Exam board: SQA Level: Advanced Higher Subject: Mathematics First teaching: August 2019 First exam: Summer 2021 Trust Scotland's most popular revision guides to deliver the results you want. The How to Pass series is chosen by students, parents and teachers again and again. > Recap and remember course content. Concise summaries and diagrams cover the important points for each Key Area in the latest SQA specification. > Test your skills and knowledge. Regular 'check-up' questions throughout the text help you to see if a topic is secure before you move on. This style of active revision is much more effective than simply reading. > Practise exam-style questions. Formal questions with mark allocations are provided at the end of each Key Area, reflecting the types of questions you will face in the exam. > Get expert tips for exam success. Hints on how to achieve top marks and avoid mistakes are based on feedback in the SQA examiners' Course Reports, giving you insight into the marking process. > Teach yourself with confidence. Independent study has never been easier with clear explanations and answers to all questions at the back of the book. > Plan and manage your revision. Checklists for each Key Area enable you to benchmark your progress against SQA's assessment standards and make sure you're on track to get the grades you need.

This bookdescribes computational financetools. It covers fundamental numerical analysis and computational techniques, such asoption pricing, and givesspecial attention tosimulation and optimization. Many chapters are organized as case studies aroundportfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website.
Shows ways to build and implement tools that help test ideasFocuses on the application of heuristics; standard methods receive limited attentionPresents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models"

This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time. The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.

This book shares the latest findings on this topic, systematically introduces readers to advances made in robotic harvesting around the globe, and explores the relations between the development of robotic harvesting and the respective social/economic conditions and agricultural business patterns in various countries/regions. Due to the unstructured setting it is used in, and to the significant differences between individual fruit and vegetable targets, robotic harvesting is currently considered to be one of the most challenging robotics technologies. Accordingly, research into this area involves the integration of various aspects, including biomechanics, optimization design, advanced perception and intelligent control. In addition to rapid and damage-free robotic harvesting, which reflects the multidisciplinary nature of the topic, further aspects addressed include gripping collisions with viscoelastic objects, using lasers to cut plant material, plant-fruit response to vacuum sucking and pulling, and performance probability distribution. Highlighting outstanding innovations and reflecting the latest advances in intelligent agricultural equipment in China, the book offers a unique and valuable resource.

The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganes, Spain, from July 3 to July 6, 2018.These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields.In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.

This book examines the problems in the field of energy and related fields (chemical, transport, aerospace, construction, metallurgy, engineering, etc.) and consists of 4 subsections: Electrical Engineering, Heat Power Engineering, Cybersecurity and Computer Science & Environmental Safety. In the first section, authors pay attention to contemporary issues related to the development of the electric power industry, electrical engineering, the physics of electrical phenomena and renewable energy sources (such as solar energy and wind energy). The second section is devoted to modern problems in heat power engineering and considers modern means and methods that increase the efficiency and reliability of the functioning of heat power facilities. The third section is devoted to issues of cybersecurity of critical facilities, in particular energy facilities, as well as the development of computer science and the introduction of modern information and measurement systems in the energy sector. The fourth subsection deals with the problems of rational use of natural resources, accounting for emissions of harmful substances, environmental issues at energy facilities, as well as the development of a methodology for environmental safety. The book includes 21 chapters. A book is for researchers, engineers, as well as lecturers and postgraduates of higher education institutions dealing with issues of control, diagnosis and monitoring of energy facilities.

Many student private pilots don't realize at the start of their course that many hours of study are required on top of the in-class schedule. This book will help those trainee pilots without science backgrounds, or those that need a refresher, to brush up on the necessary theory. It covers subjects that will be encountered many times during the PPL course, such as principles of flight, aircraft general knowledge, flight performance and planning, meteorology, navigation and human factors. The content is organized around two main groups of information, namely core knowledge, concentrating more on the concepts; and a practical toolbox, dedicated to some techniques that will be required during the course.

The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author’s best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS – a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example – explaining fully the choice of model for each particular problem. The book

The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.

Larson/Edwards' student-oriented CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 8th INTERNATIONAL METRIC Edition with WebAssign digital resources and online tutorials clearly introduces the concepts and rules behind calculus. Updated content is designed to remove barriers to learning to include all students in the learning experience. New features, such as "Big Ideas of Calculus," and updated exercises work with annotated examples and online tutorials at CalcView.com, CalcChat.com and LarsonCalculus.com to help students master key concepts. New automatically-graded Proof Problems, Expanded Problems and interactive learning modules also strengthen conceptual understanding. You can customize WebAssign online resources to deliver content that's best for your course needs.

This edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied. Contributions cover a variety of different topics and problems treated such as structure and optimization in computational harmonic analysis, sampling and approximation in shift invariant subspaces of L2( ), optimal rank one matrix decomposition, the Riemann Hypothesis, large sets avoiding rough patterns, Hardy Littlewood series, Navier-Stokes equations, sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools, harmonic functions in slabs and half-spaces, Andoni -Krauthgamer -Razenshteyn characterization of sketchable norms fails for sketchable metrics, random matrix theory, multiplicative completion of redundant systems in Hilbert and Banach function spaces. Efforts have been made to ensure that the content of the book constitutes a valuable resource for graduate students as well as senior researchers working on Harmonic Analysis and its various interconnections with related areas.

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance.

Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon s needle problem" provides a unifying theme as it is repeatedly used to illustrate many features of Monte Carlo methods.

This book provides the basic detail necessary to learn how to apply Monte Carlo methods and thus should be useful as a text book for undergraduate or graduate courses in numerical methods. It is written so that interested readers with only an understanding of calculus and differential equations can learn Monte Carlo on their own. Coverage of topics such as variance reduction, pseudo-random number generation, Markov chain Monte Carlo, inverse Monte Carlo, and linear operator equations will make the book useful even to experienced Monte Carlo practitioners.
Provides a concise treatment of generic Monte Carlo methods
Proofs for each chapter
Appendixes include Certain mathematical functions; Bose Einstein functions, Fermi Dirac functions, Watson functions"

This book presents efficient metaheuristic algorithms for optimal design of structures. Many of these algorithms are developed by the author and his graduate students, consisting of Particle Swarm Optimization, Charged System Search, Magnetic Charged System Search, Field of Forces Optimization, Democratic Particle Swarm Optimization, Dolphin Echolocation Optimization, Colliding Bodies Optimization, Ray Optimization. These are presented together with algorithms which are developed by other authors and have been successfully applied to various optimization problems. These consist of Partical Swarm Optimization, Big Band Big Crunch algorithm, Cuckoo Search Optimization, Imperialist Competitive Algorithm and Chaos Embedded Metaheuristic Algorithm. Finally a multi-objective Optimization is presented to Solve large scale structural problems based on the Charged System Search algorithm, In the second edition seven new chapters are added consisting of Enhance colliding bodies optimization, Global sensitivity analysis, Tug of War Optimization, Water evaporation optimization, Vibrating System Optimization and Cyclical Parthenogenesis Optimization algorithm. In the third edition, five new chapters are included consisting of the recently developed algorithms. These are Shuffled Shepherd Optimization Algorithm, Set Theoretical Shuffled Shepherd Optimization Algorithm, Set Theoretical Teaching-Learning-Based Optimization Algorithm, Thermal Exchange Metaheuristic Optimization Algorithm, and Water Strider Optimization Algorithm and Its Enhancement. The concepts and algorithm presented in this book are not only applicable to optimization of skeletal structure, finite element models, but can equally be utilized for optimal design of other systems such as hydraulic and electrical networks.

This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.