MATH166: Calculus II

Spring 2021 Syllabus

Building on the foundations of Calculus I, this course explores integration techniques and applications, sequences, series, and differential equations.

Course Description

Calculus II is a continuation of Calculus I, focusing on techniques and applications of integration, infinite sequences and series, power series, and an introduction to differential equations. This course emphasizes both conceptual understanding and computational proficiency, preparing students for further studies in mathematics, physics, engineering, and other quantitative disciplines.

Learning Objectives

Upon successful completion of this course, students will be able to:

• Apply various techniques of integration to solve complex problems
• Use integration to solve applications involving work, fluid pressure, centers of mass, and moments of inertia
• Model and solve problems using first-order differential equations
• Analyze sequences and determine convergence or divergence
• Test infinite series for convergence using appropriate methods
• Express functions as power series and determine their intervals of convergence
• Use Taylor series to approximate functions and estimate errors
• Understand parametric equations and polar coordinates
• Compute lengths of curves and areas in polar coordinates

Required Materials

• Textbook: "Calculus: Early Transcendentals" by James Stewart, 9th Edition
• Online Homework: WebAssign access (included with new textbook purchases or can be purchased separately)
• Calculator: A TI-83, TI-84, or equivalent graphing calculator
• Note: Calculators with computer algebra systems (CAS) like TI-89 or TI-Nspire CAS are not permitted during exams

Grading Policy

Your final grade will be determined based on the following components:

Final grades will be assigned according to the following scale:

• A: 93-100%
• A-: 90-92%
• B+: 87-89%
• B: 83-86%
• B-: 80-82%
• C+: 77-79%
• C: 73-76%
• C-: 70-72%
• D+: 67-69%
• D: 63-66%
• D-: 60-62%
• F: 0-59%

Course Schedule

Week	Dates	Topics	Textbook Sections	Assessments
1	Jan 18-22	Review of Integration Basics	5.1-5.5	None
2	Jan 25-29	Integration by Parts, Trigonometric Integrals	7.1-7.2	Quiz 1, Homework 1
3	Feb 1-5	Trigonometric Substitution, Partial Fractions	7.3-7.4	Quiz 2, Homework 2
4	Feb 8-12	Integration Strategies, Approximate Integration	7.5-7.7	Quiz 3, Homework 3
5	Feb 15-19	Improper Integrals	7.8	Review, Homework 4
6	Feb 22-26	Review, Midterm Exam 1	Chapters 5, 7	Midterm 1 (Feb 25)
7	Mar 1-5	Arc Length, Applications to Physics/Engineering	8.1-8.3	Quiz 4
8	Mar 8-12	Differential Equations	9.1-9.3	Quiz 5, Homework 5
9	Mar 15-19	Spring Break - No Classes	-	None
10	Mar 22-26	Parametric Equations, Polar Coordinates	10.1-10.4	Quiz 6, Homework 6
11	Mar 29-Apr 2	Areas and Lengths in Polar Coordinates, Conic Sections	10.4-10.5	Review, Homework 7
12	Apr 5-9	Review, Midterm Exam 2	Chapters 8, 9, 10	Midterm 2 (Apr 8)
13	Apr 12-16	Sequences, Series	11.1-11.2	Quiz 7
14	Apr 19-23	Integral Test, Comparison Tests	11.3-11.4	Quiz 8, Homework 8
15	Apr 26-30	Alternating Series, Absolute Convergence, Ratio Test	11.5-11.6	Quiz 9, Homework 9
16	May 3-7	Power Series, Representation of Functions	11.7-11.8	Review, Homework 10
17	May 10-14	Taylor and Maclaurin Series, Applications	11.9-11.10	Midterm 3 (May 13)
18	May 17-21	Final Review	All topics	Final Exam Week

Examination Policy

• Three midterm exams will be administered during class time on the dates indicated above.
• The final exam will be cumulative and scheduled during the University's designated exam period (May 18-21).
• All exams are closed-book unless otherwise specified.
• Make-up exams will only be given with a valid documented excuse (such as illness or family emergency). If possible, please notify me before missing an exam.
• Calculators with CAS functionality are not permitted during any exam.
• Photo ID is required for all exams.

Homework Policy

• Online homework assignments will be completed through WebAssign. The due dates are posted on WebAssign.
• Late homework submissions will be accepted for 24 hours after the deadline with a 20% penalty. No submissions will be accepted after this 24-hour grace period.
• Each student has a limited number of attempts for each problem (typically 5).
• While you may discuss homework problems with classmates, your final submissions must be your own work.
• Additional practice problems (not collected) will be suggested from the textbook to reinforce concepts.

Quiz Policy

• Short quizzes will be administered approximately once a week during Friday recitations.
• Quizzes normally cover material from the previous week's lectures and homework.
• Your lowest quiz score will be dropped at the end of the semester.
• No make-up quizzes will be given, but the dropped lowest grade accounts for occasional absences.

Academic Integrity

All students are expected to adhere to the University's Academic Integrity Policy. Any form of academic dishonesty, including but not limited to cheating, plagiarism, unauthorized collaboration, or falsification of data, will result in disciplinary action. For this course:

• All work you submit must be your own.
• You may discuss approaches to problems with others but must write up solutions independently.
• During exams and quizzes, you are not permitted to consult any materials other than those explicitly authorized by the instructor.
• Any violation of these principles will be reported to the Office of Student Conduct and may result in a grade penalty or failure in the course.

Attendance Policy

While attendance will not be explicitly graded, regular attendance is essential for success in this course. Material will be presented in class that may not be covered in the textbook. Additionally, important announcements and exam preparations occur during class time. You are responsible for all material covered in class, regardless of attendance.

Getting Help

If you encounter difficulties in this course, please seek help early. Resources available to you include:

• Instructor office hours: These are dedicated times for you to ask questions about course material.
• Tutoring center: The Mathematics Learning Center offers free tutoring for calculus courses. This semester, due to public health constraints, tutoring will be available online through Zoom at specified times.
• Study groups: Forming study groups with classmates can be an effective way to learn the material.
• Online resources: Supplementary videos and practice problems are available through WebAssign and other platforms like Khan Academy.

Special Accommodations

If you need disability-related accommodations or have emergency medical information to share with me, please make an appointment with me as soon as possible. If you have not yet registered with the Office of Disability Services, please do so before requesting accommodations. The Office of Disability Services contact information is: disabilityservices@university.edu, (555) 123-4567.

Changes to the Syllabus

The instructor reserves the right to make changes to this syllabus as necessary during the semester. Any changes will be communicated during class and posted on the course Blackboard page. Students are responsible for staying informed of any changes.

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