Tillämpad matematik

Advanced Engineering Mathematics, 11th Edition, is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self-contained subject matter parts for maximum flexibility. It opens with ordinary differential equations and ends with the topic of mathematical statistics. The analysis chapters address: Fourier analysis and partial differential equations, complex analysis, and numeric analysis. The book is written by a pioneer in the field of applied mathematics. This comprehensive volume is designed to equip students and professionals with the mathematical tools necessary to tackle complex engineering challenges and drive innovation.  This edition of the text maintains those aspects of the previous editions that have led to the book being so successful. In addition to introducing a new appendix on emerging topics in applied mathematics, each chapter now features a dedicated section on how mathematical modeling and engineering can address environmental and societal challenges, promoting sustainability and ethical practices. This edition includes a revision of the problem sets, making them even more effective, useful, and up-to-date by adding the problems on open-source mathematical software.

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings.  It is a revolutionary work, astounding in its foresight and contemporaneity.  The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

Using everyday computational power to tackle complex—and seemingly unsolvable—math problemsConfronted by a math problem of seemingly impenetrable difficulty, what can you do? In The Delicate Art of Brute Force, Paul Nahin shows how even if you can’t solve such a problem, you can still get an answer. The computational power of your own computer—the desktop in your home office, the laptop on your coffee table—can be deployed to overwhelm a problem’s complexity through a massive number-crunching assault. Nahin presents a series of apparently intractable math problems and shows the thought process that allows computational solution. Most of the problems are not abstract constructions but originate in the real world—one chapter is titled “How Wi-Fi Coverage and Anti-Submarine Warfare Are the Same.” For each one, Nahin compares computational and analytical approaches, demonstrating how well the computer solutions agree with theory. As a bonus, sometimes the computational solution is better, giving more insight or greater flexibility.Along the way, Nahin traces the evolution of high-speed electronic computation, explaining that it upended the way analysts approach complex math problems. After the postwar debut of ENIAC (Electronic Numerical Integrator and Computer) and the ever more powerful electronic computers that came afterward, problems that were simply too difficult or messy for analytical treatment could be defeated by the application of pure brute force—the ability of computers to perform an enormous number of simple operations in just minutes. Today, we can harness that computational power from our couches. Accessible to anyone who’s mastered high school calculus, this engaging book gives both mathematicians and nonmathematicians plenty to think about.

Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice Summaries at the end of each chapter allow for quick access to important information Includes code in Jupyter notebook format that can be directly run online

Credit Intelligence and Modelling provides an indispensable explanation of the statistical models and methods used when assessing credit risk and automating decisions. Over eight modules, the book covers consumer and business lending in both the developed and developing worlds, providing the frameworks for both theory and practice. It first explores an introduction to credit risk assessment and predictive modelling, micro-histories of credit and credit scoring, as well as the processes used throughout the credit risk management cycle. Mathematical and statistical tools used to develop and assess predictive models are then considered, in addition to project management and data assembly, data preparation from sampling to reject inference, and finally model training through to implementation.Although the focus is credit risk, especially in the retail consumer and small-business segments, many concepts are common across disciplines, whether for academic research or practical use. The book assumes little prior knowledge, thus making it an indispensable desktop reference for students and practitioners alike. Credit Intelligence and Modelling expands on the success of The Credit Scoring Toolkit to cover credit rating and intelligence agencies, and the data and tools used as part of the process.

