Advertisement
| ex 7.11 class 12 maths solutions: Advanced Calculus Lynn H. Loomis, Shlomo Sternberg, 2014 An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds. |
| ex 7.11 class 12 maths solutions: Principles of Mathematical Analysis Walter Rudin, 1976 The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics. |
| ex 7.11 class 12 maths solutions: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning. |
| ex 7.11 class 12 maths solutions: Elementary Topology O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises. |
| ex 7.11 class 12 maths solutions: All of Statistics Larry Wasserman, 2004-09-17 This book is for people who want to learn probability and statistics quickly. It brings together many of the main ideas in modern statistics in one place. The book is suitable for students and researchers in statistics, computer science, data mining and machine learning. This book covers a much wider range of topics than a typical introductory text on mathematical statistics. It includes modern topics like nonparametric curve estimation, bootstrapping and classification, topics that are usually relegated to follow-up courses. The reader is assumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. The text can be used at the advanced undergraduate and graduate level. Larry Wasserman is Professor of Statistics at Carnegie Mellon University. He is also a member of the Center for Automated Learning and Discovery in the School of Computer Science. His research areas include nonparametric inference, asymptotic theory, causality, and applications to astrophysics, bioinformatics, and genetics. He is the 1999 winner of the Committee of Presidents of Statistical Societies Presidents' Award and the 2002 winner of the Centre de recherches mathematiques de Montreal–Statistical Society of Canada Prize in Statistics. He is Associate Editor of The Journal of the American Statistical Association and The Annals of Statistics. He is a fellow of the American Statistical Association and of the Institute of Mathematical Statistics. |
| ex 7.11 class 12 maths solutions: Exercises in Modules and Rings T.Y. Lam, 2009-12-08 The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume. Only a lucky break in my schedule in 2006 enabled me to put the finishing touches on the completion of this long overdue book. This book is intended to serve a dual purpose. First, it is designed as a problem book for Lectures. As such, it contains the statements and full solutions of the many exercises that appeared in Lectures. Second, this book is also offered as a reference and repository for general information in the theory of modules and rings that may be hard to find in the standard textbooks in the field. As a companion volume to Lectures, this work covers the same math ematical material as its parent work; namely, the part of ring theory that makes substantial use of the notion of modules. The two books thus share the same table of contents, with the first half treating projective, injective, and flat modules, homological and uniform dimensions, and the second half dealing with noncommutative localizations and Goldie's theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, conclud ing with Morita's theory of category equivalences and dualities. |
| ex 7.11 class 12 maths solutions: The Definite Integral Grigoriĭ Mikhaĭlovich Fikhtengolʹt︠s︡, 1973 |
| ex 7.11 class 12 maths solutions: Mathematical Methods in the Physical Sciences Mary L. Boas, 2006 Market_Desc: · Physicists and Engineers· Students in Physics and Engineering Special Features: · Covers everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, to ODE, PDE, Transforms and more· Emphasizes intuition and computational abilities· Expands the material on DE and multiple integrals· Focuses on the applied side, exploring material that is relevant to physics and engineering· Explains each concept in clear, easy-to-understand steps About The Book: The book provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. This book helps readers gain a solid foundation in the many areas of mathematical methods in order to achieve a basic competence in advanced physics, chemistry, and engineering. |
| ex 7.11 class 12 maths solutions: Introduction to Applied Linear Algebra Stephen Boyd, Lieven Vandenberghe, 2018-06-07 A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples. |
