MA 221 Calculus 2


handouts syllabus pdf flier photographs

Office Hours

Monday 1-2, Thursday 4-5, Friday 1-3 (no appointment necessary). Feel free to make an appointment if you cannot come to my regular office hours.


No textbook required. Handouts with new material and practice problems will be distributed for each teaching unit. Also Review Sheets will be distributed in class before every exam. The material of this course (as well of Calculus 1 and Calculus 3) matches Calculus by James Stewart.


All students are required to have a graphing calculator. Instructions will be given for TI83/84.

Topics Covered

1. Review of Differentiation. Derivatives of Exponential and Logarithmic Functions.
2. Indefinite Integrals. Substitution.
3. Definite Integrals. Left and Right Sum
4. The Fundamental Theorem of Calculus
5. Areas between Curves
6. Volumes (cross-sections)
7. Volumes (shells)
8. Work. Average Value of a Function
9. Trigonometric, Inverse Trigonometric Functions and their Derivatives and Integrals
10. L'Hopital's Rule
(Exam 1)

13. Integration by Parts
14. Trigonometric Integrals
15. Partial Fractions
16. Improper Integrals
17. Approximate Integration: Trapezoidal and Simpson's Sum
18. Arc Length and Area of a Surface of Revolution
(Exam 2)

19. Differential Equations. Separable Equations
20. Direction Fields. Euler's Method
21. Autonomous Differential Equations and Population Dynamics
22. Modeling with Differential Equations. Applications
23. Linear Equations
24. Curves defined by Parametric Equations
25. Derivatives of Parametric Curves. Area
26. Arc Length and Surface Area of a Parametric Curve
(Exam 3)

27. Polar Coordinates
28. Areas and Lengths in Polar Coordinates
29. Taylor Polynomial

Tentative exam dates

Exam 1: during the 5th week of classes.
Exam 2: during the 9th week of classes.
Exam 3: during the 12th week of classes.
Final Exam: during the finals week.


Exams 1, 2 and 318% each
Final Exam24%
Grades are computed according to the following system:
A+ A A- B+ B B- C+ C C- D+ D D- F
grade 97-100 93-96 90-92 87-89 83-86 80-82 77-79 73-76 70-72 67-69 63-66 60-62 0-59

Number of credits



MA122 or MA110 or permission of instructor


It is imperative that students attend all classes. Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.


There will be three semester exams and a cumulative final exam. No makeup exam will be given unless the excuse for missing the scheduled exam is acceptable to the instructor. Any makeup exam must be taken before the next regularly scheduled exam. No exam grade will be dropped.

Assignments and Projects

There will be four assignments and two Matlab projects during the semester. There will be no makeup assignments. Assignments or projects turned in after their due date will receive an automatic reduction in grade. No assignment or project grade will be dropped.

Response time

The assignments, projects and exams are typically graded in three days after they are turned in. Special circumstances like snow days, school closing or holidays, may occasionally delay the response time. Barring special circumstances, students’ emails are usually responded to within one working day.

Course Objectives

  • Obtain a well rounded introduction to the area of integration techniques, applications of integrals, differential equations and parametric and polar functions.
  • Deepen students' knowledge of problem formulation, problem solving and modeling techniques required for successful application of mathematics obtained in previous calculus courses.
  • Competently use appropriate technology to model data, implement mathematical algorithms and solve mathematical problems.
  • Cultivate the analytical skills required for the efficient use and understanding of mathematics.

Learning outcomes

Students will:
  • be able to demonstrate proficiency in integration techniques;
  • be able to use functions in parametric form and in polar coordinates;
  • model and solve problems using the first order differential equations;
  • be able to demonstrate the use of calculus in problem solving;
  • know how to use appropriate technology to solve problems applying calculus techniques;
  • demonstrate proficiency in using mathematical software.

Academic integrity

Academic integrity is at the center of the educational experience at USciences. Students are therefore expected to uphold the highest standards of academic integrity and not engage in or tolerate academic dishonesty. Academic dishonesty includes, but is not limited to, fabrication, cheating or plagiarism, and unauthorized collaboration. Any violation of academic integrity will be investigated and, where warranted, the student will receive appropriate sanctions through the University's Student Conduct Process. Please familiarize yourself with the current USciences Student Handbook. Adheren ce to the Student Conduct Policy and Academic Integrity Policy will help to ensure that your learning and living experiences are founded on integrity.

Americans with Disabilities Act (ADA) Compliance Statement

USciences supports the educational endeavors of all students, including students with disabilities. ADA defines a disability as a mental or physical impairment that substantially limits one or more major life activities. If you believe that you have a disability that may impact your ability to fulfill your course or degree requirements, and you would like more information on applying for an accommodation under ADA, please contact the Administrator of Student Accommodations at 215-596-8758.

Mental Health Wellness Statement

USciences encourages students to recognize that academic success requires students to be emotionally and physically well. If you are having difficulty coping with stress associated with the classroom or are experiencing other personal issues, please go to USciences Health and Counseling (SHAC) located on the first floor of Whitecar Hall or call 215.596.8536. Additional emotional support is available 24/7 and can be obtained by contacting the National Suicide Prevention Hotline at 800.273.8255 or by texting “Go” to the Crisis Text Line 741-741. The services listed above are all free and confidential.