lecture_40 - MA 265 LECTURE NOTES: MONDAY, APRIL 21...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 265 LECTURE NOTES: MONDAY, APRIL 21 Differential Equations Differences vs. Differentials. Consider a function x = x ( t ). Given two points P = ( t ,x ) and Q = ( t 1 ,x 1 ) on the graph of this function, we can draw a secant line through them. The slope of this line is Slope of Secant Line at P = Δ x Δ t ( P ) = x 1- x t 1- t = x ( t + Δ t )- x ( t ) Δ t where Δ t = t 1- t is a difference . As P and Q move closer to each other, we can draw a line tangent to the curve x = x ( t ). The slope of this line is Slope of Tangent Line at P = dx dt ( P ) = lim Q → P x 1- x t 1- t = lim Δ t → x ( t + Δ t )- x ( t ) Δ t where dt is a differential . It is best to think of a differential as an infinitesimally small difference – but this quantity is nonzero! Any equation that involves differences Δ x and Δ t is called a difference equation , and any equation that involves differentials dx and dt is called a differential equation . Example. Let x = x ( t ) denote the size of a population at time t . How quickly a population grows depends on the number of people present in the population; these people may be engineers, doctors, etc. to help construct society. We see that the rate of change of growth is proportional to the number of people present:construct society....
View Full Document

This note was uploaded on 03/11/2010 for the course MA 261A 0026100 taught by Professor ... during the Spring '10 term at Purdue University Calumet.

Page1 / 3

lecture_40 - MA 265 LECTURE NOTES: MONDAY, APRIL 21...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online