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Integral Calculus through Data and Modeling

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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What's inside

Four courses

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.

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Calculus through Data & Modelling: Techniques of Integration

In this course, we extend our understanding of integrals to work with functions of more than one variable. We will learn how to integrate a real-valued multivariable function over different regions in the plane. We will also introduce vector functions and techniques to approximate definite integrals when working with discrete data.

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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.

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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. 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.

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Learning objectives

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

Numerical methods for integration

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

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Time

0 hours

Level

Intermediate

Via

Coursera

Institution

Johns Hopkins University

Instructor

Joseph W. Cutrone, PhD

Level

Intermediate

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