By George Boole

This Elibron Classics ebook is a facsimile reprint of a 1877 version by way of Macmillan and Co., London.

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**A treatise on differential equations**

This Elibron Classics e-book is a facsimile reprint of a 1877 version via Macmillan and Co. , London.

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**Extra info for A treatise on differential equations**

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It can get higher returns (rr) if it invests in risky assets, but the return is not guaranteed. A return (rs) is guaranteed if it invests in safe assets. How much should the company invest in risky assets (R), to maximize its wealth at the end of a stipulated period? Formulate the objective function for the optimization problem. 3) are made where x is an independent variable and y is a dependent variable. It is desired to fit these data with a straight line yˆ = mx + c where m and c are to be determined.

In the secant method, both the magnitude and the sign of the derivative are used to locate the zero of f′(x). 6) Further, it is assumed that f′(x) varies linearly between points x1 and x2. A secant line is drawn between the two points x1 and x2. 8). One of the points, x1 or x2, is then eliminated using the aforementioned derivative condition. 8 Secant method. for the next iteration. The iteration continues until f′(α) is close to zero. 3. On executing the code for the test problem, the output obtained is Alpha Deriv.

18 for a quick glance at the organization of the book. 18 Organization of the book. © 2015 by Taylor & Francis Group, LLC • • • • Unconstrained problem Dual problem Constrained problems Application • Gomory’s method • Balas’ method • Branch-and-bound method Introduction Chapter Highlights • In an optimization problem, we write the objective function that is to be maximized or minimized along with inequality and equality constraints. The objective function and constraints are a function of the design variables that need to be evaluated by the optimization methods.