The book begins with a short review of calculus and ordinary differential equations, then moves on to explore integral curves and surfaces of vector fields, quasi-linear and linear equations of first order, series solutions and the Cauchy Kovalevsky theorem. It then delves into linear partial differential equations, examines the Laplace, wave and heat equations, and concludes with a brief treatment of hyperbolic systems of equations.
Among the most important features of the text are the challenging problems at the end of each section which require a wide variety of responses from students, from providing details of the derivation of an item presented to solving specific problems associated with partial differential equations. Requiring only a modest mathematical background, the text will be indispensable to those who need to use partial differential equations in solving physical problems. It will provide as well the mathematical fundamentals for those who intend to pursue the study of more advanced topics, including modern theory.
This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc.
This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.
In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two?] or three?] semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.
This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings.
This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics.
The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.
Embedded & searchable equations, figures & tables
Index with linked pages numbers for easy reference
Redrawn full color figures to allow for easier identification
Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students.
The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal twoï¿1?2 or threeï¿1?2 semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has become an important subject of Mathematics and Applied Mathematics, because of its mathematical richness and its importance for applications in many areas of Physics, Biology, Economics and Finance, where random processes play an increasingly important role. One important aspect is the connection between diffusion processes and linear partial differential equations of second order, which is in particular the basis for Monte Carlo numerical methods for linear PDEs. Since the pioneering work of Peng and Pardoux in the early 1990s, a new type of SDEs called backward stochastic differential equations (BSDEs) has emerged. The two main reasons why this new class of equations is important are the connection between BSDEs and semilinear PDEs, and the fact that BSDEs constitute a natural generalization of the famous Black and Scholes model from Mathematical Finance, and thus offer a natural mathematical framework for the formulation of many new models in Finance.
Drawing on psychological and neurological studies that underscore how tightly people’s happiness and satisfaction are tied to performing hard work in the real world, Carr reveals something we already suspect: shifting our attention to computer screens can leave us disengaged and discontented.
From nineteenth-century textile mills to the cockpits of modern jets, from the frozen hunting grounds of Inuit tribes to the sterile landscapes of GPS maps, The Glass Cage explores the impact of automation from a deeply human perspective, examining the personal as well as the economic consequences of our growing dependence on computers.
With a characteristic blend of history and philosophy, poetry and science, Carr takes us on a journey from the work and early theory of Adam Smith and Alfred North Whitehead to the latest research into human attention, memory, and happiness, culminating in a moving meditation on how we can use technology to expand the human experience.
This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.
If you’ve ever thought to yourself “there has to be a better way to do this,” while using CATIA V5, then know you're probably right. There probably is a better way to complete your tasks you just don't know what it is and you don't have time to read a boring, expensive, thousand page manual on every single CATIA feature. If so, then CATIA V5 Tips and Tricks is for you. No fluff, just CATIA best practices and time savers you can put to use right away. From taming the specification tree to sketching, managing large assemblies and drawings, CATIA V5 Tips and Tricks will save you time and help you avoid common stumbling blocks.
The United States continues to mint more millionaires and billionaires than any country ever. Yet, since the great recession, three quarters of the jobs created here pay only marginally more than minimum wage. Why is there growth only at the top and the bottom?
Renowned economist and bestselling author Tyler Cowen explains that high earners are taking ever more advantage of machine intelligence and achieving ever-better results. Meanwhile, nearly every business sector relies less and less on manual labor, and that means a steady, secure life somewhere in the middle—average—is over.
In Average is Over, Cowen lays out how the new economy works and identifies what workers and entrepreneurs young and old must do to thrive in this radically new economic landscape.
Statistics for Engineering and the Sciences, Sixth Edition is designed for a two-semester introductory course on statistics for students majoring in engineering or any of the physical sciences. This popular text continues to teach students the basic concepts of data description and statistical inference as well as the statistical methods necessary for real-world applications. Students will understand how to collect and analyze data and think critically about the results.
New to the Sixth EditionMany new and updated exercises based on contemporary engineering and scientific-related studies and real data More statistical software printouts and corresponding instructions for use that reflect the latest versions of the SAS, SPSS, and MINITAB software Introduction of the case studies at the beginning of each chapter Streamlined material on all basic sampling concepts, such as random sampling and sample survey designs, which gives students an earlier introduction to key sampling issues New examples on comparing matched pairs versus independent samples, selecting the sample size for a designed experiment, and analyzing a two-factor experiment with quantitative factors New section on using regression residuals to check the assumptions required in a simple linear regression analysis
The first several chapters of the book identify the objectives of statistics, explain how to describe data, and present the basic concepts of probability. The text then introduces the two methods for making inferences about population parameters: estimation with confidence intervals and hypothesis testing. The remaining chapters extend these concepts to cover other topics useful in analyzing engineering and scientific data, including the analysis of categorical data, regression analysis, model building, analysis of variance for designed experiments, nonparametric statistics, statistical quality control, and product and system reliability.
As part of Totally Integrated Automation (TIA) Portal, the engineering software STEP 7 Basic offers a newly developed user interface, which is matched to intuitive operation. The functionality comprises all interests concerning automation: From configuring the controllers via programming in the IEC languages LAD (ladder diagram), FBD (function block diagram) and SCL (structured control language) up to program testing.
