# Integral Calculus through Data and Modeling Specialization

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

Offered By

### 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

## 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.

Students should have a working knowledge of differential calculus before starting this course.

Students should have a working knowledge of differential calculus before starting this course.

## There are 4 Courses in this Specialization

### Calculus through Data & Modelling: Series and Integration

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.

### Calculus through Data & Modelling: Techniques of Integration

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.

### Calculus through Data & Modelling: Integration Applications

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.

### Calculus through Data & Modelling: Vector Calculus

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.

## Offered by

#### Johns Hopkins University

The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.

## Frequently Asked Questions

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