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Basic Analysis: Introduction to Real Analysis
Jirí Lebl · Jirí Lebl · 2016
This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.
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OpenIntro Statistics
David Diez; Christopher Barr; Mine Cetinkaya-Rundel · OpenIntro · 2019
OpenIntro Statistics covers a first course in statistics, providing a rigorous introduction to appliedstatistics that is clear, concise, and accessible. This book was written with the undergraduate levelin mind, but it’s also popular in high schools and graduate courses.We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. • Statistics is an applied field with a wide range of practical applications.• You don’t have to be a math guru to learn from real, interesting data.• Data are messy, and statistical tools are imperfect. But, when you understand the strengthsand weaknesses of these tools, you can use them to learn about the world.
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Book of Proof
Richard Hammack · Richard Hammack · 2018
This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei,
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Fundamentals of Math, Physics, and Statistics for Future Transportation Professionals
Anurag Pande; Peyton Ratto; Ahmed Farid · Mavs Open Press · 2024
This textbook and OER material cover tools and basic knowledge required to master the prerequisite essentials of physics, mathematics, and statistics applied in transportation engineering. To our knowledge, no such textbook currently exists to build the KSTs (Knowledge, Skills, Tools) for college freshmen’ remedial courses required by most transportation engineering graduate programs that admit non-engineers (e.g., PHYS 141, MATH 142, STAT 321 at California Polytechnic State University, San Luis Obispo). The textbook modules are intended for students with undergraduate degrees in planning and other less technical fields who are interested in pursuing transportation careers where background engineering knowledge is required. This textbook is a product of the grant OERTransport: Enabling Transportation Planning Professional Advancement awarded to the University of Texas-Arlington (UTA) in consortium with California Polytechnic State University (Cal Poly) and the University of South Florida (USF). It was developed under an Open Textbooks Pilot grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education. However, its contents do not necessarily represent the policy of the Department of Education, and no endorsement by the Federal Government should be assumed
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Introduction to Biosystems Engineering
Nicholas M. Holden; Mary Leigh Wolfe; Jactone A. Ogejo; Enda J. Cummins · American Society of Agricultural and Biological Engineers (ASABE), Virginia Tech Publishing · 2021
The discipline of Biosystems Engineering emerged in the 1990s from the traditional strongholds of agricultural engineering and food engineering. Biosystems engineering integrates engineering science and design with applied biological, environmental, and agricultural sciences. Introduction to Biosystems Engineering is targeted at 1st and 2nd year university-level students with an interest in biosystems engineering but who are not yet familiar with the breadth and depth of the subject. It is designed as a coherent educational resource, also available for download as individual digital chapters. The book can be used as a localized, customizable text for introductory courses in Biosystems Engineering globally. It is written as a series of stand-alone chapters organized under six major topics: Food and Bioprocessing; Environment; Buildings and Infrastructure; Information and Communications Technology and Data; Machinery Systems; and Energy. Each chapter is organized around stated learning outcomes and describes key concepts, applications of the concepts, and worked examples. Instructors adopting or reviewing this text are encouraged to register with the publisher using this form.
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Sustainability: A Comprehensive Foundation
Tom Theis; Jonathan Tomkin · OpenStax CNX · 2015
With “Sustainability: A Comprehensive Foundation”, first and second-year college students are introduced to this expanding new field, comprehensively exploring the essential concepts from every branch of knowledge – including engineering and the applied arts, natural and social sciences, and the humanities. As sustainability is a multi-disciplinary area of study, the text is the product of multiple authors drawn from the diverse faculty of the University of Illinois: each chapter is written by a recognized expert in the field. This text is designed to introduce the reader to the essential concepts of sustainability. This subject is of vital importance seeking as it does to uncover the principles of the long-term welfare of all the peoples of the planet but is only peripherally served by existing college textbooks. The content is intended to be useful for both a broad-based introductory class on sustainability and as a useful supplement to specialist courses which wish to review the sustainability dimensions of their areas of study. By covering a wide range of topics with a uniformity of style, and by including glossaries, review questions, case studies, and links to further resources, the text has sufficient range to perform as the core resource for a semester course. Students who cover the material in the book will be conversant in the language and concepts of sustainability, and will be equipped for further study in sustainable planning, policy, economics, climate, ecology, infrastructure, and more. Furthermore, the modular design allows individual chapters and sections to be easily appropriated without the purchase of a whole new text. This allows educators to easily bring sustainability concepts, references, and case studies into their area of study. This appropriation works particularly well as the text is free downloadable to anyone who wishes to use it. Furthermore, readers are encouraged to work with the text. Provided there is attribution to the source, use
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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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Lifespan Development
Diana Riser; Rose Spielman; David Biek; Alisa Beyer · OpenStax, Rice University
Lifespan Development aligns to the topics and objectives of most introductory developmental psychology courses taught across departments. Grounded in foundational theories and scientific research, the text teaches students about core aspects of human development—physical, cognitive, social, emotional—across the lifespan. A primary goal of the book is to incorporate content, scholarship, and activities that explore a variety of perspectives that encourage all students to feel seen and included. Lifespan Development strives to openly address complex topics with scholarly responsibility and an effort to increase equity and inclusion in the research presented, as well as to foster student engagement in the classroom through relevant examples and applications. Focused on driving meaningful and memorable learning experiences, the narrative places concepts in contexts that give students the means to understand human development and how that knowledge can be applied to and improve their own lives and the lives of others.
