In calculus courses like MATH 140 and 141, students learn to calculate the derivative of a function and to use derivatives in simple applications. In MATH 250, 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 Navier-Stokes 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.
This course is completed by many students with engineering, mathematics, sciences, and secondary education majors. Students needing a more complete introduction to differential equations should consider MATH 251, which is a 4-credit course covering all the material of MATH 250 plus an introduction to partial differential equations. Students who have passed MATH 251 may not schedule this course for credit. On completing MATH 250, students may enroll in MATH 405, 411, 412, 417, and 419.
Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.