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Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
by Larisa Beilina Michael Victor KlibanovApproximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity). Two central questions for CIPs are addressed: How to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives.
Approximate Quantum Markov Chains (SpringerBriefs in Mathematical Physics #28)
by David SutterThis book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple matrix inequality can be extended to more than three matrices. Finally, we carefully discuss the properties of approximate quantum Markov chains and their implications.The book is aimed to graduate students who want to learn about approximate quantum Markov chains as well as more experienced scientists who want to enter this field. Mathematical majority is necessary, but no prior knowledge of quantum mechanics is required.
Approximation Methods in Science and Engineering
by Reza N. JazarApproximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions.
Approximation of Free-Discontinuity Problems (Lecture Notes in Mathematics #1694)
by Andrea BraidesFunctionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
Approximation Theory in the Central Limit Theorem: Exact Results in Banach Spaces (Mathematics and its Applications #32)
by V. Paulauskas A. Rackauskas
AQA, A: Revision Guide (PDF)
by Brian Greasley Jane FerrettiSpecifically written for students following the AQA GCSE Geography Specification A course. Table of Contents: Unit 1: Physical Geography Section A: The restless earth; Rocks, resources and scenery; Challenge of weather and climate; Living world Section B Water on the land; Ice on the land; The coastal zone Unit 2: Human Geography Section A: Population change; Changing urban environments; Changing rural environments Section B: The development gap; Globalisation; Tourism
AQA, A2: Geography (PDF)
by Amanda Barker David Redfern Malcolm SkinnerComprehensive coverage for AQA A2 Geography students. Written by senior examiners and leading authors, this best selling textbook give students the perfect platform to develop their understanding and skills, and prepares them for the unit exams. Clear and concise definitions of key terms Relevant and detailed case studies for key A2 skills, including issue evaluation Free online resources, including sample exam-style questions with mark schemes and detailed commentaries are available at www.hodderplus.co.uk/philipallan
AQA A-level Geography: For A-level and AS
by Ian Whittaker Paul Abbiss Helen Fyfe Philip Banks Malcolm Skinner
AQA A-level Geography Coursework Workbook: Component 3: Geography fieldwork investigation (non-exam assessment)
by David HolmesExam board: AQALevel: A-levelSubject: GeographyFirst teaching: September 2016First exams: Summer 2017 (AS); Summer 2018 (A-level)Secure higher marks in AQA A-level Geography coursework, using this step-by-step guide to complete the project with confidence.Providing a clear structure to follow, this write-in workbook contains information and activities that help students to produce a manageable, relevant and interesting fieldwork investigation.- Takes you through every stage of the process, from choosing a topic to conducting research, presenting data and writing up the report- Offers the support that students need to work independently without teacher involvement- Enables students to organise their thinking, record their progress and review their coursework against a self-assessment checklist and example paragraphs- Keeps students on track by breaking the investigation down into chunks, with tasks to undertake at each stage- Increases students' chance of success as they benefit from the expert advice of David Holmes, who has worked closely with exam boards and delivers teacher training on the fieldwork investigation
AQA A Level Geography Exam Practice
by Bob Digby Tim BaylissStudent-friendly and engaging exam practice written for the 2016 AQA A Level Geography specification. Uses Oxford's On Your Marks step-by-step framework so that students know how to answer exam questions effectively, while familiarising themselves with the demands of key geographical skills, so that they are fully prepared for the final exams.
AQA A-level Geography Fifth Edition
by Ian Whittaker Helen Fyfe Malcolm Skinner Paul Abbiss Philip BanksCramming all new-case studies and 100s of new questions into one book, this new edition of our AQA A-level Geography student book will capture imaginations as it travels around the globe. This book has been written by our expert author team and structured to provide support for learners of all abilities. The book includes:· Activities and regular review questions to reinforce geographical knowledge and build up core geographical skills· Clear explanations to help students to grapple with tricky geographical concepts and grasp links between topics· Case studies from around the world to vividly demonstrate geographical theory in action · Exciting fieldwork projects that meet the fieldwork and investigation requirements· The most up-to-date theory of plate tectonicsThis student book is supported by digital resources on our new digital platform Boost, providing a seamless online and offline teaching experience.
