Outline of Chapter 3

We work with equations of the form: ay'' + by' + cy = g(x). These are called second order liner differential equations with constant coefficients. If g(x) = 0 (for all x), the equation is a homogeneous second order liner differential equation with constant coefficients.

In either case the characteristic polynomial of the equation is ar²+br+c. Its roots play a key role in solving second order liner differential equations with constant coefficients.

• 3.1, 3.4, & 3.3 cover homogeneous second order liner equations with constant coefficients. If the roots of the characteristic polynomial are real and distinct, the method in 3.1 works. If it has a repeated real root, the method in 3.4 works. If it has a pair of complex roots, the method in 3.3 works.

• 3.2 is theoretical. This is tricky material. Many students in the past have complaned that they could not follow the textbook. So, I wrote up some notes. Here is the link: thy10.pdf.

• 3.5 & 3.6 deal with nonhomogeneous systems. Some students had trouble understanding Table 3.6.1, so I re-did it. See table.html.

• 3.7 & 3.8 deal with applications of second order systems.

• Chapter 4 is an extention of Chapter 3 topics. Everything generalizes to higher order linear equations. I cover it briefly.