Why calculus?; The derivative; The antiderived function or the integral;The geometrical significance of the derivate; The differentiation and integration of powers of x; Some theorems on differentiation and antidifferentiation; The chain rule; Maxima and minima; The definite integral; The trigonometric functions; The inverse trigonometric functions; Logarithmic and exponential functions; Differentials and the law of the mean; Further techniques of integration; Some geometric uses the definite integral; Some physical applications of the definite integral; Polar coordinates; Rectangular pramatric equations and curvilinear motion; Taylorïs theorem and inifinite series; Functions of two or more variables and their geometric representation; Partial differentiation; Multiple integrals; An introduction to differential equations; A reconsideration of the foundations.