Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.
(273 Bewertungen)
Wichtige Details
32 Aufgaben
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In diesem Kurs gibt es 5 Module
Having seen some calculus before, you may recall some of the motivations for integrals arising from area computations. We will review those classical applications, while introducing the core idea of this module -- a differential element. By computing area and volume elements, we will see how to tackle tough geometry problems in a principled manner.
Das ist alles enthalten
6 Videos2 Lektüren9 Aufgaben
There's more to geometry than just area and volume! In this module, we will take things "to the next level", ascending to higher dimensions. Coming back to the 3-d world, we will return to problems of length and area, but this time in the context of curves and surfaces. As always, the emphasis will be on how to construct the appropriate differential element for integrating.
Das ist alles enthalten
4 Videos6 Aufgaben
There is so much more to applications of integrals than geometry! So many subjects, from physics to finance, have, at heart, the need for setting up and computing definite integrals. In this short but intense module, we will cover applications including work, force, torque, mass, and present & future value.
Das ist alles enthalten
3 Videos4 Aufgaben
There is a statistical aspect to integrals that has not yet been brought up in this course: integrals are ideal for computing averages. Motivated by physical problems of mass, centroid, and moments of inertia, we will cover applications of integrals to averages.
Das ist alles enthalten
5 Videos6 Aufgaben
This capstone module gives a very brief introduction to probability, using what we know about integrals and differential elements. Beginning with common-sense uniform probabilities, we move on to define probability density functions and the corresponding probability element. Building on the physical intuition obtained from centers of mass and moments of inertia, we offer a unique perspective on expectation, variance, and standard deviation.
Das ist alles enthalten
3 Videos1 Lektüre7 Aufgaben
Dozent
Empfohlen, wenn Sie sich für Math and Logic interessieren
University of California, Santa Cruz
Northeastern University
University of Geneva
The Hong Kong University of Science and Technology
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Bewertungen von Lernenden
273 Bewertungen
- 5 stars
90,47 %
- 4 stars
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- 3 stars
1,09 %
- 2 stars
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- 1 star
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Zeigt 3 von 273 an
Geprüft am 20. Juni 2021
Phenomenal teacher. I wish he would offer more courses (I took Parts 3,4 and 5)
Geprüft am 7. Apr. 2021
Great course. Some of the mentors on the forum board are unbelievably rude and condescending.
Geprüft am 22. Juni 2016
this was simply an amazing course, perfect for my skill level and exactly what i needed to learn. Thank you for the opportunity.
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