The Coursera Data Science Specialization does not require calculus or linear algebra. Either subject would, of course, simplify presentation of topics such as linear regression, and a student will occasionally express interest in how they might apply. This is a stab at catering to such interest.
The proposed aim is to teach just enough calculus and (finite dimensional) linear algebra for an understanding of quadratic form minimization and of principal components, presupposing only familiarity with R and basic algebra. This objective's modesty is due to the experimental nature of the course, which is twofold. It would be the first "auxiliary" DSS course, supporting the specialization but not actually in it. Also, it could become an introduction or review for a contemplated linear models MOOC.
More generally, probability and calculus are the two great modeling technologies. Interest in one should breed interest in the other. In their modern forms, both arose in 17$^{th}$ Century Europe, calculus in connection with planetary motion, probability in connection with games of chance. (It was always more down to Earth.) Computers have revolutionized application of both.
Exactly what can or will be done remains to be seen. In the absence of slides and videos, a short monograph to accompany the swirl lessons is anticipated.