MA222 Calculus 3
Monday 12-1, Thursday 3-5, Friday 12-1 (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 Covered1. Three Dimensional Coordinate System. Introduction to Surfaces in Space
2. Review of Vectors. Dot and Cross Products
3. Lines and Planes in Space
4. Space Curves. Derivatives and Integrals of Curves. Arc Length
5. Functions of Several Variables
6. Partial Derivatives. Chain Rule
7.Tangent Planes. Gradient Vector. Linear Approximations
8. Maximum and Minimum Values
9. Lagrange Multipliers
10. Double Integrals. Double Integrals in Polar Coordinates
11. Surface Area. Applications
12. Parametric Surfaces
13. Triple Integrals. Substitution in Triple Integrals
14. Line Integrals
15. Fundamental Theorem.
16. Green's Theorem. Curl and Divergence
17. Sequences. Series
18. Convergence of Series and Convergence Tests
19. Power Series
20. Taylor Series
Tentative exam datesExam 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 3||18% each|
Number of credits
AttendanceIt 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.
ExamsThere 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.
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.
- 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 the 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 outcomesStudents will:
- be able to demonstrate the 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 a proficiency in using mathematical software.