Regning og matematisk analyse

Kvalitative analyseprocesser giver konkret indblik i, hvordan du kan analysere empirisk materiale. Bogen starter der, hvor mange metodebøger stopper: Når du har dit empiriske materiale i hus, hvad gør du så? Analysearbejdet er helt centralt for kvalitativ forskning – det er gennem analyserne, at resultaterne fremkommer. Alligevel er det ofte ret dunkelt, hvordan analysen egentlig er foretaget. Denne bog sætter spot på selve analyseprocessen, de analytiske greb, som er anvendt, og hvordan teoretisk begrebsarbejde har guidet analysen undervejs. På den måde inviterer bogen læseren ind i forskerens værksted og retter fokus på selve analyseprocessen med dens kringlede proces, trin og vildveje, tilrettelæggelse og strategier. Bogen er inddelt i hermeneutiske, poststrukturalistiske og dialektiske analyseperspektiver. Det er imidlertid en væsentlig pointe, at det teoretiske afsæt ikke på nogen entydig måde giver én bestemt analysemetode. Derfor præsenterer bogen forskellige analysetilgange under hver af de tre overskrifter og viser, hvordan man på forskellige måder kan arbejde sig igennem den analytiske proces. Forfatterne tilbyder desuden anvisninger i form af modeller, analytikker og spørgsmål, som man kan lade sig inspirere af, når man skal planlægge og gennemføre sine egne analyser. Kvalitative analyseprocesser henvender sig primært til studerende, der skal analysere kvalitativt empirisk materiale som led i en lang eller mellemlang videregående uddannelse eller et ph.d.-forløb. Den er især anvendelig indenfor det pædagogisk-psykologiske felt og beslægtede områder. De beskrevne analyseprocesser har dog samme relevans udover disse felter, og bogen kan derfor anvendes af alle, som ønsker at blive klædt bedre på til at gennemføre teoretisk informerede kvalitative analyser.

Mål- og integralteori har op igennem det 20. århundrede udviklet sig til at udgøre en væsentlig del af grundlaget for matematiske discipliner som f.eks. sandsynlighedsteori, statistik, matematisk fysik, funktionel-analyse og matematisk finansiering. Denne bog giver en stringent indføring i de grundlæggende elementer af mål- og integralteorien, og den kan således danne et solidt udgangspunkt for videregående studier inden for de netop nævnte matematiske discipliner."Grundlæggende mål- og integralteori" henvender sig som udgangspunkt til læsere med en matematisk baggrund svarende til et typisk første studieår på matematik-studiet ved et dansk universitet. Basale resultater og teknikker i forbindelse med grænseovergang og kontinuitet forventes således at være bekendte af læseren, men derudover opbygges teorien gennemgående fra bunden uden yderligere forudsætninger.

Bogen er et redskab til matematiklærere i arbejdet med at støtte elever i matematikvanskeligheder på mellemtrinnet.Når en elev er gået i stå i matematikundervisningen, kan læreren med dette redskab gennemføre en samtale med eleven og kortlægge elevens problemer. Kortlægningen kan inspirere læreren til handlinger, der styrker og udviklereleven positivt i matematikundervisningen. Målet er ogsåat modvirke elevens negative oplevelser og vanskelighederi faget. Materialet har fokus på de ændringer i forventninger, krav og mål, som eleverne møder i skiftet fra indskoling til mellemtrin. Samtidig er der fokus på, hvordan man som lærer opdager, kortlægger og afhjælper regnehuller i forhold til elevens færdigheder og viden.Svage præstationer i matematik kan få alvorlige personlige og sociale konsekvenser. Alle elever har derfor krav på at blive mødt med lærings- og undervisningsbetingelser, der forebygger og afhjælper matematikvanskeligheder. Materialets tilgang bygger på forfatternes begreb ’regnehuller’,der bl.a. indebærer, at matematikvanskeligheder kan imødegås med mange forskellige strategier, og at den bedste strategi ikke altid er at starte med ’at fylde hullet op’.Bogen er en del af serien Matematikvanskeligheder, der dækker grundlæggende matematik på alle alders- og klassetrin. De tre bøger har samme tilgang til undervisning af elever med matematikvanskeligheder. I denne bog er der særligt fokus på samtale i matematikundervisningen og på den direkte dialog mellem lærer og elev, når læreren skal undersøge, hvordan en elev er kommet i vanskeligheder med matematik. Erfaringer viser, at der er en stor spredning af elevers begrebsudvikling i matematik. Mange elever følger ikke den lineære progression, der er indbygget i klassetrin eller alder i den officielle beskrivelse af fagformål. Derfor kan bogen med fordel bruges i arbejdet med elever på andre klassetrin, selvom det fagfaglige udgangspunkt er mellemtrinnet.Bogen henvender sig til matematiklærere og matematikvejledere i grundskolen. Alle, der arbejder med elever i matematikvanskeligheder på ungdomsuddannelser, efterskoler, i støttecentre eller på specialskoler, vil også kunne finde inspiration i bogen.

