Digital library
Textbooks, references and open learning resources.
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Adjustment theory: an introduction
Peter Teunissen · TU Delft Open · 2024
Adjustment theory can be regarded as the part of mathematical geodesy that deals with the optimal combination of redundant measurements together with the estimation of unknown parameters. It is essential for a geodesist, its meaning comparable to what mechanics means to a civil engineer or a mechanical engineer. Historically, the first methods of combining redundant measurements originate from the study of three problems in geodesy and astronomy, namely to determine the size and shape of the Earth, to explain the long-term inequality in the motions of Jupiter and Saturn, and to find a mathematical representation of the motions of the Moon. Nowadays, the methods of adjustment are used for a much greater variety of geodetic applications, ranging from, for instance, surveying and navigation to remote sensing and global positioning. The two main reasons for performing redundant measurements are the wish to increase the accuracy of the results computed and the requirement to be able to check for errors. Due to the intrinsic uncertainty in measurements, measurement redundancy generally leads to an inconsistent system of equations. Without additional criteria, such a system of equations is not uniquely solvable. In this introductory course on adjustment theory, methods are developed and presented for solving inconsistent systems of equations. The leading principle is that of least-squares adjustment together with its statistical properties. The inconsistent systems of equations can come in many different guises. They could be given in parametric form, in implicit form, or as a combination of these two forms. In each case the same principle of least-squares applies. The algorithmic realizations of the solution will differ however. Depending on the application at hand, one could also wish to choose between obtaining the solution in one single step or in a step-wise manner. This leads to the need of formulating the system of equations in partitioned form. Different partitions
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Aviation Maintenance Technician Handbook – General (FAA-H-8083-30B)
U.S. Department of Transportation Federal Aviation Administration · Federal Aviation Administration · 2023
The Aviation Maintenance Technician Handbook–General (FAA-H-8083-30B) was developed as one of a series of three handbooks for persons preparing for mechanic certification with airframe or powerplant ratings, or both. It is intended that this handbook will provide basic information on principles, fundamentals, and technical procedures in the subject matter areas common to both the airframe and powerplant ratings. Emphasis in this volume is on theory and methods of application. The handbook is designed to aid students enrolled in a formal course of instruction preparing for FAA certification as a maintenance technician as well as for current technicians who wish to improve their knowledge. This volume contains information on mathematics, aircraft drawings, weight and balance, aircraft materials, processes and tools, physics, electricity, inspection, ground operations, and FAA regulations governing the certification and work of maintenance technicians. New to this volume is a section addressing how successful aviation maintenance technicians incorporate knowledge and awareness of ethics, professionalism and human factors in the field
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Introduction to Systems Biology: Workbook for Flipped-Classroom Teaching
Thomas Sauter; Marco Albrecht · Open Book Publishers · 2023
This book is an introduction to the language of systems biology, which is spoken among many disciplines, from biology to engineering. Authors Thomas Sauter and Marco Albrecht draw on a multidisciplinary background and evidence-based learning to facilitate the understanding of biochemical networks, metabolic modeling and system dynamics. Their pedagogic approach briefly highlights core ideas of concepts in a broader interdisciplinary framework to guide a more effective deep dive thereafter. The learning journey starts with the purity of mathematical concepts, reveals its power to connect biological entities in structure and time, and finally introduces physics concepts to tightly align abstraction with reality. This workbook is all about self-paced learning, supports the flipped-classroom concept, and kick-starts with scientific evidence on studying. Each chapter comes with links to external YouTube videos, learning checklists, and Integrated real-world examples to gain confidence in thinking across scientific perspectives. The result is an integrated approach that opens a line of communication between theory and application, enabling readers to actively learn as they read. This overview of capturing and analyzing the behavior of biological systems will interest adherers of systems biology and network analysis, as well as related fields such as bioinformatics, biology, cybernetics, and data science.
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Basic Engineering Data Collection and Analysis
Steve Vardeman; J. Marcus Jobe · Iowa State University · 2001
In Basic Engineering Data Collection and Analysis, Stephen B. Vardeman and J. Marcus Jobe stress the practical over the theoretical. Step by step, students get real engineering data and scenario examples along with chapter-long case studies that illustrate concepts in realistic, thoroughly detailed situations. This approach encourages students to work through the material by carrying out data collection and analysis projects from problem formulation through the preparation of professional technical reports—just as if they were on the job.
