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Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Calculus
- Resource Type:
- e-book
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e-book
Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Mathematics
- Resource Type:
- e-book
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e-book
Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation. In addition to the paper homework sets, algorithmetically generated online homework is available as part of a complete course shell package, which also includes a sample syllabus, teacher notes with lecture examples, sample quizzes and exams, printable classwork sheets and handouts, and chapter review problems. If you teach in Washington State, you can find the course shell in the WAMAP.org template course list. For those located elsewhere, you can access the course shell at MyOpenMath.com. A self-study version of the online course exercises is also available on MyOpenMath.com for students wanting to learn the material on their own, or who need a refresher.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Trigonometry Precalculus Algebra Textbooks
- Resource Type:
- e-book
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e-book
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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Functions of real variables Textbooks Mathematical analysis
- Resource Type:
- e-book
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e-book
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Calculus
- Resource Type:
- e-book
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e-book
The Little Book of Semaphores is a free (in both senses of the word) textbook that introduces the principles of synchronization for concurrent programming. In most computer science curricula, synchronization is a module in an Operating Systems class. OS textbooks present a standard set of problems with a standard set of solutions, but most students don't get a good understanding of the material or the ability to solve similar problems. The approach of this book is to identify patterns that are useful for a variety of synchronization problems and then show how they can be assembled into solutions. After each problem, the book offers a hint before showing a solution, giving students a better chance of discovering solutions on their own. The book covers the classical problems, including "Readers-writers," "Producer-consumer", and "Dining Philosophers." In addition, it collects a number of not-so-classical problems, some written by the author and some by other teachers and textbook writers. Readers are invited to create and submit new problems.
- Subjects:
- Computing, Data Science and Artificial Intelligence
- Keywords:
- Computer programming Textbooks Operating systems (Computers)
- Resource Type:
- e-book
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e-book
Essentials of Geographic Information Systems integrates key concepts behind the technology with practical concerns and real-world applications. Recognizing that many potential GIS users are nonspecialists or may only need a few maps, this book is designed to be accessible, pragmatic, and concise. Essentials of Geographic Information Systems also illustrates how GIS is used to ask questions, inform choices, and guide policy. From the melting of the polar ice caps to privacy issues associated with mapping, this book provides a gentle, yet substantive, introduction to the use and application of digital maps, mapping, and GIS.
In today's world, learning involves knowing how and where to search for information. In some respects, knowing where to look for answers and information is arguably just as important as the knowledge itself. Because Essentials of Geographic Information Systems is concise, focused, and directed, readers are encouraged to search for supplementary information and to follow up on specific topics of interest on their own when necessary. Essentials of Geographic Information Systems provides the foundations for learning GIS, but readers are encouraged to construct their own individual frameworks of GIS knowledge. The benefits of this approach are two-fold. First, it promotes active learning through research. Second, it facilitates flexible and selective learning—that is, what is learned is a function of individual needs and interest.
Since GIS and related geospatial and navigation technology change so rapidly, a flexible and dynamic text is necessary in order to stay current and relevant. Though essential concepts in GIS tend to remain constant, the situations, applications, and examples of GIS are fluid and dynamic. Though this book is intended for use in introductory GIS courses, Essentials of Geographic Information Systems will also appeal to the large number of certificate, professional, extension, and online programs in GIS that are available today. In addition to providing readers with the tools necessary to carry out spatial analyses, Essentials of Geographic Information Systems outlines valuable cartographic guidelines for maximizing the visual impact of your maps. The book also describes effective GIS project management solutions that commonly arise in the modern workplace.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Land Surveying and Geo-Informatics
- Keywords:
- Textbooks Geographic information systems
- Resource Type:
- e-book
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e-book
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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Statistics
- Resource Type:
- e-book
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e-book
A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class. The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Trigonometry Precalculus Algebra Textbooks
- Resource Type:
- e-book
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e-book
An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available. This textbook has been used in classes at:Boise State University,Claremont McKenna College,University of Minnesota, University of Puget Sound, Western Connecticut State University, Whitman College.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Calculus
- Resource Type:
- e-book