This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6-8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts-applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications-the book is a useful resource for students, researchers and faculty as well as practitioners.

This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Min­ kowsky lemma, coding theory and the structure of water meet one another in packing and covering theory: quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

The industrial processing of acerola generates a large amount of waste which is generally discarded or underused, causing losses of raw materials and energy, as well as environmental impact. As this agro-industrial waste is rich in antioxidant compounds, high levels of vitamin C and other bioactive compounds, it can be put to better use. Therefore, this research aimed to make use of the acerola residue by adding it to a yogurt, and to evaluate the effects of this residue on the yogurt's physicochemical and textural characteristics.

""The Elements of the Differential and Integral Calculus"" is a comprehensive mathematical textbook written by Jacob William Albert Young. The book is based on the ""Kurzgefasstes Lehrbuch der Differential und Integralrechnung"" by Walther Nernst and Arthur Schoenflies, originally published in 1900. This textbook covers the fundamental concepts of differential and integral calculus, including limits, derivatives, integrals, and applications of calculus in various fields such as physics, engineering, and economics. The book is aimed at undergraduate students and is written in a clear and concise manner, with numerous examples and exercises to aid in understanding. Overall, ""The Elements of the Differential and Integral Calculus"" is an essential resource for anyone studying calculus and its applications.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

"Differential Equations" by Dr. Upton is a captivating journey through the mathematical landscapes of calculus, offering a rich exploration of historical context, first and second-order equations, systems, Laplace transforms, numerical methods, and real-world applications. With insightful content and advanced topics, this book inspires a deep understanding of complex concepts while providing practical applications in science and engineering.

Are you above average? Is your child an A student? Is your employee an introvert or an extrovert? Every day we are measured against the yardstick of averages, judged according to how closely we come to it or how far we deviate from it.The assumption that metrics comparing us to an average?like GPAs, personality test results, and performance review ratings?reveal something meaningful about our potential is so ingrained in our consciousness that we don't even question it. That assumption, says Harvard's Todd Rose, is spectacularly?and scientifically?wrong.In The End of Average, Rose, a rising star in the new field of the science of the individual shows that no one is average. Not you. Not your kids. Not your employees. This isn't hollow sloganeering?it's a mathematical fact with enormous practical consequences. But while we know people learn and develop in distinctive ways, these unique patterns of behaviors are lost in our schools and businesses which have been designed around the mythical ?average person.? This average-size-fits-all model ignores our differences and fails at recognizing talent. It's time to change it.Weaving science, history, and his personal experiences as a high school dropout, Rose offers a powerful alternative to understanding individuals through averages: the three principles of individuality. The jaggedness principle (talent is always jagged), the context principle (traits are a myth), and the pathways principle (we all walk the road less traveled) help us understand our true uniqueness?and that of others?and how to take full advantage of individuality to gain an edge in life.Read this powerful manifesto in the ranks of Drive, Quiet, and Mindset?and you won't see averages or talent in the same way again.

The monograph is devoted to the construction of the high-order finite difference and finite element methods for numerical solving multidimensional boundary-value problems (BVPs) for different partial differential equations, in particular, linear Helmholtz and wave equations, nonlinear Burgers¿ equations, and elliptic (Schrödinger) equation. Despite of a long history especially in development of the theoretical background of these methods there are open questions in their constructive implementation in numerical solving the multidimensional BVPs having additional requirement on physical parameters or desirable properties of its approximate solutions. Over the last two decades many papers on this topics have been published, in which new constructive approaches to numerically solving the multidimensional BVPs were proposed, and its highly desirable to systematically collect these results. This motivate us to write thus monograph based on our research results obtained in collaboration with the co-authors. Since the topic is importance we believe that this book will be useful to readers, graduate students and researchers interested in the field of computational physics, applied mathematics, numerical analysis and applied sciences