| ex 7.11 class 12 maths solutions: Discrete Mathematics for Computer Science John Schlipf, Sue Whitesides, Gary Haggard, 2020-09-22 Discrete Mathematics for Computer Science by Gary Haggard , John Schlipf , Sue Whitesides A major aim of this book is to help you develop mathematical maturity-elusive as thisobjective may be. We interpret this as preparing you to understand how to do proofs ofresults about discrete structures that represent concepts you deal with in computer science.A correct proof can be viewed as a set of reasoned steps that persuade another student,the course grader, or the instructor about the truth of the assertion. Writing proofs is hardwork even for the most experienced person, but it is a skill that needs to be developedthrough practice. We can only encourage you to be patient with the process. Keep tryingout your proofs on other students, graders, and instructors to gain the confidence that willhelp you in using proofs as a natural part of your ability to solve problems and understandnew material. The six chapters referred to contain the fundamental topics. Thesechapters are used to guide students in learning how to express mathematically precise ideasin the language of mathematics.The two chapters dealing with graph theory and combinatorics are also core materialfor a discrete structures course, but this material always seems more intuitive to studentsthan the formalism of the first four chapters. Topics from the first four chapters are freelyused in these later chapters. The chapter on discrete probability builds on the chapter oncombinatorics. The chapter on the analysis of algorithms uses notions from the core chap-ters but can be presented at an informal level to motivate the topic without spending a lot oftime with the details of the chapter. Finally, the chapter on recurrence relations primarilyuses the early material on induction and an intuitive understanding of the chapter on theanalysis of algorithms. The material in Chapters 1 through 4 deals with sets, logic, relations, and functions.This material should be mastered by all students. A course can cover this material at differ-ent levels and paces depending on the program and the background of the students whenthey take the course. Chapter 6 introduces graph theory, with an emphasis on examplesthat are encountered in computer science. Undirected graphs, trees, and directed graphsare studied. Chapter 7 deals with counting and combinatorics, with topics ranging from theaddition and multiplication principles to permutations and combinations of distinguishableor indistinguishable sets of elements to combinatorial identities.Enrichment topics such as relational databases, languages and regular sets, uncom-putability, finite probability, and recurrence relations all provide insights regarding howdiscrete structures describe the important notions studied and used in computer science.Obviously, these additional topics cannot be dealt with along with the all the core materialin a one-semester course, but the topics provide attractive alternatives for a variety of pro-grams. This text can also be used as a reference in courses. The many problems provideample opportunity for students to deal with the material presented. |
| ex 7.11 class 12 maths solutions: Iterative Methods for Sparse Linear Systems Yousef Saad, 2003-04-01 Mathematics of Computing -- General. |
| ex 7.11 class 12 maths solutions: Introduction to Probability Dimitri Bertsekas, John N. Tsitsiklis, 2008-07-01 An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems. |
| ex 7.11 class 12 maths solutions: The Knot Book Colin Conrad Adams, 2004 Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics. |
| ex 7.11 class 12 maths solutions: Exploring ODEs Lloyd N.Trefethen, Asgeir Birkisson, Tobin A. Driscoll, 2017-12-21 Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration. |
| ex 7.11 class 12 maths solutions: Maths Mate 6 NEW Madhubun, 1. It is a series of eight textbooks for Classes 1 to 8 that conforms to the vision of National Curriculum Framework and is written in accordance with the latest syllabus of the CBSE. 2. Learning Objectives: Lists well what a learner will know and be able to do after studying the chapter. 3. Let’s Recall: Refreshes the concepts learnt in the form of a revision exercise to brush up the concepts taught in previous chapters or grades. 4. Let’s Begin: Introduction to the chapter. 5. My Notes: Tips to help the learner remember the important points/formulae taught in the chapter. 6. Let’s Try: Simple straight forward questions for quick practice while studying any topic based on the first two levels of Bloom’s Taxonomy —Knowledge and Understanding. 7. Error Alarm: Common mistakes which learners commit often along with the correct way of doing the same. 8. Know More: Additional information for the learners relating to the concepts learnt in the chapter 9. Maths in My Life includes questions relating Maths to daily life and which can help relate the topic with the environment (life) around us. 10. Tricky Maths: Challenge questions to help the learners build thinking skills and reasoning skills by solving tricky questions. 11. Project Work: Projects which can help learners connect Math with our daily life or that take the concepts learnt to a new level. 12. Concept Map: Summary points to list the important concepts learnt in the chapter in a crisp form. 13. Test Zone: Revision exercise of the concepts learnt in the chapter. This includes both objective and subjective type of questions. 