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.
Este curso forma parte de Programa especializado: Integral Calculus through Data and Modeling
ofrecido por
Programa especializado: Integral Calculus through Data and ModelingUniversidad Johns HopkinsAcerca de este Curso
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Nivel intermedio
Some working knowledge of differentiable calculus.
Aprox. 6 horas para completar
Inglés (English)
Subtítulos: Inglés (English)
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Nivel intermedio
Some working knowledge of differentiable calculus.
Aprox. 6 horas para completar
Inglés (English)
Subtítulos: Inglés (English)
ofrecido por
Universidad 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 - Qué aprenderás en este curso
1 hora para completar
Module 1: Average Value of a Function
In this module, we generalize the notion of the average value of a (finite) set of points. Did you ever wonder how we compute the average temperature during the day if infinitely many temperature readings are possible? Or how the average rainfall is calculated? The notions in this module will allow us to expand the idea of an average value to compute averages with (infinite) values over a continuous interval.
1 hora para completar
1 video (Total 26 minutos), 1 lectura, 1 cuestionario
2 horas para completar
Module 2: Arc Length and Curvature
What do we mean by the arc length of a curve? We might think of fitting a piece of string to the curve and then measuring the string against a ruler. But this is difficult to do when working with a complicated curve. In this module we develop the precise notion of the length and curvature of an arc of a curve in both the xy plane and in space.
2 horas para completar
3 videos (Total 51 minutos), 1 lectura, 1 cuestionario
1 hora para completar
Module 4: Velocity and Acceleration
In this module, we show how the ideas of tangent and normal vectors can be used in physics to study the motion of an object, including its velocity and acceleration, but now we focus on curves in three dimensional space. The techniques developed here then allow us to study the rates of change for more advanced functions.
1 hora para completar
1 video (Total 18 minutos), 2 lecturas, 1 cuestionario
2 horas para completar
Module 4: Areas Between Curves
Finding the area between two curves is not just an interesting application of definite integrals from a geometric view, but when working with the appropriate functions, has applications in economics, business, and even medicine.
2 horas para completar
3 videos (Total 37 minutos), 1 lectura, 2 cuestionarios
Acerca de Programa especializado: 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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