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.
Ce cours fait partie de la Spécialisation Integral Calculus through Data and Modeling
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Spécialisation Integral Calculus through Data and ModelingUniversité Johns-HopkinsÀ propos de ce cours
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Cours 3 sur 4 dans le
Niveau intermédiaire
Some working knowledge of differentiable calculus.
Approx. 6 heures pour terminer
Anglais
Sous-titres : Anglais
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Certificat partageable
Obtenez un Certificat lorsque vous terminez
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Cours 3 sur 4 dans le
Niveau intermédiaire
Some working knowledge of differentiable calculus.
Approx. 6 heures pour terminer
Anglais
Sous-titres : Anglais
Offert par
Université 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.
Programme du cours : ce que vous apprendrez dans ce cours
1 heure pour terminer
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 heure pour terminer
1 vidéo (Total 26 min), 1 lecture, 1 quiz
2 heures pour terminer
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 heures pour terminer
3 vidéos (Total 51 min), 1 lecture, 1 quiz
1 heure pour terminer
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 heure pour terminer
1 vidéo (Total 18 min), 2 lectures, 1 quiz
2 heures pour terminer
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 heures pour terminer
3 vidéos (Total 37 min), 1 lecture, 2 quiz
À propos du Spécialisation 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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