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Calculus through Data & Modelling: Series and Integration
  • Level Professional
  • Duration 9 hours
  • Course by Johns Hopkins University
  • Offered by

About

This course continues your study of calculus by introducing the notions of series, sequences, and integration. These foundational tools allow us to develop the theory and applications of the second major tool of calculus: the integral. Rather than measure rates of change, the integral provides a means for measuring 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. Through projects, we will apply the tools of this course to analyze and model real world data, and from that analysis give critiques of policy. Following the pattern as with derivatives, several important methods for calculating accumulation are developed. Our course begins with the study of the deep and significant result of the Fundamental Theorem of Calculus, which develops the relationship between the operations of differentiation and integration. If you are interested in learning more advanced mathematics, this course is the right course for you.

Modules

Sequences and Series

    • 3 Videos
    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Sequences and Series

3 Videos

  • Sequences
  • Series
  • Examples Determining Convergence and Divergence of Series

1 Readings

  • Notes: Sequences and Series

The Definite Integral

    • 5 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • The Definite Integral

5 Videos

  • Areas Under Curves
  • Area Under a Line
  • Finding Distances
  • The Definite Integral
  • Properties of the Definite Integral

1 Readings

  • Notes: The Definite Integral

The Fundamental Theorem of Calculus

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • The Fundamental Theorem of Calculus

2 Videos

  • The Fundamental Theorem of Calculus, Part 1
  • The Fundamental Theorem of Calculus, Part 2

1 Readings

  • Notes: The Fundamental Theorem of Calculus

The Indefinite Integral

    • 3 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Indefinite Integrals

3 Videos

  • Indefinite Integrals
  • Worked Examples
  • A Calc I/II Problem

1 Readings

  • Notes: The Indefinite Integral

Integration by Substitution

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Integration by Substitution

2 Videos

  • The Substitution Rule
  • Definite Integrals of Symmetric Functions

1 Readings

  • Notes: Integration by Substitution

Integration with Calculators and Tables

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Integration with Calculators

1 Videos

  • Tables of Integrals

1 Readings

  • Integration with Websites

Project: Probability and Geometric Series

    • 1 PeerReview
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1 Peer Review

  • Probability and Geometric Series

Auto Summary

"Calculus through Data & Modelling: Series and Integration" is a professional-level course in Maths & Statistics offered by Coursera. It focuses on series, sequences, and integration, exploring the integral's role in measuring quantities over intervals. The course applies these concepts to real-world data analysis and policy critique. Ideal for those seeking advanced mathematics knowledge, it spans 540 minutes and is available with a Starter subscription.

Joseph W. Cutrone, PhD
Instructor

Joseph W. Cutrone, PhD