Courses tagged with "Taking derivatives" (363)

Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher dimensions.  You may find that these courses share many of the same basic concepts, and that Multivariable Calculus will simply extend your knowledge of functions to functions of several variables.  The transition from single variable relationships to many variable relationships is not as simple as it may seem; you will find that multi-variable functions, in some cases, will yield counter-intuitive results. The structure of this course very much resembles the structure of Single-Variable Calculus I and II.  We will begin by taking a fresh look at limits and continuity.  With functions of many variables, you can approach a limit from many different directions.  We will then move on to derivatives and the process by which we generalize them to higher dimensions.  Finally, we will look at multiple integrals, or integration over regions of space as opposed to intervals. The goal of Mu…

This survey chemistry course is designed to introduce students to the world of chemistry.  Chemistry was born in ancient Egypt, when the principles of chemistry were first identified, studied, and applied in order to extract metal from ores, make alcoholic beverages, glaze pottery, turn fat into soap, and much more.  What began as a quest to build better weapons or create potions capable of ensuring everlasting life has since become the foundation of modern science.  Take a look around you: chemistry makes up almost everything you touch, see, and feel, from the shampoo you used this morning to the plastic container that holds your lunch. In this course, we will study chemistry from the ground up, learning the basics of the atom and its behavior.  We will apply this knowledge to understand the chemical properties of matter and the changes and reactions that take place in all types of matter.

This course will survey physics concepts and their respective applications.  It is intended as a basic introduction to the current physical understanding of our universe.  Originally part of “Natural Philosophy,” the first scientific studies were conducted after Thales of Miletus established a rational basis for the understanding of natural phenomena circa 600 BCE.  One of the Seven Sages of Greek philosophy, Thales sought to identify the substances that make up the natural world and explain how they produce the physical phenomena we observe.  Prior to Thales, humans had explained events by attributing supernatural causes to them; his work represents the very beginning of scientific analysis. The Scientific Method used today builds on this early foundation, but adds the essential underpinnings of evidence based on experiments or observation.  Briefly, the modern scientific method involves forming a hypothesis about the cause of a general phenomenon, using that hypothetical model to predict the outc…

The physics of the Universe appears to be dominated by the effects of four fundamental forces: gravity, electromagnetism, and weak and strong nuclear forces.  These control how matter, energy, space, and time interact to produce our physical world.  All other forces, such as the force you exert in standing up, are ultimately derived from these fundamental forces. We have direct daily experience with two of these forces: gravity and electromagnetism.  Consider, for example, the everyday sight of a person sitting on a chair.  The force holding the person on the chair is gravitational, while that gravitational force is balanced by material forces that “push up” to keep the individual in place, and these forces are the direct result of electromagnetic forces on the nanoscale.  On a larger stage, gravity holds the celestial bodies in their orbits, while we see the Universe by the electromagnetic radiation (light, for example) with which it is filled.  The electromagnetic force also makes possible the a…

This course provides an introduction to critical thinking, informal logic, and a small amount of formal logic.  Its purpose is to provide students with the basic tools of analytical reasoning, which will give them a distinctive edge in a wide variety of careers and courses of study.  While many university courses focus on the presentation of content knowledge, the emphasis here is on learning how to think effectively.  Although the techniques and concepts covered here are classified as “philosophical,” they are essential to the practice of nearly every major discipline, from the physical sciences and medicine to politics, law, and the humanities.  The course touches upon a wide range of reasoning skills, from verbal argument analysis to formal logic, visual and statistical reasoning, scientific methodology, and creative thinking.  Mastering these will help students become more perceptive readers and listeners, more persuasive writers and presenters, and more effective researchers and scientists. Th…

This course will introduce you to the basic concepts and methods of moral and political philosophy.  Its primary focus is on the development of moral reasoning skills and the application of those skills to contemporary social and political issues.  Although the course is organized around the central concept of justice, it uses this notion as a point of departure for discussing a wide range of philosophical topics and perspectives. Topics range from the value of human life, the moral standing of the free market, and the notion of fundamental human rights, to equality of opportunity, the legality of same-sex marriage, and the conditions for a moral community.  In order to investigate these topics, this course makes extensive use of Professor Michael Sandel’s video lecture course on justice, delivered at Harvard University in 2009.  In addition to these lectures, you will study a number of important moral and political philosophers, including Plato, Aristotle, John Locke, Thomas Hobbes, Jeremy Bentham, Joh…

