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Basic Analysis: Introduction to Real Analysis

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This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.

Material Type: Textbook

Author: Jiří Lebl

Business Calculus (MATH 148)

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MATH&148 is a calculus course for business students. It is designed for students who want a brief course in calculus. Topics include differential and integral calculus of elementary functions. Problems emphasize business and social science applications. Translating words into mathematics and solving word problems are emphasized over algebra. Applications are mainly business oriented (e.g. cost, revenue, and profit). Mathematical theory and complex algebraic manipulations are not mainstays of this course, which is designed to be less rigorous than the calculus sequence for scientists and engineers. Topics are presented according to the rule of four: geometrically, numerically, analytically, and verbally. That is, symbolic manipulation must be balanced with graphical interpretation, numerical examples, and writing. Trigonometry is not part of the course.

Material Type: Assessment, Full Course, Reading, Syllabus, Textbook

Calculus I

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This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)

Material Type: Assessment, Full Course, Reading, Syllabus, Textbook

Dynamical Systems

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This book addresses the following topics: Iterations and fixed points; bifurcations; conjugacy; space and time averages; the contraction fixed point theorem; Hutchinson's theorem and fractal images; hyperbolicity; and symbolic dynamics. 151 page pdf file.

Material Type: Textbook

Author: Shlomo Sternberg

Introduction to Psychology

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When you teach Introduction to Psychology, do you find it difficult – much harder than teaching classes in statistics or research methods? Do you easily give a lecture on the sympathetic nervous system, a lecture on Piaget, and a lecture on social cognition, but struggle with linking these topics together for the student? Do you feel like you are presenting a laundry list of research findings rather than an integrated set of principles and knowledge? Have you wondered how to ensure your course is relevant to your students? If so, then you have something in common with Charles Stangor.Charles Stangor's Introduction to Psychology utilizes the dual theme of behavior and empiricism to make psychology relevant to intro students.Charles wrote this book to help students organize their thinking about psychology at a conceptual level. Five or ten years from now, he does not expect his students to remember the details of most of what he teaches them. However, he does hope that they will remember that psychology matters because it helps us understand behavior and that our knowledge of psychology is based on empirical study.This book is designed to facilitate these learning outcomes, and he has used three techniques to help focus students on behavior:Chapter Openers: Each chapter opens showcasing an interesting real world example of people who dealing with behavioral questions and who can use psychology to help them answer them. The opener is designed to draw the student into the chapter and create an interesting in learning about the topic.Psychology in Everyday Life: Each chapter contains one or two features designed to link the principles from the chapter to real-world applications in business, environment, health, law, learning, and other relevant domains. For instance, the application in Chapter 7 on Development, “What makes good parents” applies the concepts of parenting styles in a mini-handbook about parenting, and the application in Chapter 3 is about the difficulties that left-handed people face performing everyday tasks in a right-handed world.Research Foci: Introduction to Psychology emphasizes empiricism throughout, but without making it a distraction from the main story line. Each chapter presents two close-ups on research -- well articulated and specific examples of research within the content area, each including a summary of the hypotheses, methods, results, and interpretations. This feature provides a continuous thread that reminds students of the importance of empirical research. The research foci also emphasize the fact that findings are not always predictable ahead of time (dispelling the myth of hindsight bias), and also help students understand how research really works.Charles Stangor's focus on behavior and empiricism has produced, Introduction to Psychology, a text that is better organized, has fewer chapters, and is somewhat shorter than many of the leading books.

Material Type: Textbook

Author: Charles Stangor

Principles of Social Psychology

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Have you ever had trouble teaching the various topics of social psychology and fitting them together to form a coherent field? Dr. Stangor felt like he was presenting a laundry list of ideas, research studies, and phenomena, rather than an integrated set of principles and knowledge. He wondered how his students could be expected to remember and understand the many phenomena that social psychologists study? How could they tell what was most important? It was then that he realized a fresh approach to a Social Psychology textbook was needed to structure and integrate student learning; thus, Principles of Social Psychology was born. This textbook is based on a critical thinking approach, and its aim is to get students thinking actively and conceptually Đ with a greater focus on the forest than the trees. Yes, there are right and wrong answers, but the answers are not the only thing. What is perhaps even more important is how students get to the answers Đ the thinking process itself. To help students better grasp the big picture of social psychology, and to provide you with a theme that you can use to organize your lectures, Dr. Stangor's text has a consistent pedagogy across the chapters.

Material Type: Textbook

Author: Charles Stangor

Introduction to Engineering Thermodynamics

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Short Description: The book is most suitable for a one-term, introductory engineering thermodynamics course at the undergraduate level. It may also be used for self-learning of fundamental concepts of classical thermodynamics. Long Description: This open book is written with a goal to support students’ learning of fundamental concepts and engineering applications of classical thermodynamics. It features concise explanations of key concepts, step-by-step solutions to engineering examples, and interactive practice problems. The book is most suitable for a one-term, introductory engineering thermodynamics course at the undergraduate level. It may also be used as self-learning materials or a supplement to other thermodynamics books. Word Count: 49571 (Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

Material Type: Textbook

Author: Claire Yu Yan