# Math 312 Differential Equations

Fall 2016: Daily Schedule

“Mathematics grips the world through differential equations.” – Andrew Gleason

Complex phenomena may result from relatively simple laws about how the phenomena change over time.  Nothing could be simpler than Newton’s Law of Motion, Force = Mass x Acceleration, yet it describes all the motion we observe in our daily lives.  In mathematical language, we might say that simple equations relating derivatives of a function can lead to the most intricate behavior for the function itself.   This observation is the starting point for the subject of differential equations.

The goals of a course in differential equations are twofold:

• Model real world phenomena with differential equations.
• Given information about the derivatives of a function, describe properties of the function itself.

Since most differential equations can not be solved algebraically, the study of differential equations necessarily includes methods to solve numerically using computer software.

Course components

• Modeling with differential equations
• First order equations
• Linear differential equations (second order)
• Nonlinear systems
• Laplace transforms
• Solving differential equations with computer software