# AMATH 250: Introduction to Differential Equations

Offered every fall, winter and spring term

## What are Differential Equations?

Three hundred and fifty years ago, Isaac Newton wrote

"it is useful to solve differential equations."

Since that time, researchers in many fields have found this statement to be true, particularly in recent times, with the advent of powerful personal computers making it possible to solve complicated differential equations numerically in a routine manner. Newton's enthusiasm was due to his success in using differential equations to give the first mathematical description of planetary orbits. Can you imagine what his reaction would be to the present widespread use of differential equations, with applications ranging from the space shuttle guidance system to epidemic models and neural networks? The essential idea is that, for many physical systems, one can, subject to suitable idealizations, formulate a differential equation to describe how the system changes in time. Understanding the solutions of the differential equation is then of paramount interest. The course AM 250 will introduce you to this fascinating area in the Mathematical Sciences.

## Brief description:

The course introduces the standard elementary methods for solving differential equations, including use of the Laplace transform, and gives a variety of applications in the sciences and in engineering. The mathematics used is primarily single variable calculus, with some dependence on linear algebra.

## Prerequisite:

Math 138 / 128 (Calculus 2)

## Intended audience:

• AM 250 provides an introduction to all Applied Mathematics programs, and is taken by all Applied Mathematics students.
• AM 250 will benefit students who are interested in Scientific Computation (e.g. CS 476, Numeric Computation for Dynamic Simulation), since differential equations form the basis for many mathematical models that have to be investigated using computers.
• AM 250 will benefit students who are interested in Actuarial Science or in the Mathematics of Finance (e.g. Pure Mathematics/Finance Option) since ordinary and partial differential equations are being applied in these areas.
• AM 250 counts as a credit for all programs in the Math Faculty, and is also open to students in other faculties. The course has been designed for students who want a one-course introduction to the world of differential equations in order to broaden their education in the mathematical sciences. From a mathematical point of view, the subject is primarily "Applied Calculus". AM 250 is thus the ideal course for students who wish to consolidate their understanding of single variable calculus while applying it to problems in the sciences and engineering.