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

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Joseph W. Cutrone, PhD

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Integral Calculus through Data and Modeling SpecializationJohns Hopkins University

About this Course

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This course continues your study of calculus by focusing on the applications of integration. The applications in this section have many common features.  First, each is an example of a quantity that is computed by evaluating a definite integral.  Second, the formula for that application is derived from Riemann sums.  
Rather than measure rates of change as we did with differential calculus, the definite integral allows us to measure the accumulation of a quantity over some interval of input values.  This notion of accumulation can be applied to different quantities, including money, populations, weight, area, volume, and air pollutants.  The concepts in this course apply to many other disciplines outside of traditional mathematics.

We will expand the notion of the average value of a data set to allow for infinite values, develop the formula for arclength and curvature, and derive formulas for velocity, acceleration, and areas between curves.  Through examples and projects, we will apply the tools of this course to analyze and model real world data.

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Course 3 of 4 in the

Integral Calculus through Data and Modeling Specialization

Intermediate Level

Some working knowledge of differentiable calculus.

Approx. 5 hours to complete

English

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Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Coursera Labs

Includes hands on learning projects.

Learn more about Coursera Labs

Course 3 of 4 in the

Integral Calculus through Data and Modeling Specialization

Intermediate Level

Some working knowledge of differentiable calculus.

Approx. 5 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructor

Joseph W. Cutrone, PhD
Top Instructor

Associate Teaching Professor and Director of Online Programs

Mathematics

55,696 Learners

16 Courses

Offered by

Johns Hopkins University

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Syllabus - What you will learn from this course

Week1

Week 1

1 hour to complete

Module 1: Average Value of a Function

In this module, we generalize the notion of the average value of a (finite) set of points. Did you ever wonder how we compute the average temperature during the day if infinitely many temperature readings are possible? Or how the average rainfall is calculated? The notions in this module will allow us to expand the idea of an average value to compute averages with (infinite) values over a continuous interval.

1 hour to complete

1 video (Total 26 min), 1 reading, 1 quiz

Week2

Week 2

2 hours to complete

Module 2: Arc Length and Curvature

2 hours to complete

3 videos (Total 51 min), 1 reading, 1 quiz

Week3

Week 3

1 hour to complete

Module 4: Velocity and Acceleration

1 hour to complete

1 video (Total 18 min), 2 readings, 1 quiz

Week4

Week 4

2 hours to complete

Module 4: Areas Between Curves

2 hours to complete

3 videos (Total 37 min), 1 reading, 2 quizzes

About the Integral Calculus through Data and Modeling Specialization

This specialization builds on topics introduced in single and multivariable differentiable calculus to develop the theory and applications of integral calculus. , The focus on the specialization is to using calculus to address questions in the natural and social sciences. Students will learn to use the techniques presented in this class 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.

Frequently Asked Questions

When will I have access to the lectures and assignments?
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.
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. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

More questions? Visit the Learner Help Center.

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Calculus through Data & Modelling: Integration Applications

About this Course