The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on linear differential equations and their applications in science and engineering. More details are given in the course goals below.
At MIT, 18.03 Differential Equations has 18.01 Single Variable Calculus as a prerequisite. 18.02 Multivariable Calculus is a corequisite, meaning students can take 18.02 and 18.03 simultaneously. From 18.02 we will expect knowledge of vectors, the arithmetic of matrices, and some simple properties of vector valued functions.
By the end of the course students will be able to:
The main equations studied in the course are driven first and second order constant coefficient linear ordinary differential equations and 2x2 systems. For these equations students will be able to:
The course, designed for independent study, has been organized to follow the sequence of topics covered in an MIT course on Differential Equations. There are four major units.
Each unit is divided into sessions, which consist of written notes, lecture videos, problem solving videos, practice problems, and problem sets. Following the practice at MIT, the problem sets are split into two parts: Part I covering simple problems designed to emphasize a specific skill or technique, and Part II covering harder, often multistep problems, designed to help the student learn to apply the skills and techniques to more realistic problems. Complete solutions are provided for all problem sets.
To help guide your learning, you will see how problem solving is taught by an experienced MIT Recitation Instructor. At the end of each unit is an exam covering the material in the unit and a practice exam to help you prepare for the exam. Solutions are included for both the exam and practice exam.
At the end of Unit IV is a final exam covering the entire course.
MIT expects its students to spend about 150 hours on this course. More than half of that time is spent preparing for class and doing assignments. It's difficult to estimate how long it will take you to complete the course, but you can probably expect to spend an average of 3 or more hours working through each of the 38 sessions.
Haynes Miller is a Professor of Mathematics at MIT. In 2005 he was an MIT MacVicar Faculty Fellow in recognition of his outstanding contributions to undergraduate education. He has taught 18.03 many times and was the prime mover behind its current design. Professor Miller contributed many of the materials used in this OCW Scholar course. He was also the principal investigator behind the development of the Interactive Java® Demonstrations called Mathlets used here.
Dr. Jeremy Orloff is a lecturer in the Department of Mathematics and in the Experimental Study Group at MIT. He has taught 18.03 many times. Dr. Orloff was the lead content developer of this OCW Scholar course and worked closely with MIT OpenCourseWare on its development.
Dr. John Lewis is a Research Affiliate and former Senior Lecturer in the Department of Mathematics. He taught 18.03 for many years in the Experimental Study Group and Concourse programs at MIT, often in collaboration with Dr. Orloff.
Arthur Mattuck is an Emeritus Professor of Mathematics at MIT. He has been a major force in the design of undergraduate mathematics classes at MIT. Professor Mattuck taught 18.03 many times and his lecture videos and written notes are used throughout this OCW Scholar course.
To learn more about the Teaching Assistants, visit the Meet the TAs page.