The long-awaited, comprehensive guide to practical credit risk modeling Credit Risk Analytics provides a targeted training guide for risk managers looking to efficiently build or validate in-house models for credit risk management. Combining theory with practice, this book walks you through the fundamentals of credit risk management and shows you how to implement these concepts using the SAS credit risk management program, with helpful code provided. Coverage includes data analysis and preprocessing, credit scoring; PD and LGD estimation and forecasting, low default portfolios, correlation modeling and estimation, validation, implementation of prudential regulation, stress testing of existing modeling concepts, and more, to provide a one-stop tutorial and reference for credit risk analytics. The companion website offers examples of both real and simulated credit portfolio data to help you more easily implement the concepts discussed, and the expert author team provides practical insight on this real-world intersection of finance, statistics, and analytics. SAS is the preferred software for credit risk modeling due to its functionality and ability to process large amounts of data. This book shows you how to exploit the capabilities of this high-powered package to create clean, accurate credit risk management models. Understand the general concepts of credit risk managementValidate and stress-test existing modelsAccess working examples based on both real and simulated dataLearn useful code for implementing and validating models in SASDespite the high demand for in-house models, there is little comprehensive training available; practitioners are left to comb through piece-meal resources, executive training courses, and consultancies to cobble together the information they need. This book ends the search by providing a comprehensive, focused resource backed by expert guidance. Credit Risk Analytics is the reference every risk manager needs to streamline the modeling process.

The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data.The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly frommedicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.

Uncover one of the most exciting frontiers of modern physics in this fascinating, insightful and accessible overview of Chaos theory.‘An exceedingly readable introduction to a new intellectual world’ ObserverFrom the turbulence of the weather to the complicated rythmns of the human heart, ‘chaos’ is at the centre of our day to day lives. Cutting across several scientific disciplines, James Gleick explores and elucidates the science of the unpredicatable with an immensely readable narrative style and flair.‘An awe-inspiring book. Reading Chaos gave me the sensation that someone had just found the light-switch’ Douglas Adams

Mathematics is playing an increasing important role in society and the sciences, enhancing our ability to use models and handle data. While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world in which we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields. This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics and engineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Explore the life-changing magic of trigonometry with Matt Parker, stand-up mathematician and No. 1 bestselling author of Humble PiWhy can no two people ever see the same rainbow? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? Why does the wake behind a duck always form an angle of exactly 39 degrees? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle.In Love Triangle, stand-up comedian, ex-maths teacher and Sunday Times number one bestselling author Matt Parker is on a mission to prove why we should all show a lot more love for triangles, along with the useful trigonometry and geometry they enable. To make his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich into three equal parts, and measure tall buildings while wearing silly shoes. But soon these hare-brained experiments begin to reveal a genuinely important truth: triangles are the hidden pattern beneath the surface of the contemporary world, used in everything from GPS to CGI via Spotify streaming, the play button and your best mate’s triangle tattoo.Join Matt Parker as he demonstrates why there’s more to triangles than Pythagoras and SOHCAHTOA. Triangles are everything and everything is triangles.

'Wooldridge is like the teacher you wish you'd had'GUARDIAN'This book is simply brilliant . . . I learned so much'SIR DAVID SPIEGELHALTER, UNIVERSITY OF CAMBRIDGE'Fresh, clever and playful'MATT RIDLEY, AUTHOR OF THE ORIGINS OF VIRTUE'Michael explains the complex, strategic structures of our world with masterful beauty'MILIND TAMBE, HARVARD UNIVERSITY'Effortlessly covers a broad swath of core ideas in game theory, with a sprinkle of British humour'EDITH ELKIND, NORTHWESTERN UNIVERSITY'A wonderful book'YOAV SHOHAM, STANFORD UNIVERSITY______A fascinating deep-dive into game theory, its history and its practical applications by award-winning expert on computer science and artificial intelligence.Most of us have some idea about game theory. Concepts like zero-sum games and the prisoner's dilemma crop up in films, novels and casual conversation, often as shorthand for cut-throat competition or inevitable betrayal. But game theory, the science behind these ideas, is widely misunderstood. All too often it's seen solely as the science of conflict and greed. In fact, this field has a lot to teach us about how to make a better world. It shows us just what it takes to enable cooperation and mutual benefit.This essential primer presents twenty one 'life lessons from game theory', which illustrate the key ideas in the field, and which are packed with real world examples: from overfishing in the Atlantic; to the Cuban Missile Crisis; to security measures at international airports; to advertising wars between major brands. This is a hopeful and practical book that highlights the value of game theory and provides a course correction for its integration into the real world.

