This is a course that studies elementary calculus, as well as the necessary geometry, trigonometry and coordinate geometry, from within its “historical flow”. The flow is historical, but the emphasis is on doing the mathematics in a pedagogically effective way. This means that the material is developed from within the relevant context: that of the contributions of Greek thinkers, Copernicus, Galileo, Kepler, Descartes, Newton and Leibniz. But, it also means that the notation is modern and that the material is selected so as to cover the basics of the subject. Calculus is developed by fusing essential insights of both Leibniz and Newton together into a complete “short calculus”. This starts from scratch, is free of most theoretical “baggage”, and concentrates on the intuitive grasp of the basic elements. What will have emerged is a basic mathematics course that is surrounded by the important scientific concerns of the times.