single variable calculus early transcendentals
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Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!Keywords:
Situation calculus
Beauty
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PREFACE Read this bit. It will save you time, because it explains the kind of book this is and, perhaps more importantly, the kind of book that it isn't, which will make it easier for you to decide whether you will benefit from reading it or whether you would get more out of doing something else instead. Right at the beginning, we want to make clear that this is not the book for you if you want to cover the world of statistics in a rigorous and exhaustive manner. The guiding principle of this book is the need to know. If you are unlikely to need a particular statistical method in order to analyse the data that you have collected for your project or dissertation, then you won't find any mention of it here. There are enough books on statistics out there, which range from relatively simple introductions to advanced mathematical expositions. This one has a different purpose. It concentrates on what you need for success in your assignment, project or dissertation, and ignores the minor roads and byways that the person very interested in statistics would be pleased to travel. As the textbooks (which, strictly speaking, this isn't) put it, by the end of this book, you will be able to choose and use an appropriate and effective statistical technique that will allow you to analyse your data and write about your results and findings convincingly. In a sense, this is the book that we wish we could have used during our own studies. We both spent far too long in a fog of not understanding which statistics to use, when we should be using them and why we should be using them. As a consequence, the book concentrates on particular statistical tests and their three Ws – what, why, and when – and mainly ignores the details of how to calculate them, leaving this area for the books that not only explain the mathematics behind the techniques, but also how to use statistical software to analyse your data. This is not the book for you if you want what any normal, self-respecting textbook currently supplies: self-check and review questions and tests, case studies, practice exercises, worked examples, activities, boxes for pauses for thought or reflection, lists of learning outcomes or a companion website. Nor will it satisfy you, if you want to know all about the theory behind the statistical calculations of the methods you use. Instead, the book is intended for you if you are undertaking a social science or business and management assignment, project or dissertation as part of an undergraduate or masters qualification. It is designed to help you choose the graphs and statistics that are suitable for your data, and having got some results from your computer, to understand what they actually tell you. The chapters that follow set out to explain the three Ws that you need so that you can produce a successful assignment, project or a dissertation. However, from now on we will just refer to any of these as a ‘project’ as it is less clumsy. Chapter 1 deals with why you can't avoid using statistics in analysing your data, whether this is qualitative or quantitative, and what using statistics can do for your research. Chapter 2 explains the language of statistics so that you understand what the various terms used for statistical techniques and results mean. Chapter 3 clarifies why, if you are using primary data, you need to link the creation of your questionnaire or interview to your analysis plans, and when to do this. Chapter 4 deals with using tables and charts to present your data so that you, and your reader (or examiner) find them easy to understand. Chapter 5 explains the statistics used to describe data and Chapter 6 deals with the statistics used to infer differences and relationships. Finally, Chapter 7 briefly considers what next. The book provides three Appendices; the first provides the types of questions and statements you are likely to use in your project, and the data types associated with them, the second appendix discusses main statistical software that you could use to do your stats calculations for you, and the third provides a table of the alphabet of statistics used in this book. At the end of the book, we give you a glossary of the statistical terms that have been used throughout the book, so that you have them all in one place. Many statistics books divide statistical tests between parametric or non-parametric tests, or they deal with the available tests in terms of their increasing rigour. The main divisions of this book are based on how you will be using statistics: displaying data, describing data and inferring differences or relationships. Explanations of terms such as parametric, non-parametric and rigour are fitted into these divisions, the term which is being explained being emboldened. In writing the book, it was not our intention to give you the information you need to understand the whole field of statistics. Instead, we provide you with the fundamental ideas and the most commonly used techniques that you will need to organise, and then make sense of, your data. Whilst there are no mathematical proofs of the techniques discussed, there is a discussion of the rationale for the chosen statistics. There are very many methods that can be used to analyse your data, many of them with strange names: Chi square, Kolmogorov-Smirnov, paired t-test. You are quite right to feel daunted and confused about which are appropriate for your needs. Which is where this book comes in. 1. It will deal with statistics for your project on a need-to-know basis. If a statistic is interesting, but too sophisticated for your purposes, it might sometimes be mentioned, but is otherwise ignored. 2. What you will therefore have is an explanation and presentation of those statistical activities that are sufficient for you to deal with your data, and to come up with the answers to your questions (and to get your qualification). A FINAL COMMENT We wrote this book because we want to end the fear and anxiety about statistics that we and our students endured, and that many students still endure, and to show you that you can succeed in statistical analysis of your data. There is no doubt that learning statistics takes an investment of time and effort, but this book provides you with the means both to save some of that time and effort, and also to enjoy your analysis without fear of failure. If, after reading this book, you can understand the statistical analysis sections of the journal articles you read, and if you have found out how to make statistics work for you, the book will have accomplished what we set out to provide for you. If you have suggestions on how to improve the book to even better meet your needs, please let us know. Reva Berman Brown Mark NK Saunders
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The essential guide to writing clear and grammatically correct English, and developing your communication skills. Can you learn how to improve your writing skills? Can the art of good writing be taught? Despite what you might feel, the answer is yes -- you can be taught. Everyone is capable of enhancing their powers of written communication simply by learning and practising the basic principles of clear, concise and coherent writing: planning, preparation and revision. Using this book, your confidence will grow as you begin to apprecaite that the English language is not a fearsome book of rules but an unrivalled communications tool that you can learn to use with the familiar ease of a knife and fork. The basic principle of this incredibly useful book is that 'clarity begins at home': say what you mean and you stand a better chance of getting what you want!
