Calculus II (MA 1022-B25)
Department of Mathematical Sciences
Worcester Polytechnic Institute
Instructor: Prof. B.S. Tilley
Department of Mathematical Sciences
Worcester Polytechnic Institute
Instructor: Prof. B.S. Tilley
Contact Information
Instructor: Prof. B.S. Tilley
Office: SH 419
E-mail: tilley@wpi.edu
read between 9am-5:30pm.
Weekdays: reply within 24 hours
Weekends: reply within 48 hours
Web: https://users.wpi.edu/~tilley
Office Hours (no appt. needed):
Mon/Thurs: 4:00pm-4:50pm, Fri: 3:00-3:50pm
PLA: Michael Herchenroder
E-mail:
Office Hours (no appt. needed):
TBA
Meeting Times:
Lecture: BL08: MTRF 2:00-2:50 am AK 116
Discussion: BD08: T 4:00-4:50 am SH 205
BD17: T 3:00-3:50 am SH 207
Course Description: This course provides an introduction to integration and its applications. Topics covered include: inverse trigonometric functions, Riemann sums, fundamental theorem of calculus, basic techniques of integration, volumes of revolution, arc length, exponential and logarithmic functions, and applications of integration to engineering.
Although the course will make use of computers, no programming experience is assumed.
Recommended Background: MA 1020 or MA 1021
Behavior Expectations: Collaborative learning and active engagement are expected. Collaborative learning means that students collaborate together to learn the material in the course. Active engagement by students means that students accept the responsibility for their own learning of the material and do not perceive the instructor (Professor, TA, or PLA) as a source of all knowledge.
In order to meet these expectations, the classroom environment must be professional and supportive. Students are expected to treat each other with mutual respect, provide constructive feedback to other students, and to realize that as humans we all need guidance at times.
At the conclusion of this course, students will be able to:
Find antiderivatives of a function
Use the Fundamental Theorem of Calculus for definite and indefinite integrals
Find the area of plane regions using integration
Use the techniques of substitution, integration by parts, trigonometric substitution, and partial fractions to evaluate indefinite integrals
Use integration to find volumes of revolution, arclength, and surfaces of revolution.
Find the moment and center of mass of a two-dimensional object.
Interpret and solve applied problems related to exponetial growth and decay.
Basic understanding of elementary techniques in numerical integration.
Pass a Basic Skills test administered by the Mathematics Department
Course Organization
The class typically meets 5 times per week: 4 lectures on MTRF, and 1 discussion section on T, along with 3 computer laboratory sessions over the term. Students are responsible for all material presented in lecture and discussion, along with the specific textbook sections presented each week. Each week will have a theme:
Week 1: Antiderivatives, Riemann Sums, Definite Integrals
Week 2: Fundamental Theorem of Calculus, U-Substitution
Week 3: Integration by Parts, Trigonometric Integrals
Week 4: Partial Fractions, Area Between Curves
Week 5: Applications: Volumes using Cross Sections, Arclength, Surface Areas of Revolution, Centers of Mass
Week 6: Logarithm Defined as an Integral, Exponential Growth, Numerical Integration, Trigonometric Substitution
Week 7: Summary and Review.
For more details, see the Lecture Schedule link above.
Class Materials:
Canvas: Course materials can be found on the Canvas page. The material is organized by Week and then by topic. In the event that lectures need to be delivered remotely, they will take place through Zoom.
Class Meeting Format
Lectures (MTRF): Initial presentation of the material which will vary in terms of theory and practice. Students are expected to attend lecture to participate in the class, such as asking questions. The afternoon lecture will be recorded on Echo 360, my lecture notes are typically posted on Canvas a day before lecture to help students prepare, and the lecture slides used in the lecture will be posted on Canvas after the lecture. Students are not expected to be expert in the topic of the lecture by the end of the lecture.
Discussion (T): Opportunity for students to ask specific questions on a homework or any relevant topic covered in the class so far, and a space for students to work on their assignments with the PLA present. No lectures are given during this time.
