Mathematical and Experimental Modeling of Physical and Biological Processes (Textbooks in Mathematics v. 4)
By: H.T. Tran (author), H. T. Banks (author), Denny Gulick (series_editor)Hardback
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Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides 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.
North Carolina State University, Raleigh, USA University of Maryland, College Park, USA
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 Mass Balance and Mass Transport Introduction Compartmental Concepts Compartment Modeling General Mass Transport Equations Heat Conduction Motivating Problems Mathematical Modeling of Heat Transfer Experimental Modeling of Heat Transfer Structural Modeling: Force/Moments Balance Motivation: Control of Acoustics/Structural Interactions Introduction to Mechanics of Elastic Solids Deformations of Beams Separation of Variables: Modes and Mode Shapes Numerical Approximations: Galerkin's Method Energy Functional Formulation The Finite Element Method Experimental Beam Vibration Analysis Beam Vibrational Control and Real-Time Implementation Introduction Controllability and Observability of Linear Systems Design of State Feedback Control Systems and State Estimators Pole Placement (Relocation) Problem Linear Quadratic Regulator Theory Beam Vibrational Control: Real-Time Feedback Control Implementation Wave Propagation Fluid Dynamics Fluid Waves Experimental Modeling of the Wave Equation Size-Structured Population Models Introduction: A Motivating Application A Single Species Model (Malthusian Law) The Logistic Model A Predator/Prey Model A Size-Structured Population Model The Sinko-Streifer Model and Inverse Problems Size Structure and Mosquitofish Populations Appendix A: An Introduction to Fourier Techniques Fourier Series Fourier Transforms Appendix B: Review of Vector Calculus References appear at the end of each chapter.
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- ID: 9781420073379
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