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Differential And Integral Calculus By Feliciano And Uy
set 7 ue 25, illinois state 24
a pair of kills by cardona put the aces up 7-2, but a kill by vazquez gave the redbirds the lead at 8-7. the aces regained the lead at 10-8 with a kill by vazquez before illinois state answered with a pair of kills of its own. feliciano answered with a kill for the aces, cutting the lead to 10-9. illinois state responded with a kill by cardona, but a vazquez ace closed the gap to 12-10. the aces took the lead at 14-12 on a kill by vazquez.
of course, if you are doing analysis, you will learn about things like functions and integration. that’s no surprise, because functions and integration are things that you study. if you are doing calculus, you learn about limits, derivatives, and integrals. however, you study these things to develop your skills as a mathematical modeler.
it is possible to find the antiderivative of an arbitrary function (f(x)), but finding the antiderivative of the special functions (e.g., the exponential function) is easier. finding an antiderivative of functions like f(x) = x and f(x) = sin(x) is easier than finding an antiderivative of a general function. these are the special functions that you study in calculus. finding an antiderivative is usually the easiest part of calculus, and finding antiderivatives is the easiest part of differential equations.
more advanced differential equations, like the differential equation in the bank balance example, are more difficult. you can only solve these if you can determine the unknowns (y0, y1, y2, y3, and y4).
the cauchy-riemann equations are often used to describe complex functions, and the cauchy-riemann equations are often used to find the antiderivative of a complex function. in the real numbers, the cauchy-riemann equations are the same as the differential equations that we have been talking about. the cauchy-riemann equations tell you what the function is doing at the endpoints of its domain (usually – at x = 0 and x = 1) and where the function is differentiable (its derivative is continuous).
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