COLLEGE OF ARTS AND SCIENCES

Department of Mathematics and Physics

§ I: MATH 1118 Calculus II Syllabus

Catalog Description

Prerequisite: a grade of C (not C - ) or higher in MATH 1117. Continuation of ﬁrst year calculus, including

the fundamental theorem of calculus, methods of integration, applications of the integral, improper integrals,

and inﬁnite series and introduction to diﬀerential equations. 4 credits

Required Textbook

Calculus: Early Transcendentals, by Briggs, Cochran, Gillett, Pearson, 3e, ISBN 9780134766850 (2019). Students

purchasing the text for MATH 1118 should be aware that each instructor may choose to use or not use the

online homework package oﬀered by the publisher as part of their assessment, e.g., counting online home-

work as part of the student’s grade, however once the seal on the software is broken, the package cannot be

returned for a refund.

All students, regardless of their instructors policies regarding online homework, are encouraged to be-

come familiar with and use online homework as a tool to augment their study of calculus.

Course Objectives

The course, MATH 1118, provides an introduction to the foundations of integral Calculus emphasizing the role

of integrals in many applications. Aside from providing many integration methods, the student is introduced

to many geometric and physical applications. The course aims to provide an introduction to integral Calculus

which will include equally weighted amounts of foundational theory, applications of standard tools, and an

understanding of each problem or concept within mathematics. In addition, developing a ability to work with

sequences and series, including working with the topics of convergence and divergence, are central to the

curriculum. Students developing an appreciation of mathematical thinking and develop an ability to:

1. Examine the components of a moving object using deﬁnite integrals;

2. Calculate areas between curves using deﬁnite integrals;

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

4. Recognize the appropriate integration technique;

5. Generate the required steps in evaluating an integral;

6. Solve basic diﬀerential equations;

7. Examine convergence and divergence of sequences using limits;

8. Assess convergence and divergence of series using a variety of tests;

9. Create the Taylor Series of basic functions; and,

10. Assess the convergence and divergence of power series.

The emphasis is on improved critical thinking skills with regard to using the methods of calculus as an en-

hanced tool for problem solving.

Student Learning Outcomes

After successfully completing this course the expectation is that students will be able to:

1. Examine physical and geometric applications of deﬁnite integrals, CC3.2.3;

2. Recognize the appropriate integration technique;

3. Generate the required steps in evaluating an integral, CC3.2.1;

4. Solve basic diﬀerential equations;

5. Assess convergence and divergence of sequences and series, CC3.2.2; and,

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6. Create the Taylor Series of basic functions, CC3.2.1.

Students will also achieve the following Core Learning Objectives:

7. the student will be able to generate mathematical models based on abstract concepts;

8. justify the correctness of a solution based on assumptions made and known limitations of methods

used; and

9. solve complex mathematical problems involving multiple mathematical forms and techniques or draw

appropriate conclusions as the result of performing quantitative data analysis based on sound assump-

tions regarding estimation and modeling.

Required Curriculum Content

Key topics covered include:

1. Integration: Review basic anti-derivatives, working with deﬁnite and indeﬁnite integrals, noting the ge-

ometric connection with areas under the curves of functions; Develop integration techniques including

the substitution rule, and applications of integration to computing areas under a curve or the area

between two curves, and, applying deﬁnite integrals to compute volumes of solids using the slicing

method, the disk method, and the shell method. Integration is extended to cover the arc length and

surface area.

2. Integration Techniques: Subtle variations on substitutions, integration by parts, trigonometric integrals,

transforming special types of integrals into trigonometric integrals, and partial fractions;

3. Improper Integrals: Solve the two types of improper integrals that involve inﬁnity as a bound or a point

of discontinuity.

