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Calculus through Data & Modelling: Integration Applications
  • Level Professional
  • المدة 6 ساعات hours
  • الطبع بواسطة Johns Hopkins University
  • Offered by

عن

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.

الوحدات

Average Value of a Function

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Average Value of a Function

1 Videos

  • Average Value of a Function

1 Readings

  • Average Value Formulas

Arc Length and Curvature

    • 3 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Arc Length and Curvature

3 Videos

  • Arc Length for a Plane Curve
  • Arc Length for a Parametrized Curve
  • Curvature

1 Readings

  • Notes: Arc Length and Curvature

Velocity and Acceleration

    • 1 Videos
    • 2 Readings
    • 1 Assignment
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1 Assignment

  • Velocity and Acceleration

1 Videos

  • Velocity and Acceleration

2 Readings

  • Notes: Velocity and Acceleration
  • Sample Problems: Velocity and Acceleration

Areas Between Curves

    • 3 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Areas Between Curves

3 Videos

  • Areas Between Curves
  • Regions Bounded by Several Curves
  • Finding Area Between Two Curves "dy"

1 Readings

  • Notes: Double Integrals and Area

Test: Applications of Integrals

    • 1 Assignment
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1 Assignment

  • Module 3 Test: Applications of Integrals

Auto Summary

Enhance your calculus skills with "Calculus through Data & Modelling: Integration Applications" on Coursera. Focused on the applications of integration, this professional-level course delves into computing quantities using definite integrals derived from Riemann sums. Explore concepts like arclength, curvature, velocity, and acceleration, and apply these tools to real-world data across various disciplines. Perfect for professionals, this 360-hour course offers practical examples and projects, available through a Starter subscription. Join now to master integration and model complex data effectively.

Joseph W. Cutrone, PhD
Instructor

Joseph W. Cutrone, PhD