Abstract
Differentiation is the inverse of integration, and its salient features are developed. Differentiation is defined by comparing two integrals that differ infinitesimally—in contrast to starting with a continuous curve and defining differentiation as the tangent to the curve. Taylor expansion is defined and used for analyzing the maximum and minimum of functions. The Hessian matrix is defined to study various types of optimization problems that occur in economics; in particular, the Cobb-Douglas production function is used for analyzing the maximization of a firm’s profit. Constrained optimization using the Lagrange multiplier is studied.
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Notes
- 1.
What is the maximum distance that the point a can be from point x and still have a valid Taylor expansion? To answer this one needs to look at the behavior of the function by first complexifying the argument x and then determining the function’s analytic structure.
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Baaquie, B.E. (2020). Differentiation. In: Mathematical Methods and Quantum Mathematics for Economics and Finance. Springer, Singapore. https://doi.org/10.1007/978-981-15-6611-0_6
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DOI: https://doi.org/10.1007/978-981-15-6611-0_6
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