MA222 Calculus 3


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Office Hours

Office hours in Spring 2022 will be by appointment. Please feel free to make an appointment whenever you have a question, no matter if it is longer or a quick one, or when you would like to work on a problem together with me.


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:
  • 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,
  • demonstrate proficiency in using mathematical software,
  • know how to use appropriate technology to solve problems applying calculus techniques.

Academic integrity

Saint Joseph’s University encourages the free and open pursuit of knowledge; we consider this to be a fundamental principle and strength of a democratic people. To this end, SJU expects its students, its faculty, its administrators, and its staff to uphold the highest standards of academic integrity. The University expects all members of the University community to both honor and protect one another’s individual and collective rights.

Student with Disabilities Statement

Reasonable academic accommodations may be provided to students who submit appropriate documentation of their disability. If students have need of assistance or questions with this issue, they are encouraged to contact the Office of Student Disability Services (SDS) at or by phone at 610.660.1774. The Office of SDS also provides an appeal/grievance procedure for complaints regarding requested or offered reasonable accommodations. More information can be found at:

Health and Wellness Statement

Saint Joseph's University recognizes that physical and mental health strongly impact one's ability to do well in school and in life. As a result, there are many helpful campus resources designed to help students to care for their physical, mental, and spiritual health. Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressure and challenges associated with relationships, mental health, alcohol or other drugs, identities, finances, etc. All of us benefit from support during times of struggle and challenges. If you are experiencing concerns, seeking assistance sooner rather than later is a courageous thing to do for yourself and those who care about you. The resources at can help you to cope with stress and to achieve your academic and personal goals.

COVID-19 policy

SJU's Covid-19 policy is available at: . In particular, it states that all faculty, staff, students and visitors are asked to carry a mask at all times while on campus and that they should wear it if asked to. Since my office is relatively small, please note that I ask you to wear a mask when you are in my office.