AQA A-level Geography for A-level and AS
by Ian Whittaker Paul Abbiss Helen Fyfe Philip Banks Malcolm SkinnerEncourage every student to develop in-depth knowledge and advanced geographical skills with this Student Book from the leading A-level Geography publisher*, fully updated for 2016 with detailed content coverage, fascinating case studies and assessment preparation materials. - Enables students of all abilities to increase, apply and revise their subject knowledge as they work through clear explanations of key terms and topics - Brings geographical theory to life by providing a rich source of up-to-date case studies for each physical and human topic - Builds the core, cartographic, graphical, statistical and ICT skills that students need to maximise their potential through a dedicated skills section tailored to AQA's 2016 specification - Helps students engage with challenging concepts, reflect on their learning and map their progress with pointer questions throughout and end-of-chapter review questions - Allows AS and A-level students to approach their exams with confidence by undertaking a variety of practice questions written by subject specialists with examining experience - Supports you in planning relevant and exciting fieldwork projects that meet the changed fieldwork and investigation requirements
AQA A-level Geography Student Guide 1: Physical Geography
by David RedfernReinforce understanding throughout the course with clear topic summaries and sample questions and answers to help students target higher grades.Written by experienced teacher and subject experts David Redfern and Catherine Owen, this Student Guide is divided into two key sections - content guidance, and sample questions and answers.Content guidance will:- Develop understanding of key concepts and terminology in key physical geography topics water and carbon cycles, hot desert systems and landscapes, glacial systems and landscapes, and hazards. - Consolidate knowledge with 'knowledge check questions' at the end of each topic and answers in the back of the book.Sample questions and answers will:- Build understanding of the different question types, so that students can approach each question with confidence.- Enable students to target top grades in their exam paper with sample answers and commentary explaining exactly why marks have been awarded.
AQA A-level Geography Student Guide 1: Physical Geography
by David RedfernWritten by experienced teacher and subject experts David Redfern and Catherine Owen, this Student Guide is divided into two key sections - content guidance, and sample questions and answers. Content guidance will: - Develop understanding of key concepts and terminology in key physical geography topics water and carbon cycles, hot desert systems and landscapes, glacial systems and landscapes, and hazards. - Consolidate knowledge with 'knowledge check questions' at the end of each topic and answers in the back of the book. Sample questions and answers will: - Build understanding of the different question types, so that students can approach each question with confidence. - Enable students to target top grades in their exam paper with sample answers and commentary explaining exactly why marks have been awarded.
AQA A-level Geography Student Guide 2: Human Geography
by David RedfernReinforce understanding throughout the course with clear topic summaries and sample questions and answers to help students target higher grades. Written by experienced teacher and subject experts David Redfern and Catherine Owen, this Student Guide is divided into two key sections - content guidance, and sample questions and answers. Content guidance will: - Develop understanding of key concepts and terminology in key human geography topics: global systems and global governance, changing places, contemporary urban environments, population and the environment, resource security. - Consolidate knowledge with 'knowledge check questions' at the end of each topic and answers in the back of the book. Sample questions and answers will: - Build understanding of the different question types, so that students can approach each question with confidence. - Enable students to target top grades in their exam paper with sample answers and commentary explaining exactly why marks have been awarded.
AQA A-level Geography Student Guide 2: Human Geography
by David RedfernReinforce understanding throughout the course with clear topic summaries and sample questions and answers to help students target higher grades. Written by experienced teacher and subject experts David Redfern and Catherine Owen, this Student Guide is divided into two key sections - content guidance, and sample questions and answers. Content guidance will: - Develop understanding of key concepts and terminology in key human geography topics: global systems and global governance, changing places, contemporary urban environments, population and the environment, resource security. - Consolidate knowledge with 'knowledge check questions' at the end of each topic and answers in the back of the book. Sample questions and answers will: - Build understanding of the different question types, so that students can approach each question with confidence. - Enable students to target top grades in their exam paper with sample answers and commentary explaining exactly why marks have been awarded.
