# Spring 2017: MTH 161

# MTH 161: Calculus IA

# General Information

## Instructors

**Irina Bobkova****Class time:**MW 2:00 – 3:15 p.m.**Class location:**Gavett 310**Office:**Hylan 801**Office Hours:**M 4:40 – 6:00 p.m., W 4:40 – 5:20 p.m.**E-mail:**ibobkova@ur.rochester.edu**Qiaofeng Zhu****Class time:**MW 4:50 – 6:05 p.m.**Class location:**Gavett 310**Office:**Hylan 717**Office Hours:**W 3:30-4:30 p.m. or by appointment**E-mail:**q.zhu@rochester.edu

## Workshop Schedule

Time |
Location |
TA |

Thursday 4:50-6:05 pm | Hylan 203 | Daniel Luftspring |

Thursday 12:30-1:45 pm | Hylan 1106B | Shashank Chorge |

Thursday 2-3:15 pm | Hylan 1106B | Shashank Chorge |

Tuesday 12:30-1:45 pm | Hylan 305 | Shashank Chorge |

Wednesday 3:25-4:40 pm | Hylan 105 | Karan Vombatkere |

## Workshop TAs

**Shashank Chorge****E-mail:**schorge@ur.rochester.edu**Daniel Luftspring****E-mail:**daniel.luftspring@rochester.edu**Karan Vombatkere****E-mail:**kvombatk@u.rochester.edu

## WeBWorK TA

**Yuxin Wang****E-mail:**ywang211@u.rochester.edu

Please note that the office hours of all instructors and TAs are open to all students taking the course, regardless of which section and workshop they are registered for.

### Textbook

*Calculus: Early Transcendentals*, 8th edition by James Stewart.

You can use any edition. The material in the book does not change significantly between editions. The suggested exercises for each section are numbered according to the 8th edition. There may be changes in exercises numbering between editions.

# Course description

MTH 161 is designed to provide a detailed introduction to the fundamental ideas of calculus. It does not assume any prior calculus knowledge, but the student is expected to be proficient working with functions and their graphs as well as manipulating expressions involving variables and solving equations using algebra. There will be a **brief** review of algebra, trigonometry, and precalculus, but students are expected to have sufficient understanding of Chapter 1 and Appendices A, B, and D in the textbook.

Throughout most of this course, we will work to solve the following problem:

Given a changing quantity, how do you calculate the exact rate of change of that quantity at a given point in time?

Or, equivalently:

Given a curve in the Cartesian plane, what is the slope of the curve at any given point?

In order to solve this, we will first cover the notion of limits, as this is necessary for understanding the definition of the instantaneous rate of change, or *derivative*. We’ll then move on to the definition of the derivative. Even though we will learn many rules to simplify the task of calculating derivatives, there will be many times that you will be expected to use the limit definition in order to calculate the derivative of a function. We will also cover standard applications of derivatives, including answering the above questions, and all of the derivative rules. During the last few weeks of the semester, we’ll move on to answering the next big question in calculus – the area question:

Given a curve in the Cartesian plane, what is the area under the curve?

In order to solve this question, we will again use limits in approximating the area under the curve. This will lead us to the definition of the *integral*, which we will then relate back to the derivative using the Fundamental Theorem of Calculus. We’ll cover only a few methods for calculating integrals; other methods will be covered in Calculus IIA (MTH 162).

# Course Objectives

At the end of this semester, you should be able to do the following:

- Calculate limits of functions; explain the relationship between a function and its graph and its limit at a point.
- Define a derivative using limits and explain its geometric significance; evaluate derivatives of various functions.
- Apply the concepts of limits and derivatives to real-world problems and curve sketching.
- Analyze the connection between derivatives and integrals in the context of the Fundamental Theorem of Calculus.
- Evaluate basic integrals using antiderivatives and substitution; recognize the geometric significance of an integral.