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This is a complete college textbook, including a detailed Table of Contents, seventeen Chapters (each with a set of relevant homework problems), a list of References, two Appendices, and a detailed Index. The book is intended to enable students to: Solve first-, second-, and higher-order, linear, time-invariant (LTI) ordinary differential equations (ODEs) with initial conditions and excitation, using both time-domain and Laplace-transform methods; Solve for the frequency response of an LTI system to periodic sinusoidal excitation and plot this response in standard form; Explain the role of the time constant in the response of a first-order LTI system, and the roles of natural frequency, damping ratio, and resonance in the response of a second-order LTI system; Derive and analyze mathematical models (ODEs) of low-order mechanical systems, both translational and rotational, that are composed of inertial elements, spring elements, and damping devices; Derive and analyze mathematical models (ODEs) of low-order electrical circuits composed of resistors, capacitors, inductors, and operational amplifiers; Derive (from ODEs) and manipulate Laplace transfer functions and block diagrams representing output-to-input relationships of discrete elements and of systems; Define and evaluate stability for an LTI system; Explain proportional, integral, and derivative types of feedback control for single-input, single-output (SISO), LTI systems; Sketch the locus of characteristic values, as a control parameter varies, for a feedback-controlled SISO, LTI system; Use MATLAB as a tool to study the time and frequency responses of LTI systems. The book's general organization is: Chapters 1-10 deal primarily with the ODEs and behaviors of first-order and second-order dynamic systems; Chapters 11 and 12 discuss the ODEs and behaviors of mechanical systems having two degrees of freedom, i.e., fourth-order systems; Chapters 13 and 14 introduce classical feedback control; Chapter 15 presents the basic features of proportional, integral, and derivative types of classical control; Chapters 16 and 17 discuss methods for analyzing the stability of classical control systems. The general minimum prerequisite for understanding this book is the intellectual maturity of a junior-level (third-year) college student in an accredited four-year engineering curriculum. A mathematical second-order system is represented in this book primarily by a single second-order ODE, not in the state-space form by a pair of coupled first-order ODEs. Similarly, a two-degrees-of-freedom (fourth-order) system is represented by two coupled second-order ODEs, not in the state-space form by four coupled first-order ODEs. The book does not use bond graph modeling, the general and powerful, but complicated, modern tool for analysis of complex, multidisciplinary dynamic systems. The homework problems at the ends of chapters are very important to the learning objectives, so the author attempted to compose problems of practical interest and to make the problem statements as clear, correct, and unambiguous as possible. A major focus of the book is computer calculation of system characteristics and responses and graphical display of results, with use of basic (not advanced) MATLAB commands and programs. The book includes many examples and homework problems relevant to aerospace engineering, among which are rolling dynamics of flight vehicles, spacecraft actuators, aerospace motion sensors, and aeroelasticity. There are also several examples and homework problems illustrating and validating theory by using measured data to identify first- and second-order system dynamic characteristics based on mathematical models (e.g., time constants and natural frequencies), and system basic properties (e.g., mass, stiffness, and damping). Applications of real and simulated experimental data appear in many homework problems. The book contains somewhat more material than can be covered during a single standard college semester, so an instructor who wishes to use this as a one-semester course textbook should not attempt to cover the entire book, but instead should cover only those parts that are most relevant to the course objectives.