14. Mental Maths: Maths problems for performing faster calculations mentally. 15. Maths Master: Involves deep critical thinking of learners about any topic, concept, relation, fact or anything related to that chapter. May have open ended questions or extension of the topic. 16. Application in Real-Life: Every chapter in each book also explains how and where it is used in daily life. 17. In the Lab: Math lab activities for helping the learners understand the concepts learnt through hands-on experience. 18. Practice Zone: Chapter-wise practice sheets includes subjective questions for additional practice which are a part of each book. |
| ex 7.11 class 12 maths solutions: Mathematics and Computation Avi Wigderson, 2019-10-29 From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography |
| ex 7.11 class 12 maths solutions: Measure, Integral and Probability Marek Capinski, (Peter) Ekkehard Kopp, 2013-06-29 The central concepts in this book are Lebesgue measure and the Lebesgue integral. Their role as standard fare in UK undergraduate mathematics courses is not wholly secure; yet they provide the principal model for the development of the abstract measure spaces which underpin modern probability theory, while the Lebesgue function spaces remain the main sour ce of examples on which to test the methods of functional analysis and its many applications, such as Fourier analysis and the theory of partial differential equations. It follows that not only budding analysts have need of a clear understanding of the construction and properties of measures and integrals, but also that those who wish to contribute seriously to the applications of analytical methods in a wide variety of areas of mathematics, physics, electronics, engineering and, most recently, finance, need to study the underlying theory with some care. We have found remarkably few texts in the current literature which aim explicitly to provide for these needs, at a level accessible to current under graduates. There are many good books on modern prob ability theory, and increasingly they recognize the need for a strong grounding in the tools we develop in this book, but all too often the treatment is either too advanced for an undergraduate audience or else somewhat perfunctory. |
| ex 7.11 class 12 maths solutions: Supergravity Daniel Z. Freedman, Antoine Van Proeyen, 2012-04-05 Supergravity, together with string theory, is one of the most significant developments in theoretical physics. Written by two of the most respected workers in the field, this is the first-ever authoritative and systematic account of supergravity. The book starts by reviewing aspects of relativistic field theory in Minkowski spacetime. After introducing the relevant ingredients of differential geometry and gravity, some basic supergravity theories (D=4 and D=11) and the main gauge theory tools are explained. In the second half of the book, complex geometry and N=1 and N=2 supergravity theories are covered. Classical solutions and a chapter on AdS/CFT complete the book. Numerous exercises and examples make it ideal for Ph.D. students, and with applications to model building, cosmology and solutions of supergravity theories, it is also invaluable to researchers. A website hosted by the authors, featuring solutions to some exercises and additional reading material, can be found at www.cambridge.org/supergravity. |
| ex 7.11 class 12 maths solutions: No Bullshit Guide to Linear Algebra Ivan Savov, 2020-10-25 This textbook covers the material for an undergraduate linear algebra course: vectors, matrices, linear transformations, computational techniques, geometric constructions, and theoretical foundations. The explanations are given in an informal conversational tone. The book also contains 100+ problems and exercises with answers and solutions. A special feature of this textbook is the prerequisites chapter that covers topics from high school math, which are necessary for learning linear algebra. The presence of this chapter makes the book suitable for beginners and the general audience-readers need not be math experts to read this book. Another unique aspect of the book are the applications chapters (Ch 7, 8, and 9) that discuss applications of linear algebra to engineering, computer science, economics, chemistry, machine learning, and even quantum mechanics. |
| ex 7.11 class 12 maths solutions: Mathematics for Computer Science Eric Lehman, F. Thomson Leighton, Albert R. Meyer, 2017-06-05 This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. The color images and text in this book have been converted to grayscale. |
