# Calculus Review

In this course you will learn how to define and describe informally the limit of a function and apply this limit to the tangent line problem. This leads to the idea of a derivative of a function, which you will learn to apply. You will also learn how to define and describe informally the integral, use the integral to answer area problems, and apply integration to the statistics problem of estimating probability density functions.

## Overview

This course is a three-week primer on calculus. Calculus at this level concerns itself with three primary concepts: the limit, the derivative and the integral. Applications involving statistics supplement the more traditional calculus examples.

• Introductory
• 3 Weeks
• Expert Instructor
• Tuiton-Back Guarantee
• 100% Online
• TA Support

## Learning Outcomes

In this course you will learn how to:

• define/describe informally the limit of a function
• apply this limit to the tangent line problem, which leads to the idea of a derivative of a function.
• apply derivatives
• define/describe informally the integral
• use the integral to answer area problems,
• apply integration to the statistics problem of estimating probability density functions

## Who Should Take This Course

Anyone planning to study topics in statistics beyond the introductory level.

## Our Instructors

#### Ms. Anuja Kulkarni

Ms. Anuja Kulkarni has managed and taught over 125 online course sessions and more than 1000 students as an Assistant Teacher at The Institute for Statistics Education. She holds a Masters’ degree in Statistics from Kolhapur University, India, where she also taught undergraduate statistics. Ms. Kulkarni teaches Statistics, Optimization Methods and Predictive Analytics and assists in several other course topics here for over six years. In all, her passion is leading new students into the fascinating and practical world of statistics through the introductory statistics course series at The Institute.

## Course Syllabus

### Limits, The Derivative

• Equations
• Lines & Slopes
• Functions
• Algebraic Properties of Functions
• Limits
• Tangent lines and derivatives
• Power Rule
• ProductRule
• Quotient Rule
• Derivative of a Sum of Functions

### Applications of the Derivative, The Integral

• Extreme Values
• First Derivative Test
• Optimization
• Example: Maximization
• Example: Maximum Likelihood
• Differentials
• Riemann Sum
• Definite integral

### Integration

• Fundamental Theorem of Calculus
• Antiderivatives
• CDF (cumulative density function)
• Indefinite integral
• Integration
• Moment generating functions

## Class Dates

### 2023

09/29/2023 to 10/20/2023
Instructors: Ms. Anuja Kulkarni

### 2024

04/26/2024 to 05/17/2024
Instructors: Ms. Anuja Kulkarni
09/27/2024 to 10/18/2024
Instructors: Ms. Anuja Kulkarni

### 2025

02/14/2025 to 03/14/2025
Instructors: Ms. Anuja Kulkarni
04/25/2025 to 05/23/2025
Instructors: Ms. Anuja Kulkarni
09/26/2025 to 10/17/2025
Instructors: Ms. Anuja Kulkarni

## Prerequisites

Familiarity with algebra

## Register For This Course

Calculus Review

#### Homework

There are assignments in this course. These will be marked by an assistant teacher, but whether you need to be concerned with these marks depends on your purpose in taking the course. Some students are interested just in learning for learning’s sake, others may require a Record of Completion showing they have completed a course, some may need academic credit (offered in selected courses only) and some are enrolled in a Programs in Analytics and Statistical Studies (PASS).

#### Course Text

We will use the short text Calculus, by Gudmund R. Iversen for readings. This text is a little short on examples, so there are lengthy course notes to accompany the text prepared for each of the three weeks. These notes are in PDF format and are intended to be printed, if desired. They have a wide right margin for taking notes, a style borrowed from Edward Tufte’s texts.

#### Software

Examples of using Sage to solve various problems are given. Sage is a free-to-use, open-source software system that can do symbolic mathematics and is available at no charge at Sage Notebook.

Calculus Review