MA222 Calculus 3


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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 texbook required. Handouts with course 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 2) matches Calculus by James Stewart.


All students are required to have a graphing calculator.

Topics Covered

1. Three Dimensional Coordinate System. Introduction to Surfaces in Space
2. Vectors. The Dot and Cross Products
3. Equations of Lines and Planes
4. Space Curves. Tangent lines. Arc Length
5. Partial Derivatives
6. Tangent Planes. Gradient Vector. Linear Approximations
7. Partial Derivatives. Chain Rule
(Exam 1)

8. Maximum and Minimum Values
9. Lagrange Multipliers
10. Double Integrals. Double Integrals in Polar Coordinates
11. Surface Area. Applications
(Exam 2)

12. Parametric Surfaces
13. Triple Integrals. Substitution in Triple Integrals
14. Line Integrals
15. Fundamental Theorem.
16. Green's Theorem. Curl and Divergence
(Exam 3)

17. Sequences. Series
18. Convergence of Series and Convergence Tests
19. Power Series
20. Taylor Series

(Final Exam)

Tentative exam dates

Exam 1: During the 4th week of classes
Exam 2: During the 7th week of classes
Exam 3: During the 11th 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



Calculus 2.


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 turned in after their due date will receive an automatic reduction in grade. No assignment, project or exam 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 multivariable function calculus and number and power series.
  • Deepen students' knowledge of problem formulation and problem solving 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 multivariable function calculus and number and power series,
  • be able to differentiate and integrate multivariable functions,
  • be able to use multivariable 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.