- Keywords:
- Differential equations Engineering mathematics Differential equations Partial Textbooks
- Resource Type:
- e-book
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e-book
Social Problems: Continuity and Change is a realistic but motivating look at the many issues that are facing our society today. As this book's subtitle, Continuity and Change, implies, social problems are persistent, but they have also improved in the past and can be improved in the present and future, provided that our nation has the wisdom and will to address them. It is easy for students to read a social problems textbook and come away feeling frustrated by the enormity of the many social problems facing us today. Social Problems: Continuity and Change certainly does not minimize the persistence of social problems, but neither does it overlook the possibilities for change offered by social research and by the activities of everyday citizens working to make a difference. Readers the book will find many examples of how social problems have been improved and of strategies that hold great potential for solving them today and in the future. You will find several pedagogical features help to convey the “continuity and change” theme of this text and the service sociology vision in which it is grounded: Each chapter begins with a “Social Problems in the News” story related to the social problem discussed in that chapter. These stories provide an interesting starting point for the chapter's discussion and show its relevance for real-life issues. Three types of boxes in each chapter provide examples of how social problems have been changed and can be changed. In no particular order, A first box, “Applying Social Research,” discusses how the findings from sociological and other social science research have either contributed to public policy related to the chapter's social problem or have the potential of doing so. A second box, “Lessons from Other Nations,” discusses how another nation or nations have successfully addressed the social problem of that chapter. A third box, “People Making a Difference,” discusses efforts by individuals, non-profit organizations or social change groups, or social movements relating to the chapter's social problem. Students will see many examples in this box of how ordinary people can indeed make a difference. A fourth box in each chapter, “Children and Our Future,” examines how the social problem discussed in that chapter particularly affects children, and it outlines the problem's repercussions for their lives as adolescents and adults. This box reinforces for students the impact of social problems on children and the importance of addressing these problems for their well-being as well as for the nation's well-being.Each chapter ends with a “Using What You Know” feature that presents students with a scenario involving the social problem from the chapter and that puts them in a decision-making role. This feature helps connect the chapter's theoretical discussion with potential real-life situations. Each chapter also ends with a “What You Can Do” feature that suggests several activities, strategies, or other efforts that students might undertake to learn more about and/or to address the social problem examined in the chapter. Like other aspects of the book, this feature helps counter “doom and gloom” feelings that little can be done about social problems. Other pedagogical features in each chapter include Learning Objectives at the beginning of a major section that highlight key topics to be learned; Key Takeaways at the end of a major section that highlight important points that were discussed in the section; For Your Review questions, also at the end of a major section, that have students think critically about that section's discussion; and a Summary that reviews the major points made in the chapter. The founders of American sociology a century or more ago in cities like Atlanta and Chicago wanted to reduce social inequality, to improve the lives of people of color, and more generally to find solutions to the most vexing social problems of their times. A former president of the Society for the Study of Social Problems, A. Javier Treviño, has used the term service sociology to characterize their vision of their new discipline. Social Problems: Continuity and Change is grounded in this vision by offering a sociological understanding of today's social problems and of possible solutions to these problems.
- Subjects:
- Sociology
- Keywords:
- Textbooks Social problems Social change
- Resource Type:
- e-book
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e-book
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).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
Recognizing that a course in economics may seem daunting to some students, we have tried to make the writing clear and engaging. Clarity comes in part from the intuitive presentation style, but we have also integrated a number of pedagogical features that we believe make learning economic concepts and principles easier and more fun. These features are very student-focused. The chapters themselves are written using a “modular” format. In particular, chapters generally consist of three main content sections that break down a particular topic into manageable parts. Each content section contains not only an exposition of the material at hand but also learning objectives, summaries, examples, and problems. Each chapter is introduced with a story to motivate the material and each chapter ends with a wrap-up and additional problems. Our goal is to encourage active learning by including many examples and many problems of different types. A tour of the features available for each chapter may give a better sense of what we mean: Start Up—Chapter introductions set the stage for each chapter with an example that we hope will motivate readers to study the material that follows. These essays, on topics such as the value of a college degree in the labor market or how policy makers reacted to a particular economic recession, lend themselves to the type of analysis explained in the chapter. We often refer to these examples later in the text to demonstrate the link between theory and reality. Learning Objectives—These succinct statements are guides to the content of each section. Instructors can use them as a snapshot of the important points of the section. After completing the section, students can return to the learning objectives to check if they have mastered the material.Heads Up!—These notes throughout the text warn of common errors and explain how to avoid making them. After our combined teaching experience of more than fifty years, we have seen the same mistakes made by many students. This feature provides additional clarification and shows students how to navigate possibly treacherous waters. Key Takeaways—These statements review the main points covered in each content section. Key Terms—Defined within the text, students can review them in context, a process that enhances learning. Try It! questions—These problems, which appear at the end of each content section and which are answered completely in the text, give students the opportunity to be active learners. They are designed to give students a clear signal as to whether they understand the material before they go on to the next topic. Cases in Point—These essays included at the end of each content section illustrate the influence of economic forces on real issues and real people. Unlike other texts that use boxed features to present interesting new material or newspaper articles, we have written each case ourselves to integrate them more clearly with the rest of the text. Summary—In a few paragraphs, the information presented in the chapter is pulled together in a way that allows for a quick review of the material.End-of-chapter concept and numerical problems—These are bountiful and are intended to check understanding, to promote discussion of the issues raised in the chapter, and to engage students in critical thinking about the material. Included are not only general review questions to test basic understanding but also examples drawn from the news and from results of economics research. Some have students working with real-world data.
- Subjects:
- Economics
- Keywords:
- Macroeconomics Textbooks
- Resource Type:
- e-book