Johns Hopkins University
Calculus through Data & Modeling: Limits & Derivatives
Johns Hopkins University

Calculus through Data & Modeling: Limits & Derivatives

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

Taught in English

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Joseph W. Cutrone, PhD

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Course

Gain insight into a topic and learn the fundamentals

4.7

(179 reviews)

Beginner level
No prior experience required
9 hours (approximately)
Flexible schedule
Learn at your own pace

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Assessments

5 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.7

(179 reviews)

Beginner level
No prior experience required
9 hours (approximately)
Flexible schedule
Learn at your own pace

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This course is part of the Differential Calculus through Data and Modeling Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
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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

Instructor ratings
4.9 (31 ratings)
Joseph W. Cutrone, PhD

Top Instructor

Johns Hopkins University
20 Courses420,458 learners

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Recommended if you're interested in Math and Logic

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