# MA 221 Calculus 2

### Syllabus

## 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.

## Textbook

**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.

## Technology

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.

## 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 |

## Number of credits

4

## Prerequisites

MA122 or MA110 or permission of instructor

## Attendance

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.## 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 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.