Linear Approximation in Mathematics for Management with Florian Rupp
"Explore the role of linear approximation in mathematics for management, understanding the behavior of functions near a point, quality of approximation, and its applications in this comprehensive guide by Prof. Dr. Florian Rupp. Learn about tangent lines, polynomial approximations, and the accuracy of linearization for functions. Dive into examples and discussions about the local approximation of functions through linearization."
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Presentation Transcript
Florian Rupp Calculus I for MGMT Applications of Differentiation Linear Approximation Mathematics for Management Supplementary Electronic Materials Applications of Differentiation The Chain Rule Implicit Differentiation Prof. Dr. Giorgi Chelidze, Prof. Dr. Malkhaz Shashiashvili & Prof. Dr. Dr. h.c. Florian Rupp Linear Approximation L Hospital s Rules & Indeterminate Forms Kutaisi International University
Approximation plays a key role in mathematics and its applications We have already seen that a tangent line can be used to locally understand the behavior of a function (linear approximation) near a point a. Taking further information into account, like second, third, order derivatives the approximation becomes more accurate for a wider range of numbers about the point of expansion a. This procedure even allows us later to write certain functions as infinite power-series. The major question in this context are that of the quality of the approximation and range on which we trust the approximation. Example: successive polynomial approximation of the sine function at 0 Next, we discuss some aspects of these two questions for linear approximations. animation
By zooming in toward a point on the graph of a differentiable function, we already noticed that the graph looks more and more like its tangent line
this gives rise to the (local) approximation of a function by its linearization
Example: Linear approximation
Example: Linear approximation
Example: Linear approximation
Example: Linear approximation
Florian Rupp Calculus I for Management Questions & Remarks? Thank You Very Much
