Understand what a function is and how it can be represented geometrically as a graph. Learn some standard function manipulations (algebraic combinations, composition, inverses, etc.) focusing on how such manipulations affect the shape of the graph. Learn algebraic and geometric properties of classic functions (polynomial, rational, exponential, logarithmic, trigonometric, etc.), emphasizing the relationship between them. Explore the basic two ideas for nearly all mathematical formulas in science: the derivative, which measures the instantaneous rate of change of a function and the definite integral, which measures the total accumulation of a function over an interval. The rules by which we can compute the derivative and the integral of any function are called calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. Approach one of the central objects of mathematical modeling: Ordinary Differential Equations. They arise in many different contexts throughout mathematics and science when quantities are defined as the rate of change of other quantities. Since various differentials, derivatives, and functions become inevitably related to each other via equations, a differential equation governing dynamical phenomena, evolution and variation is the result. After an introduction to the Cauchy Problem, the two most popular cases are studied: the separable equations and the linear equations of first and second order.