4. Diﬀerential Equations: Introduction to basic diﬀerential equations.

5. Sequences and series: Convergence and divergence criteria. convergence tests including the integral,

root, ratio tests; Comparison and the alternating series tests; power series and the approximation of

function by a series; interval and radius of convergence; and Taylor Series:

All sections of MATH 1118 Calculus II will cover, as a minimum, the material from Calculus: Early Transcenden-

tals, by Briggs, Cochran, Gillett, Pearson, 3e, ISBN 9780134766850 (2019), as listed:

Sec Textbook Topic

Chapter 5 – Integration

5.5 Substitution Rule

Chapter 6 – Applications of Integration

6.1 Velocity and Net Change

6.2 Regions between Curves

6.3 Volumes by Slicing

6.4 Volumes by Shells

6.5 Length of Curves

6.6 Surface Area

6.7 Physical Applications

Chapter 7 – Exponential, Logarithmic, and Hyperbolic Functions

7.1 Logarithmic and Exponential Functions Revisited

7.2 Exponential Models

Chapter 8 – Integration Techniques

8.1 Basic Approaches

8.2 Integration by Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitutions

8.5 Partial Fractions

8.6 Integration Strategies

Department Syllabus for MATH 1118, Spring 2019 Page 2 of 7 Rev. 1.0, January 28, 2019

Sec Textbook Topic

8.8 Numerical Integration

8.9 Improper Integrals

Chapter 9 – Diﬀerential Equations

9.1 Introduction to Diﬀerential Equations

Chapter 10 – Sequences and Inﬁnite Series

10.1 An Overview

10.2 Sequences

10.3 Inﬁnite Series

10.4 The Divergence and Integral Tests

10.5 Comparison Tests

10.6 Alternating Series

10.7 The Ratio and Root Tests

Chapter 11 – Power Series

11.1 Approximating Functions with Polynomials

11.2 Properties of Power Series

11.3 Taylor Series

11.4 Working with Taylor Series

Common Department Requirements for MATH 1118

While students in each section of MATH 1118 are assessed by the course instructor, there are general guide-

lines that apply to all sections of MATH 1118. These include:

• Calculators and other electronic devices are not allowed on any exams.

Department Syllabus for MATH 1118, Spring 2019 Page 3 of 7 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 this course without it appearing on your transcript is discussed on the

Academic Schedules and Registration web page. After the ﬁrst week of class, self-service registration will

not be enabled for students to directly add or drop classes. Students should contact the Registrar’s oﬃce

directly or the Academic Success Center for assistance with adding and dropping courses during this time.

Attendance Regulations

University attendance policy guidelines require that:

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. A dismissed

student will receive a withdrawal (W) from the course if they are still eligible for a withdrawal per the university

Withdrawal from a Course policy, or a failure (F), if not. A student who is not oﬃcially registered in the course

is not permitted to attend classes or take part in any other course activities. Students absent from any class

meeting are responsible for making up missed assignments and examinations at the discretion of the instructor.

Students are to adhere to the policy attendance policy guidelines outlined in the University Catalog under the

heading, Attendance Regulations, found online in the Undergradaduate Catalog or alternatively found in the

Student Handbook on pp.4849.

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. The College provides that,

Instructors should try to avoid scheduling exams or quizzes on religious holidays, but where such conﬂicts occur

should provide reasonable accommodations for missed assignment deadlines or exams. If a class, an assign-

ment due date, or exam interferes with the observance of such a religious holiday, it is the student’s responsibil-

ity to notify their instructor, preferably at the beginning of the term, but otherwise at least two weeks before the

holiday.

More information about religious observance policies can be found in the Student Handbook on pp.4849

under the heading, Attendance Policies: Religious Observance Policy for Students.

Withdrawal from a Course

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

line Course Withdrawal Form, or alternatively complete and hand in the pdf based Course Withdrawal Form.

The ﬁnal date to request a withdrawal is listed in the Academic Calendar. This request must be submitted to

the Registrar’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 Grade Policy

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

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Please note that it is the responsibility of the student to assure that the required paperwork and documentation is completed by the deadline.

