Summary
Differential equations have been shown to be capable of describing any phenomenon, and the provided circumstances are entirely solvable to produce a variety of solutions.
We begin with an introduction to differential equations; definition, types and some basic ideas connected to differential equations, such as degree order homogeneous and nonhomogeneous differential equations with governing equations as well as the solutions to such differential equations; Variable separable method, integrating factor method and solution of exact differential equations. This is seen in Chapter one, alongside numerous examples to illustrate.
Chapter 2 is a brief history of differential equations and its progression through time. Notable names like Isaac Newton, Gottfried Leibniz, Bernoulli brothers, Leonhard Euler, Joseph Lagrange, Simon Laplace among many others are accredited with most of the rules, equations and theorems used in differential equations till this day.
The main body of works involves, using differential equations to model real life problems; Newton’s law of cooling and warming which has numerous applications most importantly in the determination of time of death in forensic studies, Radioactive decay used in archeology, compound interest which has applications in financial sectors and the air resistance of a falling body, used in skydiving.
In the previous chapter we study population dynamics, the Malthusian model and logistic growth model, which is used in economics for population analysis, disease control as well as many others.
