Mathematical Models Volume Iii

THE MUCH ANTICIPATED THIRD INSTALLMENT IN THE WALL STREET JOURNAL BESTSELLING SERIES 'THE GREAT MENTAL MODELS'. Solve problems. Think with clarity. Achieve your goals. The secret to better decision-making is learning things that won't change. Mastering a small number of versatile concepts with broad applicability enables you to rapidly grasp new areas, identify patterns, and understand how the world works. Don't waste your time on knowledge with an expiry date - focus on the fundamentals. The Farnam Street latticework of mental models gives you the durable cognitive tools you need to avoid problems and make better decisions. A mental model is a representation of how something works. Constructing mental models helps you to navigate the world efficiently and intelligently. Time and time again, great thinkers such as Charlie Munger and Warren Buffett have found mental models indispensable in both solving problems and preventing them in the first place. Cultivating stronger mental models is one of the most powerful things you can do to become a better thinker. The Great Mental Models: Volume 3 covers essential models from mathematics and systems. In part one, you'll learn mental models from systems, helping you see unexpected connections and avoid costly mistakes. You'll discover how these concepts govern the behaviors and interactions in your life. Part one covers topics such as how to: Identify the right feedback loops to adjust for behavior change (your own and others') Leverage bottlenecks to supercharge your innovative capabilities Scale up businesses and other endeavors without damaging their longevity Reduce risk and preventing disaster by knowing when to incorporate a margin of safety Construct reliable algorithms in your mind for predictable success to get the results you want every time In part two, you'll learn mental models from mathematics that reveal logical patterns in the world. This isn't your high school math class. Part two covers topics such as how to: Reap exponential gains by investing in knowledge, relationships, and experiences that compound Utilize the surprising power of sample sizes to reshape your perspective and open your mind Embrace randomness to become less predictable and more creative Identify the fundamental components of systems that lead to failure if neglected - so you can focus your energy where it matters most Mastering The Great Mental Models helps you thrive in an uncertain world. The right cognitive tools prepare you for any type of challenge. From parenting to healthy eating, relationships to personal productivity, and from learning to product design, this book will give you new lenses for understanding life. A wonderful resource you'll keep returning to year after year. As you incorporate the models in this book into your mental toolbox, you'll see the world with fresh eyes. START BUILDING YOUR LATTICEWORK TODAY! Praise for The Great Mental Models series: "I'm really glad this exists in the world and I can see that I will be recommending it often." -- Matt Mullenweg, co-founder of WordPress, founder and CEO of Automattic "If you've read Charlie Munger's Almanack this is the book you deeply crave in its wake. ... Learn the big ideas from the big disciplines and you'll be able to twist and turn problems in interesting ways at unprecedented speeds. ... You owe yourself this book." -- Simon Eskildsen "This is what non-fiction books should aspire to be like. Informative, concise, universal, practical, visual, sharing stories and examples for context. Definitely, a must-read if you're into universal multi-disciplinary thinking." -- Carl Rannaberg "I can truly say it is one of the best books I've ever had the pleasure of getting lost in. I loved the book and the challenges to conventional wisdom and thinking it presents." -- Rod Berryman "Want to learn? Read This! This should be a standard text for high school and university students." -- Code Cubitt

This book is dedicated to the approximation of solutions of nonlinear equations using iterative methods. The study about convergence matter of iterative methods is usually based on two categories: semi-local and local convergence analysis. The semi-local convergence category is, based on the information around an initial point, to provide criteria ensuring the convergence of the method; while the local one is, based on the information around a solution, to find estimates of the radii of the convergence balls. The book is divided into two volumes. The chapters in each volume are self-contained so they can be read independently. Each chapter contains semi-local and local convergence results for single, multi-step and multi-point old and new contemporary iterative methods involving Banach, Hilbert or Euclidean valued operators. These methods are used to generate a sequence defined on the aforementioned spaces that converges with a solution of a nonlinear equation, an inverse problem or an ill-posed problem. It is worth mentioning that most problems in computational and related disciplines can be brought in the form of an equation using mathematical modelling. The solutions of equations can be found in analytical form only in special cases. Hence, it is very important to study the convergence of iterative methods. The book is a valuable tool for researchers, practitioners, graduate students, and can also be used as a textbook for seminars in all computational and related disciplines.

Mathematical Models is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Mathematical Models discusses matters of great relevance to our world such as: Basic Principles of Mathematical Modeling; Mathematical Models in Water Sciences; Mathematical Models in Energy Sciences; Mathematical Models of Climate and Global Change; Infiltration and Ponding; Mathematical Models of Biology; Mathematical Models in Medicine and Public Health; Mathematical Models of Society and Development. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

Students of mathematics learn best when taught by a teacher with a deep and conceptual understanding of the fundamentals of mathematics. In Mathematical Models for Teaching, Ann Kajander and Tom Boland argue that teachers must be equipped with a knowledge of mathematics for teaching, which is grounded in modelling, reasoning, and problem-based learning.

This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.

Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.