Functions and their graphs. Algebraic combinations, compositions, inversions of functions and their graph manipulations. Algebraic and geometric properties of polynomial, rational, exponential, logarithmic, trigonometric functions. Homographic, Gaussian and Sigmoid functions. The basic two ideas for nearly all mathematical formulas in science: the derivative, and the definite integral. The Fundamental Theorem of Calculus. Approach to one of the central objects of mathematical modeling: Ordinary Differential Equations. They arise in many different contexts throughout mathematics and science, governing dynamical phenomena. The Cauchy Problem. The separable ordinary differential equations and the linear equations of first and second order.