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.
Este curso faz parte do Programa de cursos integrados Integral Calculus through Data and Modeling
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Programa de cursos integrados Integral Calculus through Data and ModelingUniversidade Johns HopkinsInformações sobre o curso
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Prazos flexÃveis
Redefinir os prazos de acordo com sua programação.
Certificados compartilháveis
Tenha o certificado após a conclusão
100% on-line
Comece imediatamente e aprenda em seu próprio cronograma.
NÃvel intermediário
Aprox. 5 horas para completar
Inglês
Legendas: Inglês
oferecido por
Universidade Johns Hopkins
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.
Programa - O que você aprenderá com este curso
1 hora para concluir
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 hora para concluir
1 vÃdeo (Total 22 mÃn.), 2 leituras, 1 teste
1 hora para concluir
Module 2: Double Integrals Over Plane Regions
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.
1 hora para concluir
1 vÃdeo (Total 20 mÃn.), 2 leituras, 1 teste
1 hora para concluir
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 hora para concluir
1 vÃdeo (Total 18 mÃn.), 2 leituras, 1 teste
1 hora para concluir
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 hora para concluir
1 vÃdeo (Total 14 mÃn.), 1 leitura, 1 teste
Avaliações
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- 4 stars8,33%
- 1 star8,33%
Principais avaliações do CALCULUS THROUGH DATA & MODELLING: TECHNIQUES OF INTEGRATION
por YM26 de mai de 2022
I enjoyed completing Quizzes, however I'd be happy to see more practical tasks. Thank you! The lecturer is wonderful.
Sobre Programa de cursos integrados 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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