'Wooldridge is like the teacher you wish you'd had' GUARDIAN'This book is simply brilliant . . . I learned so much' SIR DAVID SPIEGELHALTER, UNIVERSITY OF CAMBRIDGE'Fresh, clever and playful' MATT RIDLEY, AUTHOR OF THE ORIGINS OF VIRTUE'Michael explains the complex, strategic structures of our world with masterful beauty'MILIND TAMBE, HARVARD UNIVERSITY'Effortlessly covers a broad swath of core ideas in game theory, with a sprinkle of British humour'EDITH ELKIND, NORTHWESTERN UNIVERSITY'A wonderful book' YOAV SHOHAM, STANFORD UNIVERSITY______A fascinating deep-dive into game theory, its history and its practical applications by award-winning expert on computer science and artificial intelligence.Most of us have some idea about game theory. Concepts like zero-sum games and the prisoner's dilemma crop up in films, novels and casual conversation, often as shorthand for cut-throat competition or inevitable betrayal. But game theory, the science behind these ideas, is widely misunderstood. All too often it's seen solely as the science of conflict and greed. In fact, this field has a lot to teach us about how to make a better world. It shows us just what it takes to enable cooperation and mutual benefit.This essential primer presents twenty one 'life lessons from game theory', which illustrate the key ideas in the field, and which are packed with real world examples: from overfishing in the Atlantic; to the Cuban Missile Crisis; to security measures at international airports; to advertising wars between major brands. This is a hopeful and practical book that highlights the value of game theory and provides a course correction for its integration into the real world.

This practical guide to optimization combines mathematical theory with hands-on coding examples to explore how Python can be used to model problems and obtain the best possible solutions. Presenting a balance of theory and practical applications, it is the ideal resource for upper-undergraduate and graduate students in applied mathematics, data science, business, industrial engineering and operations research, as well as practitioners in related fields. Beginning with an introduction to the concept of optimization, this text presents the key ingredients of an optimization problem and the choices one needs to make when modeling a real-life problem mathematically. Topics covered range from linear and network optimization to convex optimization and optimizations under uncertainty. The book's Python code snippets, alongside more than 50 Jupyter notebooks on the author's GitHub, allow students to put the theory into practice and solve problems inspired by real-life challenges, while numerous exercises sharpen students' understanding of the methods discussed.

The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists.

What is time? The Janus Point offers a ground-breaking solution to one of the greatest mysteries in physics.For over a century, the greatest minds have sought to understand why time seems to flow in one direction, ever forward. In The Janus Point, Julian Barbour offers a radically new answer: it doesn't.At the heart of this book, Barbour provides a new vision of the Big Bang - the Janus Point - from which time flows in two directions, its currents driven by the expansion of the universe and the growth of order in the galaxies, planets and life itself. What emerges is not just a revolutionary new theory of time, but a hopeful argument about the destiny of our universe.'Both a work of literature and a masterpiece of scientific thought' Lee Smolin, author of The Trouble with Physics'Profound...original...accessible to anyone who has pondered the mysteries of space and time' Martin Rees, Astronomer Royal 'Takes on fundamental questions, offering a new perspective on how the Universe started and where it may be headed' Science Magazine

This is a somewhat extended and modified translation of the third edition of the text, first published in 1969. The Swedish edition has been used for many years at the Royal Institute of Technology in Stockholm, and at the School of Engineering at Link6ping University. It is also used in elementary courses for students of mathematics and science. The book is not intended for students interested only in theory, nor is it suited for those seeking only statistical recipes. Indeed, it is designed to be intermediate between these extremes. I have given much thought to the question of dividing the space, in an appropriate way, between mathematical arguments and practical applications. Mathematical niceties have been left aside entirely, and many results are obtained by analogy. The students I have in mind should have three ingredients in their course: elementary probability theory with applications, statistical theory with applications, and something about the planning of practical investiga­ tions. When pouring these three ingredients into the soup, I have tried to draw upon my experience as a university teacher and on my earlier years as an industrial statistician. The programme may sound bold, and the reader should not expect too much from this book. Today, probability, statistics and the planning of investigations cover vast areas and, in 356 pages, only the most basic problems can be discussed. If the reader gains a good understanding of probabilistic and statistical reasoning, the main purpose of the book has been fulfilled.

