# MA222 Calculus 3

### Syllabus

## Office Hours

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

## Textbook

**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.

## Technology

All students are required to have a graphing calculator.

## Topics Covered

1. Three Dimensional Coordinate System. Introduction to Surfaces in Space2. 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

(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 classesExam 2: During the 7th week of classes

Exam 3: During the 11th week of classes

Final Exam: During the Finals week.

## Grading

Exams 1, 2 and 3 | 18% each |

Final Exam | 24% |

Assignments | 11% |

Projects/Presentation | 11% |

TOTAL | 100% |

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 |

## Prerequisites

Calculus 2.

## Attendance

Since the course is mostly based on material covered in class handouts and classwork, it is absolutely**IMPERATIVE that students attend ALL classes**. Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.

## Exams

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**.

## Course Objectives

- to obtain a well rounded introduction to the area of multivariable function calculus and number and power series;
- to deepen students' knowledge of problem formulation and problem solving techniques required for successful application of mathematics obtained in previous calculus courses;
- to competently use the appropriate technology to model data, implement mathematical algorithms and solve mathematical problems;
- to cultivate the analytical skills required for the efficient use and understanding of mathematics.

## Learning outcomes

Students 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 demonstrate the use of multivariable calculus in problem solving;
- know how to use appropriate technology to solve problems applying calculus techniques;
- demonstrate a proficiency in using mathematical software.