Digital library
Textbooks, references and open learning resources.
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Introduction to Mathematical Analysis I
Beatriz Lafferriere; Gerardo Lafferriere; Mau Nam Nguyen · Portland State University Library · 2016
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
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How We Got from There to Here: A Story of Real Analysis
Robert Rogers; Eugene Boman · Open SUNY · 2014
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.
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Introduction to Real Analysis
William Trench · A.T. Still University · 2013
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
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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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Public Speaking and Democratic Participation: Speech, Deliberation, and Analysis in the Civic Realm
Jennifer Abbott; Todd McDorman; David Timmerman; L. Jill Lamberton · PALNI · 2025
The second edition of Public Speaking and Democratic Participation: Speech, Deliberation, and Analysis in the Civic Realm equips students to effectively participate in and transform their communities through speech. Drawing on the ancient study of rhetoric, the textbook teaches students informative and persuasive speaking skills to develop and empower their public voice. Unique to this textbook, content is also provided on the democratic practices of deliberative discussion facilitation and rhetorical analysis. Together, these abilities help students recognize divisive civic discourse, counter social injustice, and nurture a healthier and more inclusive society.
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An Introduction to the Analysis of Fiction
Michael Walonen · Saint Peter's University Press · 2023
An introductory primer introducing undergraduate students to the methodology of analyzing works of fiction.
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Fundamentals, Function, and Form: Theory and Analysis of Tonal Western Art Music
Andre Mount · Milne Open Textbooks · 2020
Fundamentals, Function, and Form by Andre Mount—with editorial and pedagogical input from Lee Rothfarb—provides its readers with a comprehensive study of the theory and analysis of tonal Western art music. Mount begins by building a strong foundation in the understanding of rhythm, meter, and pitch as well as the notational conventions associated with each. From there, he guides the reader through an exploration of polyphony—the simultaneous sounding of multiple independent melodies—and an increasingly rich array of different sonorites that grow out of this practice. The book culminates with a discussion of musical form, engaging with artistic works in their entirety by considering the interaction of harmonic and thematic elements, but also such other musical dimensions as rhythm, meter, texture, and expression. Along the way, Mount supplements the text with over eight hundred musical examples which, in the online version of the text, include embedded audio files for immediate aural reinforcement of theoretical concepts. Most of these examples are drawn from the literature, including nearly 200 excerpts by women and other underrepresented groups. The reader is also given the opportunity to check their understanding of the text with interactive exercises at every step of the way. Fundamentals, Function, and Form was written with the undergraduate music student in mind, but self-guided readers would also be rewarded with a deep understanding of this musical tradition.
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DC Electrical Circuit Analysis: A Practical Approach
James Fiore · dissidents · 2020
Welcome to DC Electrical Circuit Analysis, an open educational resource (OER). The goal of this text is to introduce the theory and practical application of analysis of DC electrical circuits. It is offered free of charge under a Creative Commons non-commercial, share-alike with attribution license. For your convenience, along with the free pdf and odt files, print copies are available at a very modest charge. Check my web sites for links. This text is based on the earlier Workbook for DC Electrical Circuits, which it replaces. The original expository text has been greatly expanded and includes many examples along with computer simulations. For the convenience of those who used the Workbook, many of the problem sets are the same, with some re-ordering depending on the chapter.
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AC Electrical Circuit Analysis: A Practical Approach
James Fiore · dissidents · 2020
Welcome to the AC Electrical Circuit Analysis, an open educational resource (OER). The goal of this text is to introduce the theory and practical application of analysis of AC electrical circuits. It assumes familiarity with DC circuit analysis. If you have not studied DC circuit analysis, it is strongly recommended that you read the companion OER text, DC Electrical Circuit Analysis before continuing. Both texts are offered free of charge under a Creative Commons non-commercial, share-alike with attribution license. For your convenience, along with the free pdf and odt files, print copies are available at a very modest charge. Check my web sites for links. This text is based on the earlier Workbook for AC Electrical Circuits, which it replaces. The original expository text has been greatly expanded and includes many examples along with computer simulations. For the convenience of those who used the Workbook, many of the problem sets are the same, with some re-ordering depending on the chapter.
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Engineering Signal Analysis: From Fourier to filtering: Theory
Christian Tiberius; Max Mulder · TU Delft Open · 2026
Engineering Signal Analysis - Theory, is an introductory textbook on the analysis of signals in time and frequency. It takes an engineer’s perspective and discusses how to characterize, analyze and operate on signals. The basic theoretical concepts, Fourier series and transform, are explained in continuous time. It then introduces discrete-time signals, addressing how sampling and finite signal duration affect spectral analysis. It discusses the discrete Fourier transform and its use in spectral estimation. The book concludes with an introduction to linear systems and signal filtering.
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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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Analysis and Design of Elementary MOS Amplifier Stages
Boris Murmann · Boris Murmann · 2013
Analyzes core linear analog circuit designs: common-source, common-gate, and common-drain stages Design-oriented approach; analyzes various circuits through examples and exercises Part of the Modular Series of Microelectronic Device and Circuit Design Each module in the series provides a brief fundamental look at a specific topic "As of November 1, 2022, National Technology and Science Press ("NTS") has discontinued publication of 'Analysis and Design of Elementary MOS Amplifier Stages.' Accordingly, NTS has returned all copyrights and attendant rights with respect to the work to Boris Murmann."
