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

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Joseph W. Cutrone, PhD

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Integral Calculus through Data and Modeling SpecializationJohns Hopkins University

About this Course

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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.

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Course 2 of 4 in the

Integral Calculus through Data and Modeling Specialization

Intermediate Level

Approx. 4 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 2 of 4 in the

Integral Calculus through Data and Modeling Specialization

Intermediate Level

Approx. 4 hours to complete

English

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

Try Coursera for Business

Instructor

Joseph W. Cutrone, PhD
Top Instructor

Associate Teaching Professor and Director of Online Programs

Mathematics

54,837 Learners

16 Courses

Offered by

Johns Hopkins University

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Syllabus - What you will learn from this course

Week1

Week 1

1 hour to complete

Module 1: Iterated Integrals

In this module, we extend the idea of a definite integral to double and even triple integrals of functions of two or three variables. These ideas are then used to compute areas, volumes, and masses of more general regions. Double integrals are also used to calculate probabilities when two random variables are involved. This extension of single variable calculus is the first step towards major tools that arise later in this specialization involving theorems of vector calculus.

1 hour to complete

1 video (Total 22 min), 2 readings, 1 quiz

Week2

Week 2

1 hour to complete

Module 2: Double Integrals Over Plane Regions

1 hour to complete

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

Week3

Week 3

1 hour to complete

Vector Functions

A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector, but the output of this function is a vector. In this way, points are assigned to vectors. In this module, we will study these new types of functions and develop examples and applications of these new mathematical objects. They will play a key part in the development of vector calculus in future modules.

1 hour to complete

1 video (Total 18 min), 2 readings, 1 quiz

Week4

Week 4

1 hour to complete

Integration with Data

Despite the broad algebraic tools we have learned to find antiderivatives and evaluate definite integrals using the Fundamental Theorem of Calculus, there are times when using antiderivatives is not possible. This could be because the function is too complicated in a way where no nice antiderivative exists, or that we are working with discrete data instead of a continuous function. In this module we introduce the notions and algorithms of numerical integration, which allow us to estimate the values of definite integrals. This is the basic problem we seek to solve: compute an approximate solution to a definite integral to a given degree of accuracy. There are many methods for approximating the integral to the desired precision, and we introduce a few here.

1 hour to complete

1 video (Total 14 min), 1 reading, 1 quiz

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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What will I get if I subscribe to this Specialization?
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Calculus through Data & Modelling: Techniques of Integration

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