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Υπολογιστική Φυσική: Ένα βιβλίο του Κωνσταντίνου Αναγνωστόπουλου
Κωνσταντίνος Αναγνωστόπουλος · National Technical University of Athens · 2016
Το βιβλίο αυτό είναι μια εισαγωγή στις υπολογιστικές μεθόδους που χρησιμοποιούνται στη φυσική και άλλα επιστημονικά πεδία. Απευθύνεται σε κοινό που έχει ήδη εκτεθεί σε μαθήματα γενικής φυσικής που διδάσκονται στα δύο πρώτα έτη πανεπιστημιακών τμημάτων θετικών επιστημών και επιστημών του μηχανικού. Δεν υποθέτει κανένα υπόβαθρο αριθμητικής ανάλυσης, προγραμματισμού ή χρήσης υπολογιστή και παρουσιάζει ό,τι είναι απαραίτητο για την επίλυση των προβλημάτων που παρουσιάζονται στο βιβλίο. Μπορεί να χρησιμοποιηθεί ως κύριο σύγγραμμα σε εισαγωγικά μαθήματα υπολογιστικής φυσικής και επιστημονικού προγραμματισμού. Το βιβλίο ξεκινάει με πολύ απλά προβλήματα πάνω στην κίνηση σωματιδίου και ολοκληρώνεται με μία εις βάθος συζήτηση προχωρημένων μεθόδων προσομοίωσης Μόντε Κάρλο στη στατιστική φυσική. Το επίπεδο διδασκαλίας είναι διαβαθμισμένο ως προς τη δυσκολία του, παρουσιάζοντας προβλήματα όπως η εξίσωση διάχυσης, δυναμικά συστήματα, ηλεκτροστατική στο επίπεδο, κβαντομηχανική και οι τυχαίες διαδρομές. Όλο το υλικό που παρουσιάζεται στο βιβλίο μπορεί να διαδαχθεί άνετα σε δύο εξάμηνα. Με κατάλληλη επιλογή θεμάτων, μπορεί να χρησιμοποιηθεί και σε ένα πλήρες μάθημα ενός εξαμήνου. Το βιβλίο αποσκοπεί να δώσει στους φοιτητές το υπόβαθρο και την εμπειρία που απαιτείται ώστε να προχωρήσουν σε προγράμματα υπολογισμών υψηλής απόδοσης. Δίνει έμφαση στον εμπειρικό προγραμματισμό αριθμητικών προγραμμάτων, αλλά και στην παραγωγή, ανάλυση και φυσική ερμηνεία των δεδομένων. Επίσης γίνεται προσπάθεια να διατηρηθεί το ενδιαφέρον του αναγνώστη μέσα από την παρουσίαση της αριθμητικής επίλυσης γνωστών και ενδιαφέροντων προβλημάτων φυσικής, οπως χαοτικών συστημάτων, κβαντομηχανικής, ειδικής θεωρίας της σχετικότητας και της φυσικής των μεταβάσεων φάσης. Το βιβλίο και το συνοδευτικό λογισμικό δίνονται ελεύθερα, αδειοδοτούμενα υπό Creative Commons License/GNU public License.
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Calculo diferencial e integral
Marta Bonacina; Claudia Teti; Alejandra Haidar · LATIn Project · 2014
Esta comunidad tiene como fin construir un texto base, que pretende ser la puerta de entrada al mundo de las matemáticas superiores y sus aplicaciones en el campo de las Ciencias de la Ingeniería.
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Thermodynamics and Introduction to Quantum Mechanics
Cathrine Southern · DePaul University
This course will cover topics in thermodynamics, including thermodynamic laws, chemical potential, and both phase and chemical equilibria. In addition, the postulates of quantum mechanics will be discussed, and these postulates will applied to simple systems, allowing spectroscopic applications to be explored.
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Introduction to Anthropology: A Four Field Approach
Matthew Pawlowicz, Christopher A Brooks, Nancy Phaup, and Amy Rector · Virginia Commonwealth University
Có trong mục lục: 1.03: Applied Anthropology and Anthropology and Your Job
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Quantway Core
Carnegie Math Pathways · WestEd
Quantway Core provides a one-term introductory quantitative reasoning course solution that builds algebraic and quantitative skills and reasoning. It is designed to replace the developmental sequence and can also be used to fulfill high school and technical college program math requirements.
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Genetics, Agriculture, and Biotechnology
Walter Suza and Donald Lee · University of Iowa
Có trong mục lục: 1.07: Gene Expression- Applied Example (Part 1) · 1.08: Gene Expression- Applied Example (Part 2)
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Calculus
Gilbert Strang & Edwin Herman · MIT & University of Wisconsin-Stevens Point
Có trong mục lục: 4.08: Applied Optimization Problems
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ENVS C100: Environmental Science
Tanya Hoerer · Coastline College
Có trong mục lục: 1.2.04: Basic and Applied Science · 2.6.04: Applied Systems Toxicology · 2.6.4.02: Dose Level and Applied Toxicology
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Elementary Algebra
Wade Ellis & Denny Burzynski · LibreTexts
Có trong mục lục: 12.04: The 5-Step Method of Solving Applied Problems
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Calculus I: Differential Calculus
Doli Bambhania, Rani Fischer, Lisa Mesh & Danny Tran · De Anza College
Có trong mục lục: 4.08: Applied Optimization Problems
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Concepts of Physical Science
Jamie MacArthur · Madera Community College
Có trong mục lục: 1.5.01: Pure and Applied Science
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MKBN211: Introductory Microbiology
Jaco Bezuidenhout · Northwest University
Có trong mục lục: 1.3.02: Applied Microbiology