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A Brief Introduction to Engineering Computation with MATLAB
Serhat Beyenir · Serhat Beyenir · 2011
A Brief Introduction to Engineering Computation with MATLAB is specifically designed for students with no programming experience. However, students are expected to be proficient in First Year Mathematics and Sciences and access to good reference books are highly recommended. Students are assumed to have a working knowledge of the Mac OS X or Microsoft Windows operating systems. The strategic goal of the course and book is to provide learners with an appreciation for the role computation plays in solving engineering problems. MATLAB specific skills that students are expected to be proficient at are: write scripts to solve engineering problems including interpolation, numerical integration and regression analysis, plot graphs to visualize, analyze and present numerical data, and publish reports.
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AC Circuits
Chad Davis · University of Oklahoma Libraries · 2017
This eBook was written as the sequel to the eBook titled DC Circuits, which was written in 2016 by Chad Davis. This eBook covers Alternating Current (AC) circuit theory as well as a brief introduction of electronics. It is broken up into seven modules. Module 1 covers the basic theory of AC signals. Since only DC sources are used in the first eBook, details of AC signals such as sinusoidal waveforms (or sine waves), square waves, and triangle waves are provided. Module 2, titled AC Circuits Math Background, covers the mathematics background needed for solving AC circuit problems. The background material in Modules 1 and 2 are combined in Module 3 to solve circuits with AC sources that include resistors, inductors, and capacitors (RLC circuits).
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Notes on Diffy Qs: Differential Equations for Engineers
Jirí Lebl · Jirí Lebl · 2014
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign Sample Dirichlet problem solution (one is a 4-day-a-week, the other a 3-day-a-week semester-long course). I have also taught Math 20D at University of California, San Diego with these notes (a 3-day-a-week quarter-long course). There is enough material to run a 2-quarter course, and even perhaps a two semester course depending on lecturer speed.
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Elementary Differential Equations with Boundary Value Problems
William Trench · A.T. Still University · 2013
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
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Introduction to Probability
Charles Grinstead; J. Laurie Snell · American Mathematical Society · 2006
Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continuedto influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that finds applications in every area of scholarlyactivity from music to physics, and in daily experience from weather prediction topredicting the risks of new medical treatments. This text is designed for an introductory probability course taken by sophomores,juniors, and seniors in mathematics, the physical and social sciences, engineering,and computer science. It presents a thorough treatment of probability ideas andtechniques necessary for a form understanding of the subject. The text can be usedin a variety of course lengths, levels, and areas of emphasis. For use in a standard one-term course, in which both discrete and continuousprobability is covered, students should have taken as a prerequisite two terms ofcalculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theoryis necessary. The text can also be used in a discrete probability course. The material has beenorganized in such a way that the discrete and continuous probability discussions arepresented in a separate, but parallel, manner. This organization dispels an overlyrigorous or formal view of probability and o?ers some strong pedagogical valuein that the discrete discussions can sometimes serve to motivate the more abstractcontinuous probability discussions. For use in a discrete probability course, studentsshould have taken one term of calculus as a prerequisite. Very little computing background is assumed or necessary in order to obtain fullbenefits from the use of the comp
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Don’t Cheat Yourself: Scenarios to clarify collusion confusion
Katherine Seaton · La Trobe University · 2023
Ensuring academic integrity in mathematical tasks presents a unique challenge, for university students and for their assessors, and one that hitherto has been under-examined. Drawing on her twenty years of experience in mathematics education, the recent academic integrity research literature, and on what students say about why misconduct occurs, the author examines this issue head-on. Don’t Cheat Yourself: Scenarios to clarify collusion confusion facilitates intentional consideration of the nature and purpose of assessment in mathematics, and of how some types of interactions between students undermine that purpose. Pertinent and realistic scenarios are provided as prompts for discussion, through which students in mathematical disciplines can come to a better understanding of what constitutes copying and collusion, identify strategies for finding support, be warned of the short- and long-term consequences of misconduct, and be set up to learn collaboratively and work legitimately.