Department Syllabus for MATH 1118, Spring 2019 Page 4 of 7 Rev. 1.0, January 28, 2019

of the term. In the absence of the instructor a student should contact the Department Chair. 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 incomplete grades

must be completed no later than the last day of the spring term. Spring and summer course incomplete grades

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 discussed in the Academic Catalog under the heading, Incom-

plete (INC) Grade Policy.

Academic Integrity Policy and Procedures

The University of New Haven expects its students to maintain the highest standards of academic conduct.

Academic dishonesty is not tolerated at the University. To know what it is expected, students are responsible

for reading and understanding the statement regarding academic honesty in the Student Handbook. Specif-

ically, students are required to adhere to the Academic Integrity Policies speciﬁed in the Student Handbook,

i.e., on pp.6673.

Please ask your instructor about their expectations regarding permissible or encouraged forms of student

collaboration if there is any confusion about this topic. The Department of Mathematics and Physics 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 University’s policy on Academic Integrity. Please ask about expectations regarding permissible or encouraged

forms of student collaboration if they are unclear.

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 in the Academic Catalog under the heading, Course Work Expectations.

Please note, that MATH 1118 is a 4-credit course, and as such requires a total of 12 hours per week invested

in study and homework for the average student.

Commitment to Positive Learning Environment

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 online information about is available at Title IX.

Reporting Bias Incidents

At the University of New Haven, there is an expectation that all community members are committed to cre-

ating and supporting a climate which promotes civility, mutual respect, and open-mindedness. There also

exists an understanding that with the freedom of expression comes the responsibility to support community

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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 1118, Spring 2019 Page 5 of 7 Rev. 1.0, January 28, 2019

members’ right to live and work in an environment free from harassment and fear. It is expected that all mem-

bers of the University community will engage in anti-bias behavior and refrain from actions that intimidate,

humiliate, or demean persons or groups or that undermine their security or self-esteem.

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. Further information about this and other

reporting options may be found at Report It.

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 academic issues you may have with your instructor,

advisor, or with the the courses or department coordinator or chair, the University provides these additional

resources for students:

The Center for Academic Success and Advising (CASA)

The Academic Success Center is located in Maxcy 208 for help with your academic studies, or call 203-932-

7234 to set up an appointment.

University Writing Center

The mission of the Writing Center (an expansion of the Writer to Writer peer-tutoring program) is to provide

high-quality tutoring to undergraduate and graduate students as they write for a wide range of purposes and

audiences. Tutors are undergraduate and graduate students and they work with students at any stage in the

writing process; Bring in your assignment, your ideas, and any writing done so far. To make an appointment,

register for an account at https://newhaven.mywconline.com.

The Math Zone

Please contact the Math Zone if you wish to challenge your Math Placement by taking a Math Challenge Exam

or by taking a Math Post Placement Exam. These are discussed more extensively at http://math.newhaven.

edu/mathphysics/placement_html. The Math Zone also provides a range of tutoring and classroom support

service for students taking development math classes.

The Center for Learning Resources (CLR)

The Center for Learning Resources 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.

Accessibility Resources Center

Students with disabilities are encouraged to share, in conﬁdence, information about needed speciﬁc course

accommodations. The Accessibility Resources Center (ARC) provides comprehensive services and sup-

port that serve to promote educational equity and ensure that students are able to participate in the oppor-

tunities available at the University of New Haven. Accommodations cannot be made without written docu-

mentation 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 Com-

pliance 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 1118, Spring 2019 Page 6 of 7 Rev. 1.0, January 28, 2019

Counseling and Psychological Services

The Counseling Center oﬀers a variety of services aimed at helping students resolve personal diﬃculties and

acquire the balance, skills, and knowledge that will enable them to take full advantage of their experience at

the University of New Haven. Information about the, Counseling and Psychological Services, is available

online.

Department Syllabus for MATH 1118, Spring 2019 Page 7 of 7 Rev. 1.0, January 28, 2019