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Calculus through Data & Modelling: Vector Calculus
  • Level Professional
  • Duration 5 hours
  • Course by Johns Hopkins University
  • Offered by

About

This course continues your study of calculus by focusing on the applications of integration to vector valued functions, or vector fields. These are functions that assign vectors to points in space, allowing us to develop advanced theories to then apply to real-world problems. We define line integrals, which can be used to fund the work done by a vector field. We culminate this course with Green's Theorem, which describes the relationship between certain kinds of line integrals on closed paths and double integrals. In the discrete case, this theorem is called the Shoelace Theorem and allows us to measure the areas of polygons. We use this version of the theorem to develop more tools of data analysis through a peer reviewed project. Upon successful completion of this course, you have all the tools needed to master any advanced mathematics, computer science, or data science that builds off of the foundations of single or multivariable calculus.

Modules

Line Integrals

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

1 Assignment

  • Line Integrals

2 Videos

  • Vector Fields
  • Line Integrals

2 Readings

  • Notes: Line Integrals
  • Sample Problems: Line Integrals

Line Integrals and Conservative Vector Fields

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

1 Assignment

  • Line Integrals and Conservative Vector Fields

1 Videos

  • The Fundamental Theorem for Line Integrals

2 Readings

  • Notes: Line Integrals and Conservative Vector Fields
  • Sample Problems: Line Integrals and Conservative Vector Fields

Green's Theorem

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

1 Assignment

  • Green's Theorem

1 Videos

  • Green's Theorem

1 Readings

  • Notes and Sample Problems: Green's Theorem

Project - Approximating Area with Green's Theorem

    • 1 PeerReview
Show info about module content

1 Peer Review

  • Approximating the Area of Puerto Rico
Joseph W. Cutrone, PhD
Instructor

Joseph W. Cutrone, PhD