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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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Boundary value problems Differential equations
- Resource Type:
- e-book
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e-book
This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants. The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
Natural Resources Biometrics begins with a review of descriptive statistics, estimation, and hypothesis testing. The following chapters cover one- and two-way analysis of variance (ANOVA), including multiple comparison methods and interaction assessment, with a strong emphasis on application and interpretation. Simple and multiple linear regressions in a natural resource setting are covered in the next chapters, focusing on correlation, model fitting, residual analysis, and confidence and prediction intervals. The final chapters cover growth and yield models, volume and biomass equations, site index curves, competition indices, importance values, and measures of species diversity, association, and community similarity.
- Subjects:
- Biology
- Keywords:
- Natural resources Biometry Textbooks
- Resource Type:
- e-book
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e-book
The purpose of this book is to help boards of directors of nonprofit organizations improve their performance after completing the online board self-assessment tool found at www.boardcheckup.com. However, it can also be used as a stand-alone resource for any board seeking to enhance its effectiveness in that it also contains the diagnostic questions on which the online tool is based. The approach taken here is similar to that which lies behind health checkups for individuals. Doctors usually begin by asking us to review a lengthy list of many possible health issues and we check those about which we have concerns. The doctor and patient then focus their discussions on these issues. The typical process proceeds through the following three stages: Understanding the symptoms. The doctor and patient begin by trying to define the issues more clearly. Diagnosis. Effort is made to understand the causes of the problems through tests and further examination. Treatment. Once the problem has been properly diagnosed, a treatment program to remedy it is begun. While the Board Check-Up survey on which this book is based does not pretend to be as scientifically rigorous as a medical examination, it is based on the same logic. It begins by having those who belong to, or relate to, boards provide their perceptions of how well the board is working by guiding them through a list of potential "health issues”, i.e. statements of possible problems, issues or challenges that boards might encounter in their work. These statements have been derived from comments made by those who serve on boards or interact with them as well as from the work of researchers and consultants who have studied boards over the past 30 years. Once issues (symptoms) have been identified, they become the focal point for discussions that explore how serious they are, what might be causing them (diagnosis) and what can be done to resolve them (treatment). As noted above, this book is intended to help boards assess performance and make decisions to improve the effectiveness of the governance process. Each chapter deals with one of the nine dimensions of governance effectiveness. It starts with the items dealing with that dimension on the Board Performance Self-Assessment Questionnaire. These items represent the symptoms that indicate possible issues, problems or challenges faced by the board. This is followed by a discussion of possible reasons that such symptoms might exist (diagnosis) The third part of each chapter looks at what might be done to alleviate the symptoms once a diagnosis is made (treatment). Included in this final part of the chapter are references to websites, books and articles that provide additional advice and assistance on how to deal with the issues raised.
- Subjects:
- Management
- Keywords:
- Nonprofit organizations -- Management Directors of corporations Textbooks
- Resource Type:
- e-book
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e-book
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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Mathematical analysis
- Resource Type:
- e-book
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e-book
This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14. More information, including free downloads of .pdf versions of the text, is available at www.apexcalculus.com.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Calculus
- Resource Type:
- e-book
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e-book
Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing College Algebra and Algebra and Trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Trigonometry Precalculus Algebra Textbooks
- Resource Type:
- e-book
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e-book
Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean, which has been widely adopted. Introductory Statistics includes innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful and memorable, so that students can draw a working knowledge from it that will enrich their future studies and help them make sense of the world around them. The text also includes Collaborative Exercises, integration with TI-83,83+,84+ Calculators, technology integration problems, and statistics labs. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Statistics
- Resource Type:
- e-book
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e-book
Principles of Macroeconomics 2e covers the scope and sequence of most introductory economics courses. The text includes many current examples, which are handled in a politically equitable way. The outcome is a balanced approach to the theory and application of economics concepts. The second edition has been thoroughly revised to increase clarity, update data and current event impacts, and incorporate the feedback from many reviewers and adopters. Changes made in Principles of Macroeconomics 2e are described in the preface and the transition guide to help instructors transition to the second edition. The first edition of Principles of Macroeconomics by OpenStax is available in web view here.
- Subjects:
- Economics
- Keywords:
- Macroeconomics Textbooks
- Resource Type:
- e-book
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e-book
Welcome to Information Systems for Business and Beyond. In this book, you will be introduced to the concept of information systems, their use in business, and the larger impact they are having on our world. This book is written as an introductory text, meant for those with little or no experience with computers or information systems. While sometimes the descriptions can get a little bit technical, every effort has been made to convey the information essential to understanding a topic while not getting bogged down in detailed terminology or esoteric discussions. Learning objectives can be found at the beginning of each chapter. Of course, all chapters are recommended for use in an introductory information systems course. However, for courses on a shorter calendar or courses using additional textbooks, a review of the learning objectives will help determine which chapters can be omitted. At the end of each chapter, there is a set of study questions and exercises (except for chapter 1, which only offers study questions). The study questions can be assigned to help focus students' reading on the learning objectives. The exercises are meant to be a more in-depth, experiential way for students to learn chapter topics. It is recommended that you review any exercise before assigning it, adding any detail needed (such as length, due date) to complete the assignment.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Industrial and Systems Engineering
- Keywords:
- Business information services Management information systems Textbooks
- Resource Type:
- e-book