This volume is dedicated to the legacy of David R. Adams (1941-2021) and discusses calculus of variations, functional - harmonic - potential analysis, partial differential equations, and their applications in modeling, mathematical physics, and differential - integral geometry.

Guiding readers from the elucidation and analysis of a genomic sequence to the prediction of a protein structure and the identification of the molecular function, Introduction to Bioinformatics describes the rationale and limitations of the bioinformatics methods and tools that can help solve biological problems. Requiring only a limited mathematical and statistical background, the book shows how to efficiently apply these approaches to biological data and evaluate the resulting information.

The author, an expert bioinformatics researcher, first addresses the ways of storing and retrieving the enormous amount of biological data produced every day and the methods of decrypting the information encoded by a genome. She then covers the tools that can detect and exploit the evolutionary and functional relationships among biological elements. Subsequent chapters illustrate how to predict the three-dimensional structure of a protein. The book concludes with a discussion of the future of bioinformatics.

Even though the future will undoubtedly offer new tools for tackling problems, most of the fundamental aspects of bioinformatics will not change. This resource provides the essential information to understand bioinformatics methods, ultimately facilitating in the solution of biological problems.

Tumour evolution is a complex process involving many different phenomena. Mathematical modelling and computer simulations can help us understand these phenomena, but their development requires a multidisciplinary background-one that includes an understanding of the biological phenomena involved and knowledge of the mathematical techniques used to obtain both qualitative and quantitative results.

Cancer Modelling and Simulation builds the requisite biological foundation and presents the mathematical models and methods most useful for understanding the dynamics of tumour development and growth. In chapters contributed by an interdisciplinary team of leading researchers, this book addresses the entire modelling process, from phenomenological observation to simulation and validation, through the development of mathematical models and their qualitative and quantitative study.

This treatment effectively links the analytical, mathematical, and biological aspects of tumour growth modelling to provide researchers from multiple disciplines with the common language and practical knowledge they need to break down the barriers that can hamper interdisciplinary research. Cancer Modelling and Simulation is an important contribution to the field that undoubtedly will stimulate and remain a valuable reference for continued research for many years.

From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB(R) codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.

The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone.

Proven in the classroom and requiring only a background in high school math, "Mathematics for the Life Sciences" doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences.Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biologyCovers all the major quantitative concepts that national reports have identified as the ideal components of an entry-level course for life science studentsProvides good background for the MCAT, which now includes data-based and statistical reasoningExplicitly links data and math modelingIncludes end-of-chapter homework problems, end-of-unit student projects, and select answers to homework problemsUses MATLAB throughout, and MATLAB m-files with an R supplement are available onlinePrepares students to read with comprehension the growing quantitative literature across the life sciencesForthcoming online answer key, solution guide, and illustration package (available to professors)