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Teaching Math for Emergent Bilinguals: Building on Culture, Language, and Identity
Ji-Yeong I; Ricardo Martinez · Iowa State University · 2020
This book is designed for pre-service/in-service teachers and others who will work or work with K–12 students who have linguistically and culturally diverse backgrounds, especially students of other languages (English language learners/Emergent bilingual/multilingual). The core concept of this course is helping teachers understand the needs of various Emergent Bilinguals (a.k.a. English language learners (ELLs)/English Learners (ELs), learn to use their language and culture as a resource in mathematics classrooms and implement research-based instructional strategies that are effective to teach mathematics for Emergent Bilinguals.
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Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)
Jonathan Poritz · Jonathan Poritz · 2014
This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) out of the ambient number theory. The main cryptologic applications – being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem – come out so naturally from considerations of Euler’s Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy’s assertion [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.
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The Crystal Ball Instruction Manual
Stephen Davies · University of Mary Washington · 2020
Welcome to Volume Two of the Crystal Ball series: Foundations for Data Science! I titled the first volume “Introduction to Data Science” because it led you through a dip-your-toes-in-the-water experience. You took a brief tour through the various elements in this diverse field and got a feel for what it was all about. Since you’re still reading, this means you’re still interested, and ready to explore the next level. In Foundations, we’ll solidify your growing knowledge so that you have a firm base on which to build everything else. Future volumes in this series will cover applications, advanced techniques, and some special data types that require special treatment. But it all ultimately rests on the skill set you’ll have built in Volumes One and Two of this series.
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An Introduction to Python Jupyter Notebooks for College Math Teachers
Paul Isihara; Claire Wagner; Peter Jantsch; Thomas VanDrunen · Paul Isihara, Claire Wagner, Peter Jantsch, and Thomas VanDrunen · 2024
This book is an introduction to the use of Python Jupyter Notebooks (JNBs) for college math teachers and their students. The book is an evolving work in progress, but we hope this 1st Edition may already be quite useful to a college math teacher who is interested to use Jupyter Notebooks in their courses. Each section of the book has been written in the form of a Jupyter Notebook and can be downloaded using the download button at the top menu bar. In some cases, additional data files or image files may need to be downloaded as well. All the files are available in the src folder of the github repository https://github.com/timothyprojectGiG/JB_Math_Textbook Each chapter contains a JNB lab with solutions. Experienced teachers can modify these labs and create new labs tailored to their courses. The chapters were written by different authors/authorship teams, and as such, vary in style. Each chapter essentially can be read independently of the others as long as one has the pre-requisite mathematical knowledge. Some effort has been made to standardize the chapter formats, and the index may help the reader find specific topics of interest. There is virtually no limit to what can be done with JNBs, and we hope this work serves as a useful starting point for teachers and students to enrich and enliven the study of mathematics using this tool. The JNBs used to create this book contain special markdown code which are needed to produce features such as indexing, referencing, and highlight boxes in the Jupyter Book. Some editing of a downloaded JNB may may make it more suitable for classroom use.
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Prealgebra via Python Programming: First Steps to Perform Large Scale Computational Tasks in the Sciences and Engineerings
Sergio Rojas · Sergio Rojas · 2018
This book was written for students and instructors who want to learn how to use a computer for other than the most common uses, such as web browsing, document creation, or paying bills online. This book is for anyone who wants to perform computational tasks that they design. In other words, if you wish to learn how to program a computer, this book is for you. Because prealgebra is a subject that practically everyone is supposed to learn in grade school, it provides a platform to introduce basic computer programming concepts. Consequently, this book should also be of interest to students in middle or high school who want to learn how to program, and who are willing to invest the time and effort in learning a programming language that they could continue using throughout their schooling and in their professional life. Similarly, this book could also be of interest to pre-service and in-service mathematics teachers wishing to have at their disposal a complementary tool to assist in fostering understanding, competency, and interest in mathematics among their students. This book can be integrated with the teachers’ curriculum as way to tackle non-traditional math problems using an inexpensive modern computer language. By the end of the book, a reader will have learned enough to be able to write a preliminary, step-by-step one variable equation solver that can be expanded in the future to use with more complex equations. In other words, by the end of the book, you will be able to write code that programs their machines to solve equations. This code is foundational and readers are ecouraged to learn on their own how to build on it to suit their mathematics learning needs.