This class provides an in-depth introduction to the philosophical problems surrounding death.  It takes its starting point in the fact that everyone, eventually, will die.  This is one of the few facts that human beings can be absolutely sure about.  Given this certainty, however, death still presents us with many difficult and pressing questions. What does it mean to die in the first place?  Who or what is the “person” that dies?  Is it merely a physical body, or is it also something like a soul, and, if so, does the existence of a soul indicate that there is some hope of immortality?  Moreover, what should our attitude toward death be?  Should we think of it as a good thing or a bad thing?  And what effect should it have on the way we live our lives?  At some point in our lives, we all grapple with these questions.  This course uses the doctrines and arguments of a number of prominent philosophers concerning death as a means to investigate these and other questions.  The course is organized a…

This course is a survey of philosophical issues surrounding the concepts and practices of modern science.  The course covers the major areas of contemporary philosophy of science, including scientific reasoning, scientific progress, interpretations of scientific knowledge, and the social organization of scientific practice.  Its aim is not only to familiarize you with philosophical issues about science but also to equip you to critically interpret popular reports about contemporary scientific research. Unit 1 introduces philosophy of science as a discipline distinct from psychology of science, history of science, and sociology of science.  Unit 2 examines the nature and objectivity of observational evidence, and Unit 3 examines methods of reasoning relevant to induction, confirmation, and explanation.  Unit 4 examines accounts of theory change and scientific progress, and Unit 5 addresses the interpretation of scientific knowledge.  Finally, Unit 6 explores various topics concerning science in a social…

Existentialism is a philosophical and literary movement that first was popularized in France soon after World War II by figures such as Jean-Paul Sartre and Albert Camus. The roots of this movement can be traced back to the religious writings of Blaise Pascal in the seventeenth century and those of Søren Kierkegaard in the nineteenth century. The common thread that unites existentialists is a focus on existence, particularly the concrete existence of individual human beings. Unlike rationalist thinkers such as René Descartes and G.W. F. Hegel, existentialists reject the premise that human beings are primarily rational creatures who live in an ordered, well-designed universe. They also do not believe that the answers to life’s challenges can be solved through thoughtful consideration and reasoned deliberation. Instead, existentialists view human beings as creatures whose reason is subordinate to human passions and anxieties, and who exist in an irrational, absurd, and insignificant universe. In such…

Political thought, or political philosophy, is the study of questions concerning power, justice, rights, law, and other issues pertaining to governance. Whereas political science assumes that these concepts are what they are, political thought asks how they have come about and to what effect. Just as Socrates’s simple question “How should we be governed?” led to his execution, the question “What makes a government legitimate?” leads to political turmoil when posed at critical times. Political thought asks what form government should take and why; what duties citizens owe to a legitimate government, if any; and when it may be legitimately overthrown, if ever. Generally speaking, political thought, political philosophy, and political theory are terms often used interchangeably to mean the study of philosophical texts related to politics. This course examines major texts in the history of political thought. Many of these texts pose difficult questions concerning the political community, social order,…

This course will serve as an introduction to American government and politics. We will focus on several major themes in the course’s five constituent units. In the first unit, “American Political Foundations,” we will consider the core concepts and theoretical underpinnings of the American system of government: American political culture, the Constitution, and federalism. A solid grasp of these concepts will help you better understand the underlying reasons for the structure of the American political system. In the second unit, “American Political Behavior,” we will examine the key components of “politics” in the American system, including public opinion, the mass media, political parties, interest groups, campaigns, elections, and electoral participation. In the third unit, “American Institutions,” we will analyze the major governing bodies in the United States: Congress, the presidency and the bureaucracy, and the courts. Unit 4, “Civil Rights and Civil Liberties in America,” will high…

In the field of public policy and administration, there have been several enduring questions.  In a larger context, what is the role of government?  There has always been conflict in our society regarding the proper role of government.  How should public organizations be structured to reflect the will of the public?  How do we ensure accountability?  What is the proper role of the public administrator/analyst in policy implementation?  How should programs be evaluated? This course will provide you with an overview of the field of public administration, particularly the distinctions that set management of public organizations apart from that of private-sector organizations.  You will begin with an examination of the history and perception of the role of government in the provision of services.  You will then examine the context in which public administrators deliver services to citizens.  Public administrators must also possess a basic knowledge of managing organizations and people in order to imple…

Research is an important component of political science; it enables us to uncover evidence, develop theories, and better understand how the political world operates. This course will introduce you to some of the basic research tools in the political scientist’s “toolkit,” and discuss why and how certain tools are used to explore certain phenomena. The course will also teach you to develop and evaluate sensible and systematic scientific research designs by addressing the ways in which data and theory intersect and examining how political scientists quantify, measure, and operationalize the concepts and variables that are key to understanding the political world. You will conclude your studies by learning about the practical implementation of research design. By the end of this course, you will better understand the qualitative and quantitative techniques that are used within the field and will be able to explain why political scientists choose to use them. In this regard, you will have the opportunity to…