| ex 7.11 class 12 maths solutions: Science and Mathematics Jayant V. Narlikar, 2021-11-29 This book offers an engaging and comprehensive introduction to scientific theories and the evolution of science and mathematics through the centuries. It discusses the history of scientific thought and ideas and the intricate dynamic between new scientific discoveries, scientists, culture and societies. Through stories and historical accounts, the volume illustrates the human engagement and preoccupation with science and the interpretation of natural phenomena. It highlights key scientific breakthroughs from the ancient to later ages, giving us accounts of the work of ancient Greek and Indian mathematicians and astronomers, as well as of the work of modern scientists like Descartes, Newton, Planck, Mendel and many more. The author also discusses the vast advancements which have been made in the exploration of space, matter and genetics and their relevance in the advancement of the scientific tradition. He provides great insights into the process of scientific experimentation and the relationship between science and mathematics. He also shares amusing anecdotes of scientists and their interactions with the world around them. Detailed and accessible, this book will be of great interest to students and researchers of science, mathematics, the philosophy of science, science and technology studies and history. It will also be useful for general readers who are interested in the history of scientific discoveries and ideas. |
| ex 7.11 class 12 maths solutions: Transition to Higher Mathematics Bob A. Dumas, John Edward McCarthy, 2007 This book is written for students who have taken calculus and want to learn what real mathematics is. |
| ex 7.11 class 12 maths solutions: Solving Systems of Polynomial Equations Bernd Sturmfels, 2002 Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical. |
| ex 7.11 class 12 maths solutions: A Problem Book in Real Analysis Asuman G. Aksoy, Mohamed A. Khamsi, 2016-08-23 Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying. |
| ex 7.11 class 12 maths solutions: CRC Standard Mathematical Tables and Formulae, 32nd Edition Daniel Zwillinger, 2011-06-22 With over 6,000 entries, CRC Standard Mathematical Tables and Formulae, 32nd Edition continues to provide essential formulas, tables, figures, and descriptions, including many diagrams, group tables, and integrals not available online. This new edition incorporates important topics that are unfamiliar to some readers, such as visual proofs and sequences, and illustrates how mathematical information is interpreted. Material is presented in a multisectional format, with each section containing a valuable collection of fundamental tabular and expository reference material. New to the 32nd Edition A new chapter on Mathematical Formulae from the Sciences that contains the most important formulae from a variety of fields, including acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics New material on contingency tables, estimators, process capability, runs test, and sample sizes New material on cellular automata, knot theory, music, quaternions, and rational trigonometry Updated and more streamlined tables Retaining the successful format of previous editions, this comprehensive handbook remains an invaluable reference for professionals and students in mathematical and scientific fields. |
| ex 7.11 class 12 maths solutions: Math for Programmers Paul Orland, 2020-11-30 A gentle introduction to some of the most useful mathematical concepts that should be in your developer toolbox. - Christopher Haupt, New Relic Explore important mathematical concepts through hands-on coding. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. Summary To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks |
| ex 7.11 class 12 maths solutions: Mathematics for Physics Michael Stone, Paul Goldbart, 2009-07-09 An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030. |
| ex 7.11 class 12 maths solutions: Introduction to Partial Differential Equations with Applications E. C. Zachmanoglou, Dale W. Thoe, 2012-04-20 This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers. |
| ex 7.11 class 12 maths solutions: Mathematical Omnibus D. B. Fuks, Serge Tabachnikov, 2007 The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher. |
| ex 7.11 class 12 maths solutions: Mathematical Methods for Physics and Engineering Kenneth Franklin Riley, Michael Paul Hobson, Stephen John Bence, 1997 |
| ex 7.11 class 12 maths solutions: Foundation Mathematics for Engineers John Berry, Patrick Wainright, 1991-09-06 This book is written for students without Maths A-Level who are entering an Engineering or Applied Science degree via a preliminary year. It introduces the basic ideas of Mathematics through applications in physics and engineering, providing a firm foundation in functions and calculus for the subsequent degree. Students are encouraged to use computers and calculators effectively and to develop skills in mathematical modelling. The content and approach have been devised with university and polytechnic foundation course lecturers. |