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Evidence-based Software Engineering
Derek Jones · Knowledge Software · 2020
This book discusses what is currently known about software engineering, based on an analysis of all the publicly available data. This aim is not as ambitious as it sounds, because there is not a great deal of data publicly available. The intent is to provide material that is useful to professional developers working in industry; until recently researchers in software engineering have been more interested in vanity work, promoted by ego and bluster. The material is organized in two parts, the first covering software engineering and the second the statistics likely to be needed for the analysis of software engineering data.
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Introduction to Statistical Thinking
Benjamin Yakir · Benjamin Yakir · 2010
The target audience for this book is college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. It is assumed that the students do have basic skills in using computers and have access to one. Moreover, it is assumed that the students are willing to actively follow the discussion in the text, to practice, and more importantly, to think. Teaching statistics is a challenge. Teaching it to students who are required to learn the subject as part of their curriculum, is an art mastered by few. In the past I have tried to master this art and failed. In desperation, I wrote this book. This book uses the basic structure of generic introduction to statistics course. However, in some ways I have chosen to diverge from the traditional approach. One divergence is the introduction of R as part of the learning process. Many have used statistical packages or spreadsheets as tools for teaching statistics. Others have used R in advanced courses. I am not aware of attempts to use R in introductory level courses. Indeed, mastering R requires much investment of time and energy that may be distracting and counterproductive for learning more fundamental issues. Yet, I believe that if one restricts the application of R to a limited number of commands, the benefits that R provides outweigh the difficulties that R engenders. Another departure from the standard approach is the treatment of probability as part of the course. In this book I do not attempt to teach probability as a subject matter, but only specific elements of it which I feel are essential for understanding statistics. Hence, Kolmogorov’s Axioms are out as well as attempts to prove basic theorems and a Balls and Urns type of discussion. On the other hand, emphasis is given to the notion of a random variable and, in that context, the sample space.
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First Semester in Numerical Analysis with Python
Yaning Liu · Auraria Institutional Repository
The book is based on “First semester in Numerical Analysis with Julia”, written by Giray Ökten. The contents of the original book are retained, while all the algorithms are implemented in Python (Version 3.8.0). Python is an open source (under OSI), interpreted, general-purpose programming language that has a large number of users around the world. Python is ranked the third in August 2020 by the TIOBE programming community index, a measure of popularity of programming languages, and is the top-ranked interpreted language. We hope this book will better serve readers who are interested in a first course in Numerical Analysis, but are more familiar with Python for the implementation of the algorithms. The first chapter of the book has a self-contained tutorial for Python, including how to set up the computer environment. Anaconda, the open-source individual edition, is recommended for an easy installation of Python and effortless management of Python packages, and the Jupyter environment, a web-based interactive development environment for Python as well as many other programming languages, was used throughout the book and is recommended to the readers for easy code development, graph visualization and reproducibility.
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How to Think Like a Computer Scientist: C Version
Allen Downey; Thomas Scheffler · Green Tea Press · 1999
The goal of this book is to teach you to think like a computer scientist. I like the way computer scientists think because they combine some of the best features of Mathematics, Engineering, and Natural Science. Like mathematicians, computer scientists use formal languages to denote ideas (specifically computations). Like engineers, they design things, assembling components into systems and evaluating trade offs among alternatives. Like scientists, they observe the behavior of complex systems, form hypotheses, and test predictions.The single most important skill for a computer scientist is problem-solving. By that I mean the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills. That’s why this chapter is called “The way of the program.”
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How to Think Like a Computer Scientist: C++ Version
Allen Downey · Green Tea Press · 2012
The goal of this book is to teach you to think like a computer scientist. I like the way computer scientists think because they combine some of the best features of Mathematics, Engineering, and Natural Science. Like mathematicians,computer scientists use formal languages to denote ideas (specifically computations). Like engineers, they design things, assembling components into systems and evaluating trade offs among alternatives. Like scientists, they observe the behavior of complex systems, form hypotheses, and test predictions.The single most important skill for a computer scientist is problem-solving. By that I mean the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills. That’s why this chapter is called “The way of the program.”