CLARITY
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I read the short article by Barry Cipra about calculus teaching reforms (News, [16 Feb., p. 901][1]) with interest. I studied calculus for an entire year in college, but without really understanding it. Proving all the theorems constituted a considerable portion of the course, but I memorized the proofs. I felt then and feel now that proofs are irrelevant to the great majority of us who use calculus as a tool. In using it in physical chemistry class, I suddenly experienced an epiphany. The entire topic of calculus became clear in the course of understanding partial derivatives of thermodynamic functions; and in that one second, I learned more than I had ever learned in an entire year of calculus. If calculus were taught as a useful tool rather than as a theoretical discipline, I believe more students would learn it, understand it, and enjoy it. I have taken this same approach to my own teaching, particularly of enzyme kinetics. I find that the traditional way of teaching theory first reaches maybe 10% of students, while teaching the methodology first and then teaching the theory reaches 80 to 90% of students.
I encourage the reformers to continue, particularly in eliminating irrelevant proofs.
[1]: /lookup/doi/10.1126/science.271.5251.901b
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This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at http://explained.ai
Matrix (chemical analysis)
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Calculators are too often regarded as devices to produce answers to numerical questions. However, a graphics calculator like the Casio CFX-9850GB PLUS is much more than a tool for producing answers. It is a tool for exploring mathematical ideas, and we have written this book to offer some suggestions of how to make good use of it when learning about and using the basic mathematical concepts that underpin finance.
We assume that you will read this book with the calculator by your side, and use it as you read. Unlike some mathematics books, in which there are many exercises of various kinds to compete, this one contains only a few 'interactions' and even fewer 'investigations'. The learning journey that we have in mind for this book assumes that you will complete all interactions, rather than only some. The investigations will give you a chance to do some exploring of your own.
We also assume that you will work through this book with a companion: someone to compare your observations and thoughts with; someone to help you if you get stuck; someone to talk to about your mathematical journey. Learning mathematics is not meant to be a lonely affair; we expect you to interact with mathematics, your calculator and other people on your journey.
Throughout the book, there are some calculator instructions, written in a different font (like this). These will help you get started, but we do not regard them as a complete manual, and expect that you will already be a little familiar with the calculator and will also use our Getting Started book, the User's Guide and other sources to develop your calculator skills.
Financial mathematics is one of the topics in General mathematics, mainly because it is an important application of mathematics to the real world and fundamental to all of our lives. Much of our life is centered around controlling, or attempting to control, our own and sometimes others finances. You will learn how to write and use programs as a ready reckoner for every day situations and build on your knowledge of patterning to reinforce your understanding of interest structures.
Calculator
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Calculators are too often regarded as devices to produce answers to numerical questions. However, a graphics calculator like the Casio CFX-9850GB PLUS is much more than a tool for producing answers. It is a tool for exploring mathematical ideas. We have written this book to offer some suggestions of how to make good use of this tool for the particular areas of data analysis and probability.
We assume that you will read this book with the calculator by your side, and make use of it as you read. Unlike some mathematics books, in which there are many exercises of various kinds to complete, this one contains only a few ‘interactions’ and even fewer ‘investigations’. The learning journey that we have in mind for this book assumes that you will complete all the interactions, rather than only some. The investigations will give you a chance to do some exploring of your own.
We also assume that you will work through this book with a companion: someone to compare your observations and thoughts with; someone to help you if you get stuck; someone to talk to about your mathematical journey. Learning mathematics is not meant to be a lonely affair; we expect you to interact with mathematics, your calculator and other people on your journey.
Throughout the book, there are some calculator instructions, written in a different font (like this). These will help you to get started, but we do not regard them as a complete manual, and expect that you will already be a little familiar with the calculator and will also use the Owner’s Manual, our Getting Started book and other sources to develop your calculator skills.
Data Analysis and Probability are two of the topics in General Mathematics. Data analysis can involve data collected by other people or data that you collect for yourself. Both of these aspects are explored in this book. Meaningful interpretation of data analysis also requires some understanding of probability, which is why we have included it in this book. We have also included some exciting material on analysing data produced through simulation. An important source of data, understanding simulation also requires an understanding of the basic ideas of probability. Although we have sampled some of the possible ways of using a graphics calculator to learn about these topics, we have certainly not dealt with all of them.
Calculator
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Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
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Become a competent, confident, and critical consumer of social research with Earl Babbie's SOCIAL RESEARCH COUNTS. Written with wit, and with a desire to see you succeed in the course, the book presents the main tenets of research methods concisely and in a visually appealing, full-color format that engages you in the topics and helps you make the connection between a concept and its real-world applications. Each chapter includes features designed to guide you through the material, including Learning Objectives that offer you an easy-to-follow guide to the content, as well as Tips and Tools and Research in Real Life boxes that provide opportunities for you to better equip yourself with relevant skills. As a result of using this book, you will gain a firm footing in the foundational skills and principles of research methods.
Social Research
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Computing is revolutionizing the practice of biology. This book, which assumes no prior computing experience, provides students with the tools to write their own Python programs and to understand fundamental concepts in computational biology and bioinformatics. Each major part of the book begins with a compelling biological question, followed by the algorithmic ideas and programming tools necessary to explore it: the origins of pathogenicity are examined using gene finding, the evolutionary history of sex determination systems is studied using sequence alignment, and the origin of modern humans is addressed using phylogenetic methods. In addition to providing general programming skills, this book explores the design of efficient algorithms, simulation, NP-hardness, and the maximum likelihood method, among other key concepts and methods. Easy-to-read and designed to equip students with the skills to write programs for solving a range of biological problems, the book is accompanied by numerous programming exercises, available at www.cs.hmc.edu/CFB.
Python
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