AS/SC/MATH 2270.03W

Differential Equations I

Differential equations have played a central role in mathematics and its applications for the past three hundred years. Their importance in applications stems from the interpretation of the derivative as a rate of change, a familiar example being velocity. Many of the fundamental laws of physical science are best formulated as differential equations. In other areas, such as biology and economics, which involve the study of growth and change, such equations are of fundamental importance.

In this course we will use fundamental ideas of calculus and linear algebra to study some important types of differential equations and their solutions. The important class of linear equations will be dealt with in detail, and here the basic notions of linear algebra are important. The course will also include solutions in series form, and solutions by use of the Laplace Transform. Some of the simpler non-elementary functions will be introduced. Applications will be discussed from time to time.

Students should have completed MATH2010.03 or MATH2015.03 or MATH2310.03 or equivalent before starting this course. In particular, they should be completely familiar with various methods of integration (substitutions, partial fractions, integration by parts) as well as the rules of differentiation, limits, theory of series, the Fundamental Theorem of Calculus, and properties of the logarithmic, exponential and trigonometric functions. Some partial differentiation is also required. It must be strongly emphasized that students cannot begin this course without a thorough mastery of this material from basic calculus.

The text will be announced later.