# Calculus 1

### Syllabus

## Office Hours

TBA at the beginning of each semester (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 2 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. Limits2. Infinite Limits, Limits at Infinity, Horizontal and Vertical Asymptotes

3. Continuity. Squeeze Theorem. Applications of Limits

4. The Derivative, the Rate of Change

5. Finding and Using Derivative

6. Higher Derivatives. Differentiability

(Exam 1)

7. The Product, Quotient, and Chain Rules

8. Derivatives of Exponential, Logarithmic and Trigonometric Functions

9. Linear Approximation. Differentials

10. Implicit Differentiation

11. Related Rates

(Exam 2)

12. Increasing/Decreasing Test. Extreme Values and the First Derivative Test

13. Concavity and Inflection Points. The Second Derivative Test

14. Absolute Extrema and Constrained Optimization

(Exam 3)

15. Antiderivatives and the Indefinite Integral

16. Substitution

17. Integrals of Exponential and Trigonometric Functions. Integrals Producing Logarithmic Functions

18. Definite Integral. Left and Right Sums

19. Fundamental Theorem of Calculus. The Total Change Theorem.

20. Areas between Curves

## 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.

## Grading

Exams 1, 2 and 3 | 18% each |

Final Exam | 24% |

Assignments | 11% |

Projects | 11% |

TOTAL | 100% |

A | A- | B+ | B | B- | C+ | C | C- | D+ | D | F | |

grade | 93-100 | 90-92 | 87-89 | 83-86 | 80-82 | 77-79 | 73-76 | 70-72 | 67-69 | 60-66 | 0-59 |

## Number of credits

4

## Prerequisites

Precalculus or permission of instructor

This is a rigorous course. You should plan to spend a minimum of twice the number of class hours on reading, homework assignments, and practice problems. The assigned homework is the minimum amount of practice you should complete. It is your responsibility to come to class prepared to ask questions on any covered concept.

## 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 in-class exams**plus a

**two hour comprehensive 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 homework assignments**and

**three Matlab projects**. There will be no makeup assignments. Assignments or projects turned in after their due date will receive an automatic reduction in grade.

**No assignment and 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

- to obtain a well rounded introduction to the area of limits, differentiation and basic integration techniques;
- to develop basic knowledge of calculus problem formulation, problem solving and modeling techniques required for successful application of mathematics;
- to competently use 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:- know the basic concepts of differential and integral calculus;
- demonstrate proficiency in differentiation and integration techniques;
- be able to interpret and critique graphs using calculus techniques;
- be able to understand and solve multidisciplinary application problems using calculus;
- demonstrate proficiency in using mathematical software;
- know how to use appropriate technology to solve problems applying calculus techniques.