Above all, successful niche modeling requires a deep understanding of the process of creating and using probability. Off-the-shelf statistical packages are tailored exactly to applications but can hide problematic complexities. Recipe book implementations fail to educate users in the details, assumptions, and pitfalls of analysis, but may be able to adapt to the specific needs of each study. Examining the sources of errors such as autocorrelation, bias, long term persistence, nonlinearity, circularity, and fraud, this seminal reference provides an understanding of the limitations and potential pitfalls of prediction, emphasizing the importance of avoiding errors.

This book­ the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys­ tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded.

Additional topical coverage includes:

• Sets and functions
• Real numbers
• Vector functions
• Normed vector spaces
• First- and higher-order derivatives
• Diffeomorphisms and manifolds
• Multiple integrals
• Integration on manifolds
• Stokes’ theorem
• Basic point set topology

Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants.

This high-level research text is recommended for all those researching or studying in the fields of applied mathematics, applied engineering, and physics-particularly in the areas of stochastic differential equations, dynamical systems, stability, and control theory.

For anyone who needs to learn calculus, the best place to start is by gaining a solid foundation in precalculus concepts. This new book provides that foundation. It includes only the topics that they’ll need to succeed in calculus. Axler explores the necessary topics in greater detail. Readers will benefit from the straightforward definitions and examples of complex concepts. Step-by-step solutions for odd-numbered exercises are also included so they can model their own applications of what they’ve learned

The book begins with a summary of set theory and then introduces probability and its axioms. The author has carefully avoided a theorem-proof type of presentation. He includes all of the theory but presents it in a conversational rather than formal manner, while relying on the assumption that undergraduate engineering students have a solid mastery of calculus. He explains mathematical theory by demonstrating how it is used with examples based on engineering applications. An important aspect of the text is the fact that examples are not presented in terms of “balls in urns”. Many examples relate to gambling with coins, dice and cards but most are based on observable physical phenomena familiar to engineering students.

This approach combines interactive decision trees with Bayesian partition models and supports and interactive, iterative and intuitive way of causal investigation. The proposed method considers dependencies, in particular taxonomic and partonomic relationships among influencing variables and indentifies the most likely, semantically meaningful partitions that are close to the concept that actually caused a quality issue. An evaluation on test data and real-world case studies illustrate how the approach can be used by engineers to investigate cause-effect relationships.

It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi­ tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

This volume also provides a mathematical programming perspective on open questions in auction theory, and provides a glimpse of the growing area of dynamic pricing.