THE INTERNATIONAL BESTSELLER'An entertaining tour that will change how you see the world' Sean Carroll, author of Something Deeply HiddenIs there a secret formula for improving your life? For making something a viral hit? For deciding how long to stick with your current job, Netflix series, or even relationship?This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians - until now.With wit and clarity, mathematician David Sumpter shows that it isn't the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone can learn.Empowering and illuminating, The Ten Equations that Rule the World shows how maths really can change your life.

A half-century ago, advanced calculus was a well-de?ned subject at the core of the undergraduate mathematics curriulum. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached. Over time, certain aspects of the course came to be seen as more signi?cant—those seen as giving a rigorous foundation to calculus—and they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core. Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. In fact, a bifurcation occurred. In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III. In my experience, though, it does not manage to accomplish what the old advancedcalculus course did. Multivariable calculusnaturallysplits intothreeparts:(1)severalfunctionsofonevariable,(2)one function of several variables, and (3) several functions of several variables. The ?rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester. To put it another way: Green’s theorem ?ts comfortably; Stokes’ and Gauss’ do not.

Nonlinear waves are of significant scientific interest across many diverse contexts, ranging from mathematics and physics to engineering, biosciences, chemistry, and finance. The study of nonlinear waves is relevant to Bose-Einstein condensates, the interaction of electromagnetic waves with matter, optical fibers and waveguides, acoustics, water waves, atmospheric and planetary scales, and even galaxy formation. The aim of this book is to provide a self-contained introduction to the continuously developing field of nonlinear waves, that offers the background, the basic ideas, and mathematical, as well as computational methods, while also presenting an overview of associated physical applications.Originated from the authors' own research activity in the field for almost three decades and shaped over many years of teaching on relevant courses, the primary purpose of this book is to serve as a textbook. However, the selection and exposition of the material will be useful to anyone who is curious to explore the fascinating world of nonlinear waves.

This book offers an accessible introduction to random walk and diffusion models at a level consistent with the typical background of students in the life sciences. In recent decades these models have become widely used in areas far beyond their traditional origins in physics, for example, in studies of animal behavior, ecology, sociology, sports science, population genetics, public health applications, and human decision making.  Developing the main formal concepts, the book provides detailed and intuitive step-by-step explanations, and moves smoothly from simple to more complex models. Finally, in the last chapter, some successful and original applications of random walk and diffusion models in the life and behavioral sciences are illustrated in detail. The treatment of basic techniques and models is consolidated and extended throughout by a set of carefully chosen exercises.

Very Short Introductions: Brilliant, Sharp, Inspiring Fluid mechanics is an important branch of physics concerned with the way in which fluids, such as liquids and gases, behave when in motion and at rest. A quintessential interdisciplinary field of science, it interacts with many other scientific disciplines, from chemistry and biology to mathematics and engineering.This Very Short Introduction presents the field of fluid mechanics by focusing on the underlying physical ideas and using everyday phenomena to demonstrate them, from dripping taps to swimming ducks. Eric Lauga shows how this set of fundamental physical concepts can be applied to a wide range of flow behaviours and highlights the role of fluid motion in both the natural and industrial worlds. This book also considers future applications of fluid mechanics in science.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory.Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variablesmartingalespercolationMarkov chains and electrical networksconstruction of stochastic processesPoisson point process and infinite divisibilitylarge deviation principles and statistical physicsBrownian motionstochastic integrals and stochastic differential equations.The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts.This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.