Ordinary Differential Equations
In this course, students will learn how derivatives commonly appear in equations used to describe the world. Equations involving derivatives are called differential equations. Differential equations play an important role in modeling the real world. Newton's laws, Maxwell's laws of electromagnetism, Einstein's equations of general relativity, Euler and Bernoulli's beam equation, the Black-Scholes equation from finance, Perelson's viral-dynamics equations in biology, and the million-dollar NavierStokes equations are all differential equations used daily in their respective disciplines. Today, differential equations are one of the fundamental mathematical tools for the study of systems that change over time, and are used in most areas of science, engineering, and mathematics. MATH 250 is an introductory course on ordinary differential equations. Ordinary differential equations are equations that involve derivative of a function with respect to only one variable. The goal of this course is to teach the students some of the elementary techniques in dealing with several fundamental types of equations. Some topics include linear equations involving only first and second derivatives, Laplace transforms, systems of linear equations involving only first derivatives, and phase-plane analysis.