Courses tagged with "Taking derivatives" (363)

This course is designed to equip you with the basic academic, professional, and personal skills you will need to be successful in college.  You are probably already familiar with some of the skills and topics covered; others will be brand new ideas.  For example, perhaps you have already learned some effective test-taking strategies that work well for you, but you have never heard of the concept of learning styles.  Or, maybe you do know your learning style, but you want to improve your listening skills.  Each student will have a different skill set when they start this course.  In addition, some of the skills this course presents may take a lifetime to master!  The point of the course is to give you, a new college student or a person considering a college education, a purposeful, thorough review of the many tools and skills needed for success and to help you understand how you can improve each of the tools and skills over time.  Keep in mind that the terms “tools” and “resources” can refer to…

In ASTR101, you will be introduced to our current understanding of the universe and how we have come to this understanding.  We will start with the ancient Greeks and their belief that the universe was an orderly place capable of being understood.  We will continue through history, as we acquired more information on the nature of the universe and our models of the universe changed to reflect this.  This will take us through several different worldviews. As noted above, we will begin with the Greek worldview, which was characterized by the belief that the earth was the immovable center of the universe; this was known as the “geocentric” model.  Although this worldview is wrong in many of its details, it was a very important first step.  It explained the universe well enough that it lasted almost two thousand years.  By 1600, this belief was beginning to be challenged by such people as Copernicus, Kepler, and Galileo; finally, it was completely done away with by the physics of Newton.  By 1700, the…

Human societies have always been dependent upon local and regional environments for critical natural resources, and loss of these resources (either due to environmental changes or human overuse) has often reduced a society’s resilience to future challenges.  When resilience decreases, the risk of societal collapse increases.  Today, our globalized, highly connected societies have increased access to environmental resources, yet they leave us more vulnerable to disruptions and disasters that begin in other regions or systems.  By understanding how our societies are connected to each other and to the environment, we can better manage our interactions so that they do not increase the potential for societal collapse.  This course will use a complex systems theory perspective to investigate how coupled human-environment systems interact to either increase or decrease their risk of collapse.  This complex systems approach works across many disciplines, so that human-environment linkages can be understood fro…

Geography is the study of the physical features of the Earth and its atmosphere including landscape development, weather and climate, and geologic concepts as well as the influence of human activity including cultural, economic, and political activity on those physical features.  Geography students, as they study the many aspects of our physically and culturally diverse world, tend to become more adept at tasks that require both spatial and critical thinking skills. World Regional Geography covers the basic elements noted above but within a regional context.  Ultimately, World Regional Geography is concerned with the physical and human characteristics that make the regions of our world distinctive.  As you progress through the course, the units will discuss each major world region in detail, placing particular emphasis on cultural and societal structures.  Regions will be discussed within a global framework in the hope that you will gain a better comprehension of how the world map is being defined a…

This course provides an introductory survey of the Western classical tradition, exploring music both as a phenomenon of sound and culture.  The focus of this course is the development of aural skills that lead to an understanding and appreciation of music.  Making use of live performances and streaming audio available on the Internet, we will listen to and explore some of the most important and influential repertoires and genres of music that emerged in the last four centuries: High Renaissance vocal music, the cantatas and oratorios of Bach and Handel, Mozart’s comic operas, the monumental orchestral works of the Romantic movement, and the major musical movements of twentieth-century Europe and America, revealing significant connections with contemporary pop and jazz styles.  These styles have become an enduring part of the world of music in the twenty-first century, traveling out of the concert hall and conservatory into the larger world via movies, television, and the Internet. This course will begi…

Sociology is the scientific study of society. As such, it closely examines human interactions and cultural phenomena, including topics like inequality and urbanization and the effects of these on groups and individuals. To do their work, sociologists rely on a philosophy of science called positivism, which you will study in Unit 1. The philosophy of positivism asserts that authentic knowledge, or truth, can only be gained through empirical observations. In other words, we need to be able to experience our observations or use scientific measurement with a form of sensory experience, as opposed to using faith-based or emotional experiences. Another central concept to sociology is that of the sociological imagination. The sociological imagination allows sociologists to make connections between personal experiences and larger social issues. For example, did you know the U.S. has the highest rate of teen pregnancy in the industrialized world? In order to understand this trend, sociologists use scientific methods…