The book presents all of the hardware components of the automation system S7-1200, as well as its configuration and parameterization. A profound introduction into STEP 7 Basic V11 illustrates the basics of programming and trouble shooting. Beginners learn the basics of automation with SIMATIC S7-1200 and advanced users of S7-200 and S7-300 receive the knowledge required to work with the new PLC.
Users of STEP 7 Professional V12 will easily get along with the descriptions based on the V11. With start of V12, the screens of the technology functions might differ slightly from the V11.
Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
If you are new to pinball machines you can quickly learn how the pinball machine works and what to do about problems.
For the experienced technicians this book provides invaluable references, test points and pinouts for effective troubleshooting.
This book refers to the Williams/Bally WPC System and the System 11 however, many troubleshooting techniques and principles of operation will apply for pinball machines of different systems and manufacturers.
The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
A comprehensive shopping guide includes the hardware and software components you need in your tool box. You will learn to use Arduino UNO, Arduino Ethernet shield, and Arduino WiFi shield.
Building Arduino PLCs shows you how to build and test a simple Arduino UNO-based 5V DC logic level PLC with Grove Base shield by connecting simple sensors and actuators. You will also learn how to build industry-grade PLCs with the help of ArduiBox.
What You'll Learn
Map Arduino PLCs into the cloud using NearBus cloud connector to control the PLC through the Internet
Use do-it-yourself light platforms such as IFTTT
Enhance your PLC by adding Relay shields for connecting heavy loads
Who This Book Is For
Engineers, designers, crafters, and makers. Basic knowledge in electronics and Arduino programming or any other programming language is recommended.
As the data deluge continues in today’s world, the need to master data mining, predictive analytics, and business analytics has never been greater. These techniques and tools provide unprecedented insights into data, enabling better decision making and forecasting, and ultimately the solution of increasingly complex problems.
Learn from the Creators of the RapidMiner Software
Written by leaders in the data mining community, including the developers of the RapidMiner software, RapidMiner: Data Mining Use Cases and Business Analytics Applications provides an in-depth introduction to the application of data mining and business analytics techniques and tools in scientific research, medicine, industry, commerce, and diverse other sectors. It presents the most powerful and flexible open source software solutions: RapidMiner and RapidAnalytics. The software and their extensions can be freely downloaded at www.RapidMiner.com.
Understand Each Stage of the Data Mining Process
The book and software tools cover all relevant steps of the data mining process, from data loading, transformation, integration, aggregation, and visualization to automated feature selection, automated parameter and process optimization, and integration with other tools, such as R packages or your IT infrastructure via web services. The book and software also extensively discuss the analysis of unstructured data, including text and image mining.
Easily Implement Analytics Approaches Using RapidMiner and RapidAnalytics
Each chapter describes an application, how to approach it with data mining methods, and how to implement it with RapidMiner and RapidAnalytics. These application-oriented chapters give you not only the necessary analytics to solve problems and tasks, but also reproducible, step-by-step descriptions of using RapidMiner and RapidAnalytics. The case studies serve as blueprints for your own data mining applications, enabling you to effectively solve similar problems.
In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.
Table of Contents:
Chapter 1. Fourier series
1.1 Basic concepts
1.2 Fourier series and Fourier coefficients
1.3 A minimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem
1.4 Convergence of Fourier series
1.5 The Parseval formula
1.6 Determination of the sum of certain trigonometric series
Chapter 2. Orthogonal systems
2.1 Integration of complex-valued functions of a real variable
2.2 Orthogonal systems
2.3 Complete orthogonal systems
2.4 Integration of Fourier series
2.5 The Gram-Schmidt orthogonalization process
2.6 Sturm-Liouville problems
Chapter 3. Orthogonal polynomials
3.1 The Legendre polynomials
3.2 Legendre series
3.3 The Legendre differential equation. The generating function of the Legendre polynomials
3.4 The Tchebycheff polynomials
3.5 Tchebycheff series
3.6 The Hermite polynomials. The Laguerre polynomials
Chapter 4. Fourier transforms
4.1 Infinite interval of integration
4.2 The Fourier integral formula: a heuristic introduction
4.3 Auxiliary theorems
4.4 Proof of the Fourier integral formula. Fourier transforms
4.5 The convention theorem. The Parseval formula
Chapter 5. Laplace transforms
5.1 Definition of the Laplace transform. Domain. Analyticity
5.2 Inversion formula
5.3 Further properties of Laplace transforms. The convolution theorem
5.4 Applications to ordinary differential equations
Chapter 6. Bessel functions
6.1 The gamma function
6.2 The Bessel differential equation. Bessel functions
6.3 Some particular Bessel functions
6.4 Recursion formulas for the Bessel functions
6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions
6.6 Bessel series
6.7 The generating function of the Bessel functions of integral order
6.8 Neumann functions
Chapter 7. Partial differential equations of first order
7.2 The differential equation of a family of surfaces
7.3 Homogeneous differential equations
7.4 Linear and quasilinear differential equations
Chapter 8. Partial differential equations of second order
8.1 Problems in physics leading to partial differential equations
8.3 The wave equation
8.4 The heat equation
8.5 The Laplace equation
Answers to exercises; Bibliography; Conventions; Symbols; Index
Written on an advanced level, the book is aimed at advanced undergraduates and graduate students with a background in calculus, linear algebra, ordinary differential equations, and complex analysis. Over 260 carefully chosen exercises, with answers, encompass both routing and more challenging problems to help students test their grasp of the material.