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