Functons Modeling Change

The third edition of this ground-breaking text continues the authors' goal - a targeted introduction to precalculus that carefully balances concepts with procedures. Overall, this text is designed to provide a solid foundation to precalculus that focuses on a small number of key topics thereby emphasizing depth of understanding rather than breath of coverage. Developed by the Calculus Consortium, FMC 3e is flexible enough to be thought-provoking for well-prepared students while still remaining accessible to students with weaker backgrounds. As multiple representations encourage students to reflect on the material, each function is presented symbolically, numerically, graphically and verbally (the Rule of Four). Additionally, a large number of real-world applications, examples and problems enable students to create mathematical models that will help them understand and interpret the world in which they live.

An accessible Precalculus text with concepts, examples, and problems The sixth edition of Functions Modeling Change: A Preparation for Calculus helps students establish a foundation for studying Calculus. The text covers key Precalculus topics, examples, and problems. Chapters examine linear, quadratic, logarithmic, exponential, polynomial, and rational functions. They also explore trigonometry and trigonometric Identities, plus vectors and matrices. The end of each chapter offers details on how students can strengthen their knowledge about the topics covered.

Functions Modeling Change, 6th edition prepares students for Calculus by stressing conceptual understanding and the connections among mathematical ideas. The authors emphasize depth of understanding rather than breadth of coverage. Each function is presented symbolically, numerically, graphically and verbally (the Rule of Four.) Students are encouraged to create mathematical models that relate to the world around them and are exposed to a large number of real-world applications, examples, and problems.

FUNCTIONS AND CHANGE: A MODELING APPROACH TO COLLEGE ALGEBRA, 4E, INTERNATIONAL EDITION provides an alternative to a traditional college algebra course for students who either will not take another math course or may go on to a business calculus course. The authors wrote this text for the many college algebra students who are poorly served by books that focus on preparing them for a course they will never take, traditional calculus.

You want increased customer satisfaction, faster development cycles, and less wasted work. Domain-driven design (DDD) combined with functional programming is the innovative combo that will get you there. In this pragmatic, down-to-earth guide, you'll see how applying the core principles of functional programming can result in software designs that model real-world requirements both elegantly and concisely - often more so than an object-oriented approach. Practical examples in the open-source F# functional language, and examples from familiar business domains, show you how to apply these techniques to build software that is business-focused, flexible, and high quality. Domain-driven design is a well-established approach to designing software that ensures that domain experts and developers work together effectively to create high-quality software. This book is the first to combine DDD with techniques from statically typed functional programming. This book is perfect for newcomers to DDD or functional programming - all the techniques you need will be introduced and explained. Model a complex domain accurately using the F# type system, creating compilable code that is also readable documentation---ensuring that the code and design never get out of sync. Encode business rules in the design so that you have "compile-time unit tests," and eliminate many potential bugs by making illegal states unrepresentable. Assemble a series of small, testable functions into a complete use case, and compose these individual scenarios into a large-scale design. Discover why the combination of functional programming and DDD leads naturally to service-oriented and hexagonal architectures. Finally, create a functional domain model that works with traditional databases, NoSQL, and event stores, and safely expose your domain via a website or API. Solve real problems by focusing on real-world requirements for your software. What You Need: The code in this book is designed to be run interactively on Windows, Mac and Linux.You will need a recent version of F# (4.0 or greater), and the appropriate .NET runtime for your platform.Full installation instructions for all platforms at fsharp.org.

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?