Mathematical and Experimental Modeling of Physical and Biological Processes [Hardcover]

Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processesprovides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model.

Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. The authors also describe the hardware and software tools used to design the experiments so faculty/students can duplicate them.

Integrating real-world applications into the traditional mathematics curriculum, this textbook deals with the formulation and analysis of mathematical models in science and engineering. It gives students an appreciation of the use of mathematics and encourages them to further study the applied topics. Real experimental data for projects can be downloaded from CRC Press Online.

Introduction: The Iterative Modeling Process

Modeling and Inverse Problems

Mechanical Vibrations

Inverse Problems

Mathematical and Statistical Aspects of Inverse Problems

Probability and Statistics Overview

Parameter Estimation or Inverse Problems

Computation of sigmaⁿ, Standard Errors, and Confidence Intervals

Investigation of Statistical Assumptions

Statistically Based Model Comparison Techniques