"Solutions of the Cahn Hilliard Equations" is a groundbreaking exploration of the Cahn Hilliard equations, a set of partial differential equations that describe the evolution of phase boundaries in materials. This comprehensive guide provides a thorough analysis of the equations and their solutions, offering valuable insights for researchers, engineers, and students in the field of materials science and engineering.The book begins with a detailed introduction to the Cahn-Hilliard equations, providing a clear and accessible overview of their mathematical formulation and physical significance. It then delves into the various analytical and numerical methods for solving the equations, offering step-by-step guidance on how to obtain accurate and reliable solutions.Throughout the book, the author presents a wealth of real-world examples and case studies, demonstrating the practical applications of the Cahn-Hilliard equations in materials science and engineering. From phase separation in polymers to microstructure evolution in alloys, readers will gain a deep understanding of how these equations can be used to model and predict the behavior of complex materials systems.With its comprehensive coverage and practical approach, "Solutions of the Cahn Hilliard Equations" is an indispensable resource for anyone seeking to understand and apply these important equations in their research or professional work. Whether you are a seasoned researcher or a student new to the field, this book will empower you to tackle challenging problems and make meaningful contributions to the advancement of materials science and engineering.

This book constitutes the refereed proceedings of the 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, held in Kanazawa, Japan, during March 18¿20, 2024. The 28 full papers presented in this book, together with two extended abstracts of invited talks, were carefully reviewed and selected from 80 submissions. They cover diverse areas of algorithms and computation, that is, approximation algorithms, algorithmic graph theory and combinatorics, combinatorial algorithms, combinatorial optimization, computational biology, combinatorial reconfiguration, computational complexity, computational geometry, discrete geometry, data structures, experimental algorithm methodologies, graph algorithms, graph drawing, parallel and distributed algorithms, parameterized algorithms, parameterized complexity, network optimization, online algorithms, randomized algorithms, and string algorithms.

This book gathers outstanding papers on numerical modeling in Mechanical Engineering (Volume 2) as part of the 2-volume proceedings of the 5th International Conference on Numerical Modeling in Engineering (NME 2021), which was held in Ghent, Belgium, on August 23-24, 2022. The overall objective of the conference was to bring together international scientists and engineers in academia and industry from fields related to advanced numerical techniques, such as the finite element method (FEM), boundary element method (BEM), isogeometric analysis (IGA), and their applications to a wide range of engineering disciplines. This book addresses numerical simulations of various mechanical and materials engineering industrial applications such as aerospace applications, acoustic analysis, bio-mechanical applications, contact problems and wear, heat transfer analysis, vibration and dynamics, transient analysis, nonlinear analysis, composite materials, polymers, metal alloys, fracture mechanics, fatigue of materials, creep, mechanical behavior, micro-structure, phase transformation, and crystal plasticity. The book is intended for academics, including graduate students and researchers, as well as industrial practitioners working in the numerical modeling in mechanical engineering topics.

This book contains select papers on mathematical analysis and modeling, discrete mathematics, fuzzy sets, and soft computing. All the papers were presented at the international conference on FIM28-SCMSPS20 virtually held at Sri Sivasubramaniya Nadar (SSN) College of Engineering, Chennai, India, and Stella Maris College (Autonomous), Chennai, from November 23-27, 2020. The conference was jointly held with the support of the Forum for Interdisciplinary Mathematics. Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters).

This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the third edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.

This study is part of a research project carried out under the R&D program regulated by the Brazilian National Electric Energy Agency (ANEEL), which developed two smart greenhouses for the protected cultivation of banana and orchid seedlings. The greenhouses feature control and automation systems, bioclimatic architecture and strategies and power systems (artificial lighting system, artificial heating system, evaporative cooling system and photovoltaic system). A sensor network monitors internal environmental variables, and an automatic weather station monitors external environmental variables. A computer system based on artificial intelligence is responsible for the autonomous control of the greenhouses. This article presented the development, application and analysis of power systems applied to smart greenhouses. The power systems were defined using computer modeling and simulation tools. The proposed systems were installed in two prototype smart greenhouses located in Alpestre/RS and Santa Rosa do Sul/SC, southern Brazil.