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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

By : Ranja Sarkar, Dr. Ranja Sarkar
4.1 (7)
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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

4.1 (7)
By: Ranja Sarkar, Dr. Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
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1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Summary

In this chapter, we explored the Kalman filter – the estimation and prediction algorithm utilized to solve problems in signal processing, navigation, and control systems. There are linear and univariate (one-dimensional) Kalman filters in which the system dynamics are assumed to be linear. Many dynamic processes, however, have more than one dimension, and in such cases, we utilize multivariate and mostly non-linear (or extended) Kalman filters. For example, the state vector that describes a moving object’s position and velocity in space is six-dimensional, and a non-linear Kalman filter is utilized to determine the displacement (and velocity) in space of such an object. Also, the Kalman filter consumes low computational power (leading to a shorter runtime) due to the usage of matrices in its operation that occupy less computer memory. The Kalman filter is arguably the best estimation algorithm with noisy data as it mitigates the uncertainty by combining the information...

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