| ex 7.11 class 12 maths solutions: Galois Theory Through Exercises Juliusz Brzeziński, 2018-03-21 This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study. |
| ex 7.11 class 12 maths solutions: The Analysis of Fractional Differential Equations Kai Diethelm, 2010-08-18 Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations. |
| ex 7.11 class 12 maths solutions: Reinforcement Learning, second edition Richard S. Sutton, Andrew G. Barto, 2018-11-13 The significantly expanded and updated new edition of a widely used text on reinforcement learning, one of the most active research areas in artificial intelligence. Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the field's key ideas and algorithms. This second edition has been significantly expanded and updated, presenting new topics and updating coverage of other topics. Like the first edition, this second edition focuses on core online learning algorithms, with the more mathematical material set off in shaded boxes. Part I covers as much of reinforcement learning as possible without going beyond the tabular case for which exact solutions can be found. Many algorithms presented in this part are new to the second edition, including UCB, Expected Sarsa, and Double Learning. Part II extends these ideas to function approximation, with new sections on such topics as artificial neural networks and the Fourier basis, and offers expanded treatment of off-policy learning and policy-gradient methods. Part III has new chapters on reinforcement learning's relationships to psychology and neuroscience, as well as an updated case-studies chapter including AlphaGo and AlphaGo Zero, Atari game playing, and IBM Watson's wagering strategy. The final chapter discusses the future societal impacts of reinforcement learning. |
| ex 7.11 class 12 maths solutions: OpenIntro Statistics David Diez, Christopher Barr, Mine Çetinkaya-Rundel, 2015-07-02 The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources. |
| ex 7.11 class 12 maths solutions: Integral Equations and Their Applications Matiur Rahman, 2007 The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations. |
| ex 7.11 class 12 maths solutions: Feedback Control Theory John Comstock Doyle, Bruce A. Francis, Allen Tannenbaum, 2009 An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems. |
| ex 7.11 class 12 maths solutions: A Course in Universal Algebra S. Burris, H. P. Sankappanavar, 2011-10-21 Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests. Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included. Chapter II develops the most general and fundamental notions of uni versal algebra-these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free algebras are discussed in great detail-we use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous results-the refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character ization of languages accepted by finite automata-can be presented using universal algebra. We predict that such applied universal algebra will become much more prominent. |
| ex 7.11 class 12 maths solutions: Precalculus Robert F. Blitzer, 2013-03-07 Books a la Carte are unbound, three-hole-punch versions of the textbook. This lower cost option is easy to transport and comes with same access code or media that would be packaged with the bound book. Bob Blitzer has inspired thousands of students with his engaging approach to mathematics, making this beloved series the #1 in the market. Blitzer draws on his unique background in mathematics and behavioral science to present the full scope of mathematics with vivid applications in real-life situations. Students stay engaged because Blitzer often uses pop-culture and up-to-date references to connect math to students' lives, showing that their world is profoundly mathematical. |
| ex 7.11 class 12 maths solutions: Mathematical Proofs Gary Chartrand, Albert D. Polimeni, Ping Zhang, 2013 This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. |
What is the origin of "ex"? - English Language & Usage Stack …
Dec 22, 2015 · Origin of ex-ex-is a word-forming element, which in English simply means "former" in this case, or mainly "out of, from," but also "upwards, completely, deprive of, without. It most …
abbreviations - What's the difference between "e.g." and "ex ...
Mar 13, 2011 · "Ex." is not very common, but it may be used to refer to a cited example, eg "See ex. 3". "E.g." is much more common, and is used to introduce an example, or series of examples. In …
Why use "ex post facto" when "post facto" means the same thing?
Oct 4, 2015 · Being a Latin locution, it must be used as such, ex means from: Ex post facto: from or by subsequent action; subsequently; retrospectively; retroactively. Word Origin: from Latin ex …
Is there an equivalent to "née" (birth name) for an *ex*-spousal name?
