[MA122] - Midterm Exam Guide - Comprehensive Notes for the exam (17 pages long!)

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If rate of growth of a population is proportional to population, and if the population is small, Differential equation (de): equation that involves the derivatives of a function. Order: order of a de is the order of the highest derivative. Rate of change of population with respect to time. For large populations, p>m where m is a critical size, then dp/dt < 0 (logistic de) V0 is the initial amount invested r is the annual interest rate (units of % per year) m is the number of times the investment is compounded per year. Taking the limit yields v0ert (solution to above equation) Euler"s method yn+1 = yn + hf(xn, yn) y(x+h) = y(x) + hf(x, y) these formulas are the same! And xn = xn-1 + nh (so x1 = x0 + h, and x2 = x1 + 2h) Note: when it says to estimate y(0. 4) for example, and h = (cid:1004). (cid:1005), the(cid:374) (cid:455)ou"(cid:396)e fi(cid:374)di(cid:374)g (cid:455)4.

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