Differential Equations

Big Ideas

• Deterministic models are often described by systems of differential equations.

• Apply analytical methods to solve differential equations in special cases such as first order separable equations and second order constant coefficient equations.

• Use SciPy to approximate solutions of any system of differential equations. A computational approach to mathematical modelling allows us to spend more time simulating models as opposed to studying analytical methods.

• Every higher order system of differential equations is equivalent to a first order system in higher dimensions therefore numerical methods are designed for first order systems and we transform higher order systems into first order systems to apply numerical methods.

Learning Goals

• Classify differential equations: order, dimension, separable, linear, autonomous, homogeneous

• Apply analytical methods to solve first order separable equations

• Apply analytical methods to solve homogeneous second order equations with constant coefficients

• Transform higher order systems of differential equations into first order systems

• Compute and visualize numerical solutions of differential equations