May 31, 2016 · EX. is also interesting because . 1) Someone's ex is the person they used to be married to or used to have a romantic or sexual relationship with. and. 2) ex- as a prefix is added …
Is there a rule for the correct pronunciation of words starting with …
Jan 12, 2012 · If the syllable ex-is stressed or if what follows is a voiceless consonant, it is pronounced /-ks-/; otherwise, it is /-gz-/. A voiceless consonant is one that does not involve …
Is there a single word for someone who left the company that does …
May 16, 2018 · The person could be called the resignee.A person who resigns from a position or job. It meets your requirement of not being "overly negative" and could indeed be thought to be …
etymology - Why "e.g." and not "f.e."? Why "i.e." and not "t.i ...
Feb 18, 2014 · Actually Jon answer says only slightly more than this answer. The information it adds is that 1) Latin was used by educated people in all Europe (although linked by this answer), and …
Do you capitalize both parts of a hyphenated word in a title?
Given the huge difference between how likely people are to capitalise the second component in Ex-wife compared to Co-Founder, I think choose a rule and be consistent with it is terrible advice. …
Is there a proper term for an ex-friend? - English Language & Usage ...
Aug 13, 2015 · You could say. frenemy. friend-no-more. friend-at-the-time. enemy-to-become. He who shall remain nameless. Hugo the Treacherous (or whatever the person's name is)
terminology - Is there a term for your parent's ex-spouse who is not ...
Feb 12, 2014 · You can have several step-fathers in succession. Simply because you are no longer living with him doesn't erase your relationship with him. Your mother doesn't become your ex …
What is the origin of "ex"? - English Language & Usage Stack …
Dec 22, 2015 · Origin of ex-ex-is a word-forming element, which in English simply means "former" in this case, or mainly "out of, from," but also "upwards, completely, deprive of, without. It most …
abbreviations - What's the difference between "e.g." and "ex ...
Mar 13, 2011 · "Ex." is not very common, but it may be used to refer to a cited example, eg "See ex. 3". "E.g." is much more common, and is used to introduce an example, or series of …
Why use "ex post facto" when "post facto" means the same thing?
Oct 4, 2015 · Being a Latin locution, it must be used as such, ex means from: Ex post facto: from or by subsequent action; subsequently; retrospectively; retroactively. Word Origin: from Latin …
Is there an equivalent to "née" (birth name) for an *ex*-spousal …
May 31, 2016 · EX. is also interesting because . 1) Someone's ex is the person they used to be married to or used to have a romantic or sexual relationship with. and. 2) ex- as a prefix is …
Is there a rule for the correct pronunciation of words starting with …
Jan 12, 2012 · If the syllable ex-is stressed or if what follows is a voiceless consonant, it is pronounced /-ks-/; otherwise, it is /-gz-/. A voiceless consonant is one that does not involve …
Is there a single word for someone who left the company that …
May 16, 2018 · The person could be called the resignee.A person who resigns from a position or job. It meets your requirement of not being "overly negative" and could indeed be thought to …
etymology - Why "e.g." and not "f.e."? Why "i.e." and not "t.i ...
Feb 18, 2014 · Actually Jon answer says only slightly more than this answer. The information it adds is that 1) Latin was used by educated people in all Europe (although linked by this …
Do you capitalize both parts of a hyphenated word in a title?
Given the huge difference between how likely people are to capitalise the second component in Ex-wife compared to Co-Founder, I think choose a rule and be consistent with it is terrible …
Is there a proper term for an ex-friend? - English Language
Aug 13, 2015 · You could say. frenemy. friend-no-more. friend-at-the-time. enemy-to-become. He who shall remain nameless. Hugo the Treacherous (or whatever the person's name is)
terminology - Is there a term for your parent's ex-spouse who is …
Feb 12, 2014 · You can have several step-fathers in succession. Simply because you are no longer living with him doesn't erase your relationship with him. Your mother doesn't become …
