introduced to many geometric and physical applications. The course

aims to provide an overview of both diﬀerential 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, diﬀerential 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 Proﬁcient in the calculation of derivatives using a variety of tools;

3. Have knowledge of the many applications of derivatives across several ﬁelds of physical science;

4. Be able to Examine the components of a moving object using the deﬁnite integral.

5. Calculate areas between curves using deﬁnite integrals;

6. Compute volumes of solids generated from curves using deﬁnite integrals;

7. Solve physical problems using integration techniques;

8. Solve elementary diﬀerential 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 diﬀerentiation, related rates, applications of the derivative and optimization problems,

methods of integration, applications of the integral, improper integrals, diﬀerential equations, and an intro-

duction to inﬁnite 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

Functions

1.1 Review of functions

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Chapter Textbook Topic

1.2 Representing functions

1.3 Trigonometric functions and their inverses

2 Limits

2.1 The idea of limits

2.2 Deﬁnitions of limits

2.3 Techniques for computing limits

2.4 Inﬁnite limits

2.5 Limits at inﬁnity

2.6 Continuity

3 Derivatives

3.1 Introducing the derivative

3.2 Rules of diﬀerentiation

3.3 The product and quotient rules

3.5 Derivatives as rates of change

3.6 The Chain Rule

3.7 Implicit diﬀerentiation

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 diﬀerentials

4.6 Mean Value Theorem

4.9 Antiderivatives

5 Integration

5.2 Deﬁnite 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 Diﬀerential Equations

9.1 Basic ideas

9.3 Separable diﬀerential equations

9.4 Special ﬁrst-order diﬀerential equations

9.5 Modeling with diﬀerential equations

Department Syllabus for MATH 6610, Spring 2019 Page 2 of 6 Rev. 1.0, January 28, 2019

Chapter Textbook Topic

10 Sequences and Inﬁnite Series

10.2 Sequences

10.3 Inﬁnite 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 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 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 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 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 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 6610, 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 6610, Spring 2019 Page 6 of 6 Rev. 1.0, January 28, 2019