Students are expected to spend an additional 8-12 hours per week studying outside of class: reading the text, organizing notes, and solving problems. In previous years, the average time, self-reported, spent outside of class on this course is 10 hours
Course Grades and Policies
Grading:
Grades will be determined based on homework assignments, labs, and in-person quizzes and exams:
WebWorK: 5%: There will be assignments using this online tool to understand your basic knowledge of the topics for that day's lecture. You receive full credit for correct answers, independent of the number of attempts made. The assignments are due on the last day of class (December 12, 2025, 11:59pm). However, "due dates" for these assignments are given in Canvas so that you can maintain an appropriate pace in the course.
Quizzes: 10%: During Discussion, students will take a 20-minute in-person written quiz based on the prior week's WebWorK assignments. These quizzes will take place on October 21, 2025, October 28, 2025, November 11, 2025, November 18, 2025, and December 2, 2025, The top four quiz scores count toward this quiz average.
Labs: 10% During this term, you will attend 3 in-person lab sessions. In each session, a short lecture will be presented, and then you will have time to start working on the lab assignment in groups of two or three. The lab assignments extend the ideas presented in lecture as well as explore applications of the material using a variety of software.
All logistical information related to the labs may be found on the Calculus 2 Lab Canvas site for your section.
The dates of the in-person sessions are,
Riemann Sum Approximations: Wednesday October 22, 2025 and Thursday October 23, 2025 (Due October 29)
Inverses and Arclength: Wednesday November 5, 2025 and Thursday November 6, 2025 (Due November 12)
Trapezoidal Rule: Wednesday November 19, 2025 and Thursday November 20, 2025 (Due December 3)
All questions/ concerns related to the labs should be directed to the lab instructors :
Jane Bouchard bouchard@wpi.edu
Caroline Labenski clabenski@wpi.edu
Basic Skills Test: 5%. This, closed book, no electronics, no calculator, no-partial-credit test must be passed in order for a student to pass the course. Students will have multiple opportunities to pass this requirement over the course of the term. A pass on this exam earns the full 10% credit, a fail on this exam earns no credit. Some dates where the exam is given in OH 107, 5pm-6pm: TBD. Students can also make an appointment to take the exam in my office, with the days/times to be determined.
Two In-Lecture Exams: 40% Two in-class 45-minute exams will take place at the dates below. Exams are closed book, closed notes, no calculators and no use of any electronic devices. The better score is worth 25% and the worse score is worth 15%. The exam dates are: Exam 1: November 3, 2025 and Exam 2: November 25, 2025
Final Exam: 30% This exam takes place on December 11, 2025 at 7:00pm-9:00pm. This exam is a comprehensive exam.
Grading Policy: Students have two business days after grades are posted to contact the instructor about potential errors in grading any assignment (homework or exams) after receiving their graded work via Gradescope. Beyond this time, the grade on that assignment is final.
Generative AI Policy: Students should feel free to find online resources that describe the Calculus topics covered here that may present the material in a different style or structure that may be helpful. These resources are designed with the intention to aid students in learning the material. Generative AI tools like Gemini, Chat-GPT, or Copilot, are more general use tools to help the user find potentially relevant information quickly and in a format that appears conversational. Do: experiment with it and use if for brainstorming, and do cite the source/engine when communicating the output, Do not: give an assignment prompt as input and paste the output as your submission. Students who submit AI-generated content as their own work will receive no credit for that work.
Accommodations: Students with approved academic accommodations should plan to submit their accommodation letters through the Office of Accessibility Services Student Portal. Should you have any questions about how accommodations can be implemented in this particular course, please contact me as soon as possible. Students who are not currently registered with the Office of Accessibility Services (OAS) but who would like to find out more information about requesting accommodations, documentation guidelines, and what the accommodated interactive process entails should plan to contact OAS either by email: AccessibilityServices@wpi.edu, by phone (508) 831-4908, or by stopping by the office on the 5th floor of Unity Hall.
Final Grades
The final grades will follow the approximate distribution
90%-100% A
80%-89% B
70-79% C
0% - 70% NR