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Calculus through Data & Modelling: Techniques of Integration

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Calculus through Data & Modelling: Techniques of Integration

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

Instructor: Joseph W. Cutrone, PhD

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4 modules

Gain insight into a topic and learn the fundamentals.

54 reviews

Intermediate level

Some related experience required

5 hours to complete

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

54 reviews

Intermediate level

Some related experience required

5 hours to complete

Flexible schedule

Learn at your own pace

Skills you'll gain

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

3 assignments¹

AI Graded see disclaimer

Taught in English

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

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There are 4 modules in this course

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.

Module details

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.

What's included

1 video2 readings1 assignment

For integrals of a function f(x), the region over which we integrate is always an interval of the real line. But for double integrals, we want to expand our abilities to integrate a multivariable function f(x,y) not only over rectangles, but also over more general regions in the plane. In this module, we develop the tools and techniques to do that.

What's included

1 video2 readings1 assignment

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.

What's included

1 video2 readings1 assignment

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.