AQA A-level Geography Student Guide 3: Hazards; Population and the Environment (PDF)
by David RedfernExam Board: AQA Level: AS/A-level Subject: Geography First Teaching: September 2016 First Exam: June 2018 Reinforce students' geographical understanding throughout their course; clear topic summaries with sample questions and answers help students improve their exam technique and achieve their best. Written by a teacher with extensive examining experience, this guide: - Helps students identify what they need to know with a concise summary of the topics examined at AS and A-level - Consolidates understanding through assessment tips and knowledge-check questions - Offers opportunities for students to improve their exam technique by consulting sample graded answers to exam-style questions - Develops independent learning and research skills - Provides the content students need to produce their own revision notes
AQA A-level Geography Student Guide 4: Geographical Skills and Fieldwork
by David RedfernReinforce students' geographical understanding throughout their course; clear topic summaries with sample questions and answers help students improve their exam technique and achieve their best.Written by a teacher with extensive examining experience, this guide:- Helps students identify what they need to know with a concise summary of the topics examined at AS and A-level- Consolidates understanding through assessment tips and knowledge-check questions- Offers opportunities for students to improve their exam technique by consulting sample graded answers to exam-style questions- Develops independent learning and research skills- Provides the content students need to produce their own revision notes
AQA A-level Geography Workbook 1: Physical Geography
by Philip BanksSupport and encourage students in their study of AQA A-level Geography with these revised and restructured write-in Workbooks.These new edition Workbooks have been fully updated for 2021 and focused to help students practise their skills and improve their subject knowledge both inside and outside the classroom.- Develop and consolidate understanding using practice questions targeting each Assessment Objective including calculations and worked examples- Build key skills and practise the different question types- Support assessment preparation using exam-style questions on every topic- Use flexibly alongside your existing textbooks and schemes of work as homework, classwork and for intervention- Answers provided online
AQA AS: Student's Guide (PDF)
by Amanda BarkerComprehensive and accessible coverage for AQA AS Geography students. Written by senior examiners and leading authors, this best selling textbook give students the perfect platform to develop their understanding and skills, and prepares them for the unit exams. - In-depth coverage of the skills required for Unit 2: Applied Geography - Relevant and detailed case studies so students are fully informed - Free online resources, including sample exam-style questions with mark schemes and detailed commentaries are available at www.hodderplus.co.uk/philipallan
AQA AS/A-level Geography Student Guide: Physical Geography (PDF)
by David RedfernExam Board: AQALevel: AS/A-levelSubject: GeographyFirst Teaching: September 2016First Exam: September 2017Reinforce students' geographical understanding throughout their course; clear topic summaries with sample questions and answers help students improve their exam technique and achieve their best.Written by a teacher with extensive examining experience, this guide:- Helps students identify what they need to know with a concise summary of the topics examined at AS and A-level- Consolidates understanding through assessment tips and knowledge-check questions- Offers opportunities for students to improve their exam technique by consulting sample graded answers to exam-style questions- Develops independent learning and research skills- Provides the content students need to produce their own revision notes
AQA AS/A-Level Geography Workbook 1: Physical Geography (PDF)
by Phil Banks Paul AbbissExam Board: AQA Level: A-Level Subject: Geography First Teaching: September 2016 First Exam: Summer 2017 Create confident and well-prepared students with this exam practice workbook that covers all the core and optional physical topics for the new AQA assessment requirements; brought to you by the leading A-level Geography publisher and a team of expert teachers and examiners. This Student Workbook builds understanding of each topic and develops the exam skills students need, as well as providing ready-made lesson solutions. - Supplements key resources such as textbooks with targeted, topic-by-topic exam practice that enables students to apply their learning - Helps students understand examination language and command words as they become familiar with different question types - Reinforces knowledge and understanding through condensed topic summaries and exam-style activities - Encourages students to undertake independent learning and assessment by supplying answers to all questions online - Offers time-saving and economical solutions for classwork, extension or revision tasks
AQA AS/A-Level Geography Workbook 2: Human Geography (PDF)
by Philip Banks Paul AbbissExam Board: AQA Level: A-Level Subject: Geography First Teaching: September 2016 First Exam: Summer 2017 Create confident and well-prepared students with this exam practice workbook for the new AQA assessment requirements; brought to you by the leading A-level Geography publisher and a team of expert teachers and examiners. This Student Workbook builds understanding of each topic and develops the exam skills students need, as well as providing ready-made lesson solutions. - Supplements key resources such as textbooks with targeted, topic-by-topic exam practice that enables students to apply their learning - Helps students understand examination language and command words as they become familiar with different question types - Reinforces knowledge and understanding through condensed topic summaries and exam-style activities - Encourages students to undertake independent learning and assessment by supplying answers to all questions online - Offers time-saving and economical solutions for classwork, extension or revision tasks
AQA AS/A2: Geography (PDF)
by Amanda BarkerPerfect for revision, this guide explains the unit requirements, summarises the content and includes specimen questions with graded answers. AQA AS/A2 Geography Student Unit Guide: Unit 2 and 4a New Edition Geographical Skills including Fieldwork provides ideal preparation for your unit exam:nbsp;Feel confident you understand the unit: this guide comprehensively covers the unit content and includes topic summaries, knowledge check questions and a reference index.nbsp;Get to grips with the exam requirements: the specific skills on which you will be tested are explored and explained . Analyse exam-style questions: graded student responses will help you focus on areas where you can improve your exam technique and performance
