Johns Hopkins University
Calculus through Data & Modelling: Vector Calculus
Johns Hopkins University

Calculus through Data & Modelling: Vector Calculus

Joseph W. Cutrone, PhD

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Gain insight into a topic and learn the fundamentals.
4.7

(36 reviews)

Intermediate level

Recommended experience

4 hours to complete
3 weeks at 1 hour a week
Flexible schedule
Learn at your own pace
Gain insight into a topic and learn the fundamentals.
4.7

(36 reviews)

Intermediate level

Recommended experience

4 hours to complete
3 weeks at 1 hour a week
Flexible schedule
Learn at your own pace

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Assessments

3 assignments

Taught in English

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This course is part of the Integral Calculus through Data and Modeling Specialization
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There are 3 modules in this course

In this module, we define the notion of a Vector Field, which is a function that applies a vector to a given point. We then develop the notion of integration of these new functions along general curves in the plane and in space. Line integrals were developed in the early19th century initially to solve problems involving fluid flow, forces, electricity, and magnetism. Today they remain at the core of advanced mathematical theory and vector calculus.

What's included

2 videos2 readings1 assignment

In this module, we introduce the notion of a Conservative Vector Field. In vector calculus, a conservative vector field is a vector field that is the gradient of some function f, called the potential function. Conservative vector fields have the property that the line integral is path independent, which means the choice of any path between two points does not change the value of the line integral. Conversely, path independence of the line integral is equivalent to the vector field being conservative. We then state and formalize an important theorem about line integrals of conservative vector fields, called the Fundamental Theorem for Line Integrals. This will allow us to show that for a conservative system, the work done in moving along a path in configuration space depends only on the endpoints of the path.

What's included

1 video2 readings1 assignment

In this module we state and apply a main tool of vector calculus: Green's Theorem. Green's theorem gives a relationship between the line integral of a two-dimensional vector field over a closed path in the plane and the double integral over the region it encloses. The fact that the integral of a two-dimensional conservative field over a closed path is zero is a special case of Green's theorem.

What's included

1 video1 reading1 assignment1 peer review

Instructor

Instructor ratings
5.0 (7 ratings)
Joseph W. Cutrone, PhD

Top Instructor

Johns Hopkins University
20 Courses542,897 learners

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