Learn integral Calculus through modelling.. Master integration techniques for single and multivariable functions.

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43 ratings

Joseph W. Cutrone, PhD

Top Instructor

1,757 already enrolled

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Integral Calculus through Data and Modeling SpecializationJohns Hopkins University

What you will learn

Model and analyze data using techniques of integration for both single and multivariable functions.
Numerical methods for integration

Skills you will gain

About this Specialization

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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.

Applied Learning Project

In each module, learners will be provided with solved sample problems that they can use to build their skills and confidence followed by graded quizzes to demonstrate what they've learned. Through a cumulative project, students will apply their skills to model random chance events, evaluate a policy on air pollution regulation, and use calculus to estimate surface areas of land masses.

Shareable Certificate

Earn a Certificate upon completion

100% online courses

Start instantly and learn at your own schedule.

Flexible Schedule

Set and maintain flexible deadlines.

Intermediate Level

Approximately 4 months to complete

Suggested pace of 1 hour/week

English

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Shareable Certificate

Earn a Certificate upon completion

100% online courses

Start instantly and learn at your own schedule.

Flexible Schedule

Set and maintain flexible deadlines.

Intermediate Level

Approximately 4 months to complete

Suggested pace of 1 hour/week

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

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How the Specialization Works

Take Courses

A Coursera Specialization is a series of courses that helps you master a skill. To begin, enroll in the Specialization directly, or review its courses and choose the one you'd like to start with. When you subscribe to a course that is part of a Specialization, you’re automatically subscribed to the full Specialization. It’s okay to complete just one course — you can pause your learning or end your subscription at any time. Visit your learner dashboard to track your course enrollments and your progress.

Hands-on Project

Every Specialization includes a hands-on project. You'll need to successfully finish the project(s) to complete the Specialization and earn your certificate. If the Specialization includes a separate course for the hands-on project, you'll need to finish each of the other courses before you can start it.

Earn a Certificate

When you finish every course and complete the hands-on project, you'll earn a Certificate that you can share with prospective employers and your professional network.

There are 4 Courses in this Specialization

Course1

Course 1

Calculus through Data & Modelling: Series and Integration

4.9

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27 ratings

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.

Course2

Course 2

Calculus through Data & Modelling: Techniques of Integration

4.5

stars

15 ratings

In this course, we build on previously defined notions of the integral of a single-variable function over an interval. Now, we will extend our understanding of integrals to work with functions of more than one variable. First, we will learn how to integrate a real-valued multivariable function over different regions in the plane. Then, we will introduce vector functions, which assigns a point to a vector. This will prepare us for our final course in the specialization on vector calculus. Finally, we will introduce techniques to approximate definite integrals when working with discrete data and through a peer reviewed project on, apply these techniques real world problems.

Course3

Course 3

Calculus through Data & Modelling: Integration Applications

5.0

stars

10 ratings

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.

Course4

Course 4

Calculus through Data & Modelling: Vector Calculus

4.8

stars

26 ratings

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.

Instructor

Joseph W. Cutrone, PhD
Top Instructor

Associate Teaching Professor and Director of Online Programs

Mathematics

50,899 Learners

16 Courses

Offered by

Johns Hopkins University

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Yes! To get started, click the course card that interests you and enroll. You can enroll and complete the course to earn a shareable certificate, or you can audit it to view the course materials for free. When you subscribe to a course that is part of a Specialization, you’re automatically subscribed to the full Specialization. Visit your learner dashboard to track your progress.
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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. If you only want to read and view the course content, you can audit the course for free. If you cannot afford the fee, you can apply for financial aid.
Is this course really 100% online? Do I need to attend any classes in person?
This course is completely online, so there’s no need to show up to a classroom in person. You can access your lectures, readings and assignments anytime and anywhere via the web or your mobile device.
Will I earn university credit for completing the Specialization?
This Specialization doesn't carry university credit, but some universities may choose to accept Specialization Certificates for credit. Check with your institution to learn more.
What background knowledge is necessary?
A working knowledge of differentiable calculus (https://www.coursera.org/specializations/differential-calculus-data-modeling)
Do I need to take the courses in a specific order?
The recommended order is the layout of the courses in the specialization.

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Integral Calculus through Data and Modeling Specialization

What you will learn

Skills you will gain

About this Specialization

Applied Learning Project