After completing this section, students should be able to do the following.Use reduction formulas and the Pythagorean identity to compute integrals involving trigonometric functions.Recognize the patterns that appear in trigonometric integrals, and use appropriate substitutions to compute them.Compute integrals involving powers of sine and cosine.
After completing this section, students should be able to do the following.Use Pythagorean identities to simplify expressions.Substitute trigonometric functions to simiplify integrals.Complete the square to change the form of an integral.
After completing this section, students should be able to do the following.State the definition of a vector.Calculate the magnitude of a vector.Work with vectors in two or three dimensions.Multiply vectors by scalars.Add and subtract vectors.Find unit vectors.Use vectors in applied settings.
After completing this section, students should be able to do the following.Identify real numbers.Compute the distance between points.Find the equations for planes.Give the equation for a circle.Give the equation for a sphere or ball.
Calculus is about the very large, the very small, and how things change—the surprise is that something seemingly so abstract ends up explaining the real world.
This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems. One learns calculus by doing calculus, and so this course is based around doing practice problems.
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
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.
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.
This textbook introduces aspects of the history of Canada since Confederation. “Canada” in this context includes Newfoundland and all the other parts that come to be aggregated into the Dominion after 1867. Much of this text follows thematic lines. Each chapter moves chronologically but with alternative narratives in mind. What Aboriginal accounts must we place in the foreground? Which structures (economic or social) determine the range of choices available to human agents of history? What environmental questions need to be raised to gain a more complete understanding of choices made in the past and their ramifications? Each chapter is comprised of several sections and some of those are further divided. In many instances you will encounter original material that has been contributed by other university historians from across Canada who are leaders in their respective fields. They provide a diversity of voices on the subject of the nation’s history and, thus, an opportunity to experience some of the complexities of understanding and approaching the past. Canadian History: Post-Confederation includes Learning Objectives and Key Points in most chapter sections, intended to help identify issues of over-arching importance. Recent interviews with historians from across Canada have been captured in video clips that are embedded throughout the web version of the book. At the end of each chapter, the Summary section includes additional features: Key Terms, Short Answer Exercises, and Suggested Readings. The key terms are bolded in the text, and collected in a Glossary in the appendix.
Canadian History: Pre-Confederation is a survey text that introduces undergraduate students to important themes in North American history to 1867. It provides room for Aboriginal and European agendas and narratives, explores the connections between the territory that coalesces into the shape of modern Canada and the larger continent and world in which it operates, and engages with emergent issues in the field. The material is pursued in a largely chronological manner to the early 19th century, at which point social, economic, and political change are dissected. Canadian History: Pre-Confederation provides, as well, a reconnaissance of historical methodology and debates in the field, exercises for students, Key Terms and a Glossary, and section-by-section Key Points. Although this text can be modified, expanded, reduced, and reorganized to suit the needs of the instructor, it is organized so as to support learning, to broaden (and sometimes provoke) debate, and to engage students in thinking like historians. Written and reviewed by subject experts drawn from colleges and universities, this is the first open textbook on the topic of Canadian history.
This is a Principles of Macroeconomics course utilizing exclusively Open Educational Resources and designed in Canvas. This course is mapped to the Learning Outcomes for ECON 2301 as established under the Texas Higher Education Coordinating Board Academic Course Guide Manual. This course is based on Openstax Principles of Macroeconomics 2e textbook and incorporates key components from EDUC 1301: Learning Frameworks, designed to enhance the student’s experience as well as to improve overall student learning.
The course was developed by a faculty team from Collin College as part of the Texas Higher Education Coordinating Board OER Course Development and Implementation Grant Program.
The Virtual Tour for the Castillo de San Marcos National Monument in St. Augustine, Florida. Photos, maps, podcasts, and more!
Cells: Molecules and Mechanisms is a CC-licensed, open access textbook that can be effectively used as a resource in both introductory (underclassmen) and more advanced (upperclassmen) college cell and molecular biology courses. This book was written and designed for the student learning process, and is not designed to be an encyclopedic text. Rather, it is designed and written to communicate major themes as clearly as possible while providing enough advanced detail to serve as a springboard for higher-level students to delve into primary literature. This text is available in its entirety or in individual chapters as PDF files.
In The Centrality of Style, editors Mike Duncan and Star Medzerian Vanguri argue that style is a central concern of composition studies even as they demonstrate that some of the most compelling work in the area has emerged from the margins of the field. Calling attention to this paradox in his foreword to the collection, Paul Butler observes, "Many of the chapters work within the liminal space in which style serves as both a centralizing and decentralizing force in rhetoric and composition. Clearly, the authors and editors have made an invaluable contribution in their collection by exposing the paradoxical nature of a canon that continues to play a vital role in our disciplinary history."
This video talka about what is easily one of the most fundamental and profound concepts in statistics and maybe in all of mathematics. And that's the central limit theorem.
Age-related declines in capabilities may compromise older adults’ ability to maintain their homes thus threatening successful aging in place. Structured interviews were conducted with forty-four independently living older adults (Mage = 76.1, SD = 4.7) to discuss difficult home maintenance tasks and how they managed those tasks. Solutions to managing difficulties were categorized as person-related or environment-related. The majority (85%) of responses were person-related solutions. An understanding of the specific challenges that older adults face in maintaining their homes can guide redesign efforts and interventions to effectively support older adults’ desire to age in place.