There are many real life applications of differential equations, which sometimes surprises high school calculus students! Many students don't understand why they are bothering to learn differential equations at all, but differential equations are important parts of the study of economics, biology, engineering and physics.Since differential equations can describe exponential growth and decay, they
. are used to describe the half-lives of radioactive isotopes, the population growth of species or the change in investment return over time. When biological scientists explore population growth in species, though, they don't just rely on exponential growth and decay "" they also use differential equations to explore the relationships between species and the total size of populations. For example, differential equations can describe the relationship of predators and prey in an ecosystem, the rates of hybrid selection or the consequences of over-population, under-population or over-harvesting in various species. Medical science uses similar equations to determine rates of growth of tumors and to try to understand cancer growth. In engineering, differential equations describe the way electrical currents move through circuits. In chemistry, they describe the rates of chemical reactions. Economists use differential equations to describe investment returns, sales practices, equilibrium and stability in economic markets and even the results of advertising in the Sethi advertising model.In addition to the general, every-day uses, many of the equations that describe major concepts in physics and engineering are differential equations: Newton's Second Law (sometimes simply expressed as "force equals mass times acceleration") is a differential equation, as is his law of cooling. The Einstein field equations that describe his general theory of relativity also rely on differential equations. When physicists describe waves of light, sound and water, they use differential wave equations. Although these are all real-world applications of differential equations, they are not commonly used "" they are important for physicists, but the average person won't use the equations every day. More reference links: http://college.cengage.com/mathematics/larson/calculus_applied/6e/shared/appendices/appdx_c_sec_04.pdf http://serc.carleton.edu/sencer/ode_real_world/linking_mathematics_social_issues.html