This course provides an introduction to the history of technology for the Science, Technology, and Society (STS) major. The course surveys major technological developments from ancient to modern times with particular attention to social, political, and cultural contexts in Europe and the United States. You will also think critically about the theory of technological determinism, the ways in which technology has defined “progress” and “civilization”, and the major ethical considerations surrounding today’s technological decisions. This course begins with discussions of the promotion of technology in centralized states of the ancient and medieval worlds: the Roman Empire, Song and Ming China, and the Islamic Abbasid Empire. After a period of relative decline, the states of Western Europe centralized and flourished once again, having benefited from the westward transmission of key ideas and technologies from the East. The focus of the course then shifts to the West, to the technologies of the Renai…

This course will introduce you to the art and architecture of the African continent from the prehistoric to the present. The objects, images, and sites featured in this course represent a small cross-section of the diverse ethnic and artistic heritage in Africa. This course emphasizes the role of art as manifested in the lifestyles, spiritualities, and philosophies of particular African societies, while also breaching aesthetic principles and the study and display of African art. Many works produced in Africa are used for spiritual purposes that include ritual and performance. The study of masks and ceremonies will enable you to become more familiar with the significant role art plays in the everyday lives of the citizens of African nations. For example, most traditional African art was not meant to be displayed, but rather viewed in use and in motion, especially in mixed-media masquerades. Body adornment and textiles have long been important forms of visual communication and expression in Africa, whereas pai…

In this course, you will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations. You will apply these skills to solve real-world problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond. It will begin with a review of some math concepts formed in pre-algebra, such as ordering operations and simplifying simple algebraic expressions, to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction. This course provides students the opportuni…

The SAT is a timed standardized test, taken by most students in their junior or senior year of high school, often required for college admission.  In the increasingly competitive college admission process, students today are looking for any and all ways to improve their candidacy.  One element of your college application that can definitely be improved on to help your chances of admission is your SAT score. The test is made up of 10 sections, drawn from three subjects: reading, mathematics, and writing.  All of these subjects review topics you have already learned in school: critical reading skills, arithmetic, algebra, geometry, grammar, and essay writing.  You already have basic knowledge on these subjects.  However, you can gain an extra edge and improve your score by reviewing the specific material that will be covered on the test and by becoming familiar with the rules and strategies specific to correctly answering SAT questions. Doing well on the test provides important information about you as…

Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. For example, the heat equation can be used to describe the change in heat distribution along a metal rod over time. PDEs arise as part of the mathematical modeling of problems connected to different branches of science, such as physics, biology, and chemistry. In these fields, experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. These connections must be exploited to find an explicit way of calculating the unknown quantity, given the values of the independent variables  that is, to derive certain laws of nature. While we do not know why partial differential equations provide what has been termed the “unreasonable effectiveness of mathematics in the natural sciences” (the title of a 1960 paper by physicist…

This introductory course in biology starts at the microscopic level, with molecules and cells. Before we get into the specifics of cell structure and behavior, however, let’s take a cursory glance at the field of biology more generally. Though biology as we know it today is a relatively new field, we have been studying living things since the beginning of recorded history. The invention of the microscope was the turning point in the history of biology; it paved the way for scientists to discover bacteria and other tiny organisms and ultimately led to the modern cell theory of biology. You will notice that, unlike the core program courses you took in chemistry and physics, introductory biology does not have many mathematical “laws” and “rules” and does not require much math. Instead, you will learn a great number of new terms and concepts that will help you describe life at the smallest level. Over the course of this semester, you will recognize the ways in which the tiniest of molecules are involved…

Welcome to BIO101B, Introduction to Molecular and Cellular Biology.  This course is intended for the student interested in understanding and appreciating common biological topics in the study of the smallest units within biology: molecules and cells. Molecular and cellular biology is a dynamic field.  There are thousands of opportunities within the medical, pharmaceutical, agricultural, and industrial fields (just to name a few) for a person with a concentrated knowledge of molecular and cellular processes.  This course will give you a general introduction of these topics.  In addition to preparing for a diversity of career paths, an understanding of molecular and cell biology will help you make sound decisions in your everyday life that can positively impact your diet and health. Note that this course is an alternative to BIO101A [1], and that you may choose to take either BIO101A or BIO101B in order to learn about Molecular and Cellular Biology.  These courses cover the same material, but in a slig…

