This course is part of the Differential Calculus through Data and Modeling Specialization

Joseph W. Cutrone, PhD

Offered By

Differential Calculus through Data and Modeling SpecializationJohns Hopkins University

About this Course

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.

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Course 2 of 4 in the

Differential Calculus through Data and Modeling Specialization

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Beginner Level

Approx. 10 hours to complete

English

Subtitles: English

Instructor

Joseph W. Cutrone, PhD

Senior Lecturer and Director of Online Programs

Mathematics

2,701 Learners

7 Courses

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 2 of 4 in the

Differential Calculus through Data and Modeling Specialization

Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

Approx. 10 hours to complete

English

Subtitles: English

Offered by

Johns Hopkins University

The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.

Syllabus - What you will learn from this course

Week

Week 1

2 hours to complete

The Limit of a Function

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.

2 hours to complete

5 videos (Total 59 min), 2 readings, 1 quiz

5 videos

Introduction to Limits1m

The Tangent Problem7m

Finding Limits with Graphs and Tables19m

One-Sided Limits14m

Limits Involving Infinity16m

2 readings

Notes: The Limit of a Function10m

Sample Problems: The Limit of a Function10m

1 practice exercise

The Limit of a Function30m

Week

Week 2

1 hour to complete

The Limit Laws

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.

1 hour to complete

3 videos (Total 46 min), 1 reading, 1 quiz

3 videos

Limit Laws17m

Examples to Find Limits16m

Squeeze Theorem12m

1 reading

Notes: The Limit Laws10m

1 practice exercise

The Limit Laws30m

Week

Week 3

2 hours to complete

Continuity

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.

2 hours to complete

3 videos (Total 47 min), 2 readings, 1 quiz

3 videos

Continuity16m

Week 4

1 hour to complete

Limits at Infinity

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.

1 hour to complete

1 video (Total 27 min), 2 readings, 1 quiz

1 video

Limits at Infinity26m

2 readings

Notes: Limits at Infinity10m

Sample Problems: Limits at Infinity10m

1 practice exercise

Limits at Infinity30m

About the Differential Calculus through Data and Modeling Specialization

This specialization provides an introduction to topics in single and multivariable calculus, and focuses on using calculus to address questions in the natural and social sciences. Students will learn to use the tools of calculus to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

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When will I have access to the lectures and assignments?
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What will I get if I subscribe to this Specialization?
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.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You'll be prompted to complete an application and will be notified if you are approved. You'll need to complete this step for each course in the Specialization, including the Capstone Project. Learn more.
Will I earn university credit for completing the Course?
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Calculus through Data & Modeling: Limits & Derivatives