ABSTRACT
This chapter considers a variety of problem-solving methods, models, concepts, and techniques that give the reader some of the basic tools needed in solving and analyzing systems of differential equations, and describes phase portraits. Phase portraits provided qualitative viewing of solutions of systems of differential equations. The phase portrait shows the traces of possible solution curves. The chapter explores the use of numerical solutions to systems of differential equations. It shows the Euler and Runge-Kutta methods and how to obtain both the phase portraits of the system and the plots of approximate numerical solutions. Interactive situations occur in the study of economics, ecology, electrical engineering, mechanical systems, control systems, systems engineering, and so forth. For example, the dynamics of population growth of various species is an important ecological application of applied mathematics. The problem-solving models come from a variety of disciplines in science and engineering, including chemistry, physics, biology, fluids mechanics, Newtonian Mechanics, environmental engineering, and financial mathematics.
