This first course on concepts of single variable calculus will introduce the notions of limits of a function to define the derivative of a function. In mathematics, the derivative measures the sensitivity to change of the function. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. This fundamental notion will be applied through the modelling and analysis of data.
![Johns Hopkins University](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera-university-assets.s3.amazonaws.com/74/7ae340ec6911e5b395490a2a565172/JHU-Logo-Square-Mini_180px.png?auto=format%2Ccompress&dpr=1&w=28&h=28)
![Johns Hopkins University](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera-university-assets.s3.amazonaws.com/74/7ae340ec6911e5b395490a2a565172/JHU-Logo-Square-Mini_180px.png?auto=format%2Ccompress&dpr=1&h=45)
Calculus through Data & Modeling: Limits & Derivatives
This course is part of Differential Calculus through Data and Modeling Specialization
Taught in English
Some content may not be translated
![Joseph W. Cutrone, PhD](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera-instructor-photos.s3.amazonaws.com/13/ea96b194c24ba99e6792888bfd2902/Cutrone.jpg?auto=format%2Ccompress&dpr=1&w=75&h=75&fit=crop)
Instructor: Joseph W. Cutrone, PhD
Top Instructor
6,916 already enrolled
Included with
Course
(179 reviews)
Details to know
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/31ebcba3851b87d1d8609abf15d0ff7e.png?auto=format%2Ccompress&dpr=1&w=24&h=24)
Add to your LinkedIn profile
5 quizzes
Course
(179 reviews)
See how employees at top companies are mastering in-demand skills
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/74c8747e8210831049cf88dd4eefe26c.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=320)
Build your subject-matter expertise
- Learn new concepts from industry experts
- Gain a foundational understanding of a subject or tool
- Develop job-relevant skills with hands-on projects
- Earn a shareable career certificate
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/a7c5400e51272c78b710ce9b56fd3178.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=562)
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/de1a6556fbe605411e8c1c2ca4ba45f1.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=259)
Earn a career certificate
Add this credential to your LinkedIn profile, resume, or CV
Share it on social media and in your performance review
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/de1a6556fbe605411e8c1c2ca4ba45f1.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=333)
There are 6 modules in this course
One of the goals in studying Calculus is to analyze rates of change and movement. In this module, we introduce the central ideas which will help us achieve this goal: the notions of the limit and the derivative. Rather than evaluating a function at a single point, the limit allows for the study of the behavior of a function in an interval around that point. In this module, you will find limits of functions by a variety of methods, both visually and algebraically. Finally, we will apply limits to define the key idea of Differentiable Calculus, the derivative.
What's included
5 videos2 readings1 quiz
Using calculators or graphs is an imprecise way to find the limit of a function. In this module, we will state and use algebraic properties of limits, called the Limit Laws, to calculate the exact values of limits. A solid understanding of these laws will allow us to derive theorems which in turn can be used to study the behavior of more advanced functions.
What's included
3 videos1 reading1 quiz
In the last module, there were several types of functions where the limit of a function as x approaches a number could be found by simply calculating the value of the function at the number. Functions with this property will be called continuous and in this module, we use limits to define continuity. We will see that the mathematical definition of continuity will correspond closely with the English meaning of the word continuity used in every day language.
What's included
3 videos2 readings1 quiz
In this module, we allow for x to become arbitrarily large in the positive or negative direction to understand the end-behaviors of functions. This will allow for the formal definition of a horizontal asymptote and to provide classifications of end-behavior of certain types of functions.
What's included
1 video2 readings1 quiz
The problem of finding the slope of the tangent line to a curve and the problem of finding the instantaneous velocity of an object both involve finding the same type of limit. This special type of limit is called the derivative and in this module, we will see that this notion of the derivative can be interpreted as a rate of change in any of the natural or social sciences or engineering.
What's included
7 videos2 readings1 quiz
In this final project, we will apply the tools and language of differentiable calculus to analyze trends in data. This project will focus on modelling and analyzing gender ratios in educational attainment over time in several regions of the world.
What's included
1 peer review
Instructor
![Joseph W. Cutrone, PhD](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera-instructor-photos.s3.amazonaws.com/13/ea96b194c24ba99e6792888bfd2902/Cutrone.jpg?auto=format%2Ccompress&dpr=1&w=75&h=75&fit=crop)
Offered by
Recommended if you're interested in Math and Logic
Johns Hopkins University
Johns Hopkins University
Johns Hopkins University
Johns Hopkins University
Why people choose Coursera for their career
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Felipe_Moitta.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Jennifer_John.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Larry_Tao_Wang_1.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Chaitanya_Anand.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
Learner reviews
Showing 3 of 179
179 reviews
- 5 stars
84.35%
- 4 stars
10.05%
- 3 stars
2.79%
- 2 stars
1.11%
- 1 star
1.67%
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/7a1c0e2e779c1ff27cae62480adfe003.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=120)
Open new doors with Coursera Plus
Unlimited access to 7,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription
Advance your career with an online degree
Earn a degree from world-class universities - 100% online
Join over 3,400 global companies that choose Coursera for Business
Upskill your employees to excel in the digital economy
Frequently asked questions
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
If you subscribed, you get a 7-day free trial during which you can cancel at no penalty. After that, we don’t give refunds, but you can cancel your subscription at any time. See our full refund policy.