This course is designed to introduce you to the study of calculus. You will learn concrete applications of how calculus is used and, more importantly, why it works. Calculus is not a new discipline; it has been around since the days of Archimedes. However, Isaac Newton and Gottfried Leibniz, two seventeenth-century European mathematicians concurrently working on the same intellectual discovery hundreds of miles apart, were responsible for developing the field as we know it today. This brings us to our first question, what is today’s calculus? In its simplest terms, calculus is the study of functions, rates of change, and continuity. While you may have cultivated a basic understanding of functions in previous math courses, in this course you will come to a more advanced understanding of their complexity, learning to take a closer look at their behaviors and nuances. In this course, we will address three major topics: limits, derivatives, and integrals, as well as study their respective foundations and appl…

American Government belongs to the Saylor.org CLEP® PREP Program. In taking this version of POLSC232, you will master the subject of American Government and Politics. This course is also designed to prepare you to take the CLEP® exam in American Government [1]. The CLEP® (College Level Examination Program) exams are designed by the College Board, the organization which administers the AP and SAT exam programs you may have encountered or taken in high school. CLEP® exams test for the mastery of college-level material that you may have acquired through any number of ways college-level course instruction, independent study, work experience, or any other program of study you have pursued. In other words, CLEP® exams are freestanding exams that any individual can pay to take in order to prove that he or she has mastered a given subject area at the college level. Over 2,900 US colleges and universities recognize and award college credit for a satisfactory score on a CLEP® exam. A student who earns a satisf…

Effective time management is the key to getting the most out of your day. It helps you improve performance, increase productivity, and reduce stress. Time management is critical to maximizing your day and surviving mounting responsibilities and pressures. Time is your most important resource. Therefore, it is necessary to clarify your objectives and determine priorities daily. Every action you take represents a priority decision. The problem is rarely that you aren’t capable of completing a task; the problem, most often, is time eventually you will run out of it. This course will provide learners with several time management tools and techniques that can be applied to most work and life situations. From juggling multiple tasks, to managing e-mail, to beating deadlines: you will learn how to budget time wisely, and overcome distractions and time wasters.

This course will introduce you to the fundamental principles of psychology and to the major subjects of psychological inquiry. It has been designed to not only provide you with the tools necessary for the study of psychology but to present you with a sampling of the major areas of psychology research. The course begins with a short overview of how psychology developed as an academic discipline and an introduction to a number of the principle methodologies most commonly deployed in its study. The subsequent units are arranged around broad areas of research, including emotion, development, memory, and psychopathology. We will focus on well-substantiated research and current trends within each of these categories. This course is designed to align with Excelsior College’s UExcel Psychology examination. Visit the Excelsior website [1] to download the content guide for the PSYX-101 exam.  For more information about this partnership, and earning credit through Excelsior College, go here [2].    [1] http:/…

Calculus AB is primarily concerned with developing your understanding of the concepts of calculus and providing you with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Broad concepts and widely applicable methods are also emphasized. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types, but rather, the course uses the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling to become a cohesive whole. The course is a yearlong high school mathematics course designed to prepare you to write and pass the AP Calculus AB test in May. Passing the test can result in one semester of college credit in mathematics.

Geometry comes from the Greek roots geo-, meaning Earth, and metron, meaning measure. Thus, geometry literally means the process of measuring the Earth. In a more mathematical sense, this course looks at geometric figures that we see in everyday life to understand the patterns in their attributes and how their measures relate to these patterns. It expands on the basic geometric concepts learned in previous math courses, through the applications of these concepts in new contexts. You will learn to develop formal proofs that support patterns and rules of geometric figures previously investigated, including congruent and similar figures, triangles, quadrilaterals, and circles. From here, the course expands on your knowledge about triangles and the Pythagorean theorem, introducing trigonometry of both right triangles and general triangles. The course will help you develop links between the attributes of two-dimensional and three-dimensional figures; help you develop formulas for calculating the volume of prisms…

This course is designed to prepare Saylor’s consulting educators to build K-12 subject courses that are aligned with the Common Core State Standards in English Language Arts & Literacy in History/Social Studies, Science and Technical Subjects and Mathematics.  You will begin this course by gaining an overview of what the set of Common Core State Standards is, why Saylor is focused on developing courses around the Common Core State Standards, and the main benchmarks for ensuring that a course is compliant with the Common Core State Standards.  In unit 2 of this course, you will look at the Common Core State Standards in detail and identify key takeaways from them.  In unit 3 of this course, you will explore how to develop content that meets the Common Core State Standards and how to integrate the standards through the development of learning assignments based on specific texts and activities.  In unit 4 of this course, you will take a look at the different assessment strategies often used for Common Core…