By K.T. Leung
ISBN-10: 9622090133
ISBN-13: 9789622090132
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Extra resources for Elementary set theory
Example text
We shall see that a DE can often tell us information about the behavior of its solutions even if you do not have any solutions in hand. 5 we examine DEs analytically. This means we study specialized techniques for obtaining implicit and explicit solutions. In Sections 2. 3. 6 we discuss a simple technique for "solving" a DE numerically. This means, in contrast to the analytical approach where solutions are equations or formulas, that we use the DE to construct a way of obtaining quantitative information about an unknown solution.
11. Devise a mathematical model for the temperature body within this environment. 5 gal/min? 12. 3 Differential Equations as Mathematical Models 25 cin is the con c(t) is the concentration of the salt in the tank as well as in the outflow at time t (measured in pounds of salt per gallon), and A(t) is the amount of salt in the tank at time t. respectively (measured in gallons per minute), centration of the salt in the inflow, 16. 15. Determine a differential equation for the charge q(t) on the capacitor if the resistance is R, the capacitance is C, and the impressed voltage is E(t).
Population Growth where P is the number of individuals in the community and rate, is = O? How fast is the population time tis measured in years. How fast, that is, at what Beginning in the next section we will the population increasing at t see that differential equations can be used to describe or model increasing when the population is 500? many different physical systems. 3 = 100, Differential Equations as Mathematical Models Introduction In this section we introduce the notion of a mathematical model.
Elementary set theory by K.T. Leung
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