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Exploring Perspectives: A Concise Guide to Analysis
Randall Fallows · Saylor Foundation · 2011
The reason why Randall Fallows wrote Exploring Perspectives: A Concise Guide to Analysis is simple: to help give students a better understanding of how to discover, develop, and revise an analytical essay. Here is how his 5 chapter book goes about doing just that: The first two chapters focus on the nature of an analysis and what's involved in writing an analytical essay. Randall shows that analysis consists of a balance of assertions (statements which present their viewpoints or launch an exploration of their concerns), examples (specific passages/scenes/events which inspire these views), explanations (statements that reveal how the examples support the assertions), and significance (statements which reveal the importance of their study to personal and/or cultural issues). After showing why each feature should be present throughout an essay, he reveals how to "set the stage" for producing one of their own. He first helps students to evaluate their own views on a subject and to examine how these views emerge from their own experiences, values and judgments. He, then, shows them how to research what others have said about the subject and provides suggestions for evaluating and incorporating this research into their own perspectives. Finally, Randall discusses the nature of writing, not as a linear procedure, but as a recursive process where the discovery and clarification of a concept occur simultaneously. The remaining three chapters reveal more specific advice on how to develop an analytical essay. Exploring Perspectives: A Concise Guide to Analysis by Randall Fallows is a great text to prepare any student to write analytical essays for the argument and persuasion courses.
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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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Introduction to the Modeling and Analysis of Complex Systems
Hiroki Sayama · Open SUNY · 2015
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.
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Strategic Management and Case Analysis: An Integrated Approach
Lori Anderson; Dirk Buengel; Joseph Simpson · Virginia Tech Publishing · 2025
Strategic Management and Case Analysis: An Integrated Approach is intended for students in undergraduate business programs taking a course in strategic management. Because strategic management synthesizes many business topics and takes a holistic view of business, strategic management courses are often senior-level capstone courses. Most undergraduate business school students begin their business education with a broad introductory business course and then concentrate on courses in their major. Then they return to a broader lens of business to cap off their business education at a higher-level of learning. This textbook supports this level of comprehensive learning. If used with a senior-level capstone course, this textbook supports seniors to synthesize their business education through the lens of strategic management and helps them understand how businesses become successful by leveraging their competitive advantage. This textbook integrates strategic management and case analysis, with cases linked from an open access collection of business strategy cases, RMIT Strategic Management Case Studies. Students will get the most out of this textbook if it is used with cases that students analyze. Strategic Management and Case Analysis: An Integrated Approach, integrates strategic management as a research-led field of study and practice-informed area of business practice with an experiential learning approach to conducting a case analysis. The book explains how strategic leaders and managers analyze their firm’s organizational performance, and external and internal environments; formulate corporate level and business level strategy, and innovation, sustainability and ethics, technology, and multinational strategy, which are embedded in business level strategies; and implement strategy across an organization. Students are in an active and engaged role with the subject and practice of strategic management as they apply the theories, concepts, and analytical frameworks and t
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Introduction to Financial Analysis
Kenneth Bigel · Open Touro · 2022
This Open Textbook is a dynamic guide incorporating the essential skills needed to build a foundation in Financial Analysis. Students and readers will learn how to insightfully read a Financial Statement, utilize key financial ratios in order to derive forward-looking investment-related inferences from the accounting data, engage in elementary forecasting and modeling, master the theory of the Time Value of Money, and learn to price stocks and bonds in an environment in which interest rates constantly change. Ample problems and solutions, and review questions are provided to the student so that s/he can gauge his/her progress. This text will be continually updated in order to provide novel information and enhance students’ experiences.
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Equilibrium Displacement Models: Theory, Applications, & Policy Analysis
Gary Brester; Joseph Atwood; Michael Boland · University of Minnesota Libraries Publishing · 2023
Applied economists frequently use equilibrium displacement models (EDMs), also termed linear elasticity models, for policy analyses because they can be used to estimate changes in prices and quantities that result from exogenous economic or policy shocks. These models are also widely used to estimate changes in producer and consumer surplus caused by exogenous economic shocks and to quantify the short- and long-term impacts of a variety of economic and regulatory actions across multiple markets. For the first time, a textbook that contains all of the theory and applications of EDMs along with a set of spreadsheet files is available in one place.
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Policy Analysis of Multi-Actor System
Ben Enserink; Pieter Bots; Els van Daalen · TU Delft Open · 2022
Policy of Multi-Actor Systems is an introduction into the art of craft of problem exploration and problem structuring. It positions policy analysis as a scientific discipline focused on systems analysis in a multi-actor context to support better informed decision-making. The approach presented in this book is considered to be the cornerstone of the curricula of the Faculty of Technology, Policy and Management of Delft University of Technology and underlies the research on (the governance of) socio-technical systems. Systems thinking applied in a multi-actor environment and its inherent multi-disciplinary character is what makes this work stand out from traditional hard- and soft systems approaches. The core of the book is dedicated to systems analysis, actor- or stakeholder-analysis and discusses methods for dealing with uncertainty. These analytical activities combined lead to a rich problem description and to plans for further research. Due to the stepwise approach this book serves as a basis for any problem analysis both for our bachelor and master students, our alumni worldwide and any interested practitioners.
NorthStar: Listening & Speaking 1 – Fourth Edition
Polly Merdinger and Laurie Barton · Pearson Education · 2020
NorthStar is rigorous in its approach to critical thinking by systematically engaging students in tasks and activities that prepare them to move into high-level academic courses. The cognitive domains of Bloom’s taxonomy provide the foundation for the critical thinking activities. The Reading & Writing strands are designed to challenge students to move beyond basic comprehension to higher-level analysis.