This course will cover American political thought from the nation’s early, formative years as a fledgling republic through the 1960s, exploring the political theories that have shaped its system of governance.  As there is no one philosopher or idea that represents the totality of American political thought, you will survey the writings and speeches of those who have had the greatest impact over this period of time. You will begin by examining pre-revolutionary thought before moving on to the ideals and debates that brought forth the Constitution and the American governmental structure.  Next, you will study the people and events that shaped the emergent nation, delving into concepts such as individualism, capitalism, and industrialism.  You will also investigate the notions of slavery, equality, social progressivism, as well as the ideals explored in the civil rights movement. You will notice that much of the study required in this course is based on the original texts and speeches of those who infl…

The purpose of this course is to provide you with an overview of the major political theorists and their work from the 18th century to the present.  Common themes seen in contemporary political thought include governance, property ownership and redistribution, free enterprise, individual liberty, justice, and responsibility for the common welfare.  You will read the works of theorists advocating capitalism, socialism, communism, egalitarianism, utilitarianism, social contract theory, liberalism, conservatism, neo-liberalism, neo-conservatism, libertarianism, fascism, anarchy, rational choice theory, and multiculturalism.  By studying the evolving constructs of political theory in the past two centuries, you will gain insight into different approaches that leaders use to solve complex problems of governance and maintenance of social order.

Comprehending the role that feminism has played in identifying, critiquing, and, at times, altering the distribution of political and economic power is integral to understanding democratic citizenship and government.  In this course, we will examine the history of feminist thought, beginning in the late eighteenth century and continuing through the early twenty-first century.  An overarching goal of this course is to encourage you to develop and shape your own concepts and ideas about feminist political thought as a potent and multifaceted global force.  In working toward this goal, we begin the course by defining feminism and engaging with some of the cultural and political stereotypes of feminism and feminist thinking in contemporary politics and popular culture.  Next, we explore the history of feminist thinking.  We conclude by examining current topics in feminist politics. Throughout the course, we will examine and discuss questions important to feminist politics, such as citizenship, political pa…

Students of political science should understand how ethics, culture, religion, and morality help to shape public debate, policymaking, and policy execution. This course will provide you with an overview of the role that ethical, cultural, religious, and moral principles play in the formulation and execution of public policy by lawmakers and other public officials. After studying the foundational theories of ethics and morality in politics, you will review arguments about existing issues in domestic and international policy, studying each dilemma from a variety of perspectives.  Common themes seen in ethics debates include justice, equality, fairness, individual liberty, free enterprise, charity, fundamental human rights, and minimizing harm to others. These themes are integrated into various decision-making models, such as the Utilitarian Approach, the Fairness and Justice Approach, and the Rights Approach. In the execution of public policy, it is impossible to do no harm to others; often, public policy…

How might you define, understand, and uphold justice in a global and globalizing world?  That question forms the focal point of this course.  It leads to an examination of whether or not global justice is impossible because of a chaotic and extremely diverse world, or to varying degrees, whether or not justice by its very nature demands a global context and scope of applicability.  Justice, whether considered in abstraction or applied contexts, is fundamentally about human rights.  We will begin this course with an exploration of human rights, a subject that grounds the entire course.  Embedded in the human rights context is an analysis of the political theories of justicethrough a cursory review of some of the seminal texts on global justicealong with an examination of applied and distributive justice focusing on specific issues or problems that have arisen in contemporary global dynamics.  Thus, gender/sexuality, race/ethnicity, genocide, self-determination, environmental concerns, class, and particip…

What is the best way to respond to global nuclear proliferation? Under what circumstances should American soldiers be sent to war? How should U.S. policymakers navigate a global economy? Will a global energy crisis precipitate a third world war? How does history inform contemporary U.S. foreign policymakers, and what issues will challenge future leaders? Such questions can seem beyond the scope of an individual, but they are questions that foreign policy decision makers in the United States must confront. Further, the issues that such questions raise must also be considered by members of the government bureaucracy and any citizen that wishes to be an informed participant in American democracy. The prominent role of the United States and a global leader makes examining and understanding the actions that the U.S. takes toward the rest of the world and how these decisions are made important for both American and citizens of other nations alike. This course will provide history, theory, and perspectives on curren…

This course will provide you with a basic understanding of two core concepts in International Relations and, more generally, Political Science: international governance and international government.  Governance refers to the processes of decision-making, while government is the formal institutions associated with those processes. These two dynamics are interdependent; it is necessary to study both to fully understand this subfield of international relations. Thus, this course will serve as the basis for further studies in the International Relations field within the Political Science major; it also serves as a companion course or “alter-ego” for the International Law course. You will begin studying the fundamental issues of international organization by exploring some conceptual frameworks pertaining to governance dynamics.  This will be followed by investigating the three primary ways in which the participants in global affairs, both state and non-state actors, organize themselves: intergovernmental,…