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

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Joseph W. Cutrone, PhD

Top Instructor

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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 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.

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Course 4 of 4 in the

Integral Calculus through Data and Modeling Specialization

Intermediate Level

Working knowledge of differentiable calculus and some integral calculus of a single variable function.

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.

Course 4 of 4 in the

Integral Calculus through Data and Modeling Specialization

Intermediate Level

Working knowledge of differentiable calculus and some integral calculus of a single variable function.

Approx. 5 hours to complete

English

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Instructor

Joseph W. Cutrone, PhD
Top Instructor

Associate Teaching Professor and Director of Online Programs

Mathematics

41,523 Learners

15 Courses

Offered by

Johns Hopkins University

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Syllabus - What you will learn from this course

Week

Week 1

1 hour to complete

Module 1: Vector Fields and Line Integrals

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.

1 hour to complete

2 videos (Total 40 min), 2 readings, 1 quiz

Week

Week 2

1 hour to complete

Module 2: The Fundamental Theorem for Line Integrals

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.

1 hour to complete

1 video (Total 20 min), 2 readings, 1 quiz

Week

Week 3

2 hours to complete

Module 3: Green's Theorem

2 hours to complete

1 video (Total 23 min), 1 reading, 2 quizzes

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TOP REVIEWS FROM CALCULUS THROUGH DATA & MODELLING: VECTOR CALCULUS

by THApr 1, 2022

This is an excellent course to learn advanced calculus. Very well taught!

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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.

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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.
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Calculus through Data & Modelling: Vector Calculus

About this Course