Courses tagged with "Taking derivatives" (363)

This introductory mathematics course is for you if you have a solid foundation in arithmetic (that is, you know how to perform operations with real numbers, including negative numbers, fractions, and decimals).  Numbers and basic arithmetic are used often in everyday life in both simple situations, like estimating how much change you will get when making a purchase in a store, as well as in more complicated ones, like figuring out how much time it would take to pay off a loan under interest. The subject of algebra focuses on generalizing these procedures.  For example, algebra will enable you to describe how to calculate change without specifying how much money is to be spent on a purchase-it will teach you the basic formulas and steps you need to take no matter what the specific details of the situation are.  Likewise, accountants use algebraic formulas to calculate the monthly loan payments for a loan of any size under any interest rate.  In this course, you will learn how to work with formulas that a…

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 course is a continuation of MA001: Beginning Algebra [1]. Algebra allows us to formulate real-world problems in an abstract mathematical term or equation. These equations can then be solved by using techniques you will learn in this course. For example, if I can ride my bicycle at 5 miles per hour and I live 12 miles from work, how long will it take me to get to work? Or, suppose I am a pitcher for the St. Louis Cardinals and my fast ball is 95 miles per hour, how much time does the hitter have to react to the baseball? And, can you explain why an object thrown up into the air will come back down? If so, can you tell how long it will take for the object to hit the ground? These are all examples of problems that can be stated as an algebraic equation and then solved. In this course you will study compound inequalities and solve systems of linear equations. You will then study radicals and rational exponents, followed by quadratic equations and techniques used to solve these equations. Finally, you will…

In this course, we will study the history of Western art, beginning with the first objects created by prehistoric humans around 20,000 years ago and ending with the art and architecture of the High Gothic period in fourteenth-century Europe.  The information presented in this course will provide you with the tools to recognize important works of art and historical styles, as well as to understand the historical context and cultural developments of Western art history through the end of the medieval period.  Introductory readings paired with detailed lectures will provide you with a well-rounded sense of the history, art, and culture of the West up through the medieval period. At the end of this course, you will be able to identify key works of art and artistic periods in Western history.  You will also be able to discuss the development of stylistic movements and relate those developments to important historical events.  Completion of this course will prepare you for ARTH111, which surveys the history o…

This chemistry survey is designed to introduce students to the world of chemistry.  The principles of chemistry were first identified, studied, and applied by ancient Egyptians 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 use this knowledge to understand the chemical properties of matter and the changes and reactions that take place in all types of matter.

In this second semester course, we will cover a wide-ranging field of topics, learning everything from the equation that made Einstein famous to why you can’t replace a dead car battery with a household battery. In General Chemistry I (CHEM101 [1]), we studied the basic tools you need to explore different fields in chemistry, such as stoichiometry and thermodynamics.  This second-semester course will cover several of the tools needed to study chemistry at a more advanced level.  We will identify the factors that affect the speed of a reaction, learn how an atom bomb works on a chemical level, and discover how chemistry powers a light bulb.  Topics in advanced organic and inorganic chemistry courses will build upon what you learn in this class.  We will end with discussion of organic chemistry, a topic that is as important to biology as it is to chemistry. [1] http:///courses/chem101/…

In BUS103 [1] (Financial Accounting), we learned that firms need to track various forms of data in order to report to investors, regulators, and potential business associates such as customers and vendors.  Firm managers, however, often need information that is much more detailed than the data provided in these financial reports.  They use what is known as “managerial accounting” to make various decisions about their businesses.  To avoid information overload, much of their data is tailored to the needs of a particular business unit instead of generally applicable to the firm as a whole. As you might expect, different managers have different needs.  However, almost all management decisions deal with the same key issues: cost, price, and profit.  This course will examine this sort of decision-making, identifying the tools and methods managers use to make the best-informed decisions possible.  We will begin with an introduction to the terms that will be referenced in the later units.  We will then…

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…

In this course, you will build on and apply what you learned in the introductory macroeconomics course (ECON102 [1]).   You will use the concepts of output, unemployment, inflation, consumption, and investment to study the dynamics of an economy at a more advanced level.   For example, now that you understand the relationship between supply and demand in general terms, you will be asked to examine the effects that short-run and long-run price changes have on full employment and output.  As the course progresses, you will gain a better appreciation for how policy shifts and changes in one sector impact the rest of the macroeconomy (whether the impacts are intended or unintended).  You will also examine the causes of inflation and depression, and discuss various approaches to responding to them.  By the end of this course, you should be able to think critically about the economy and develop your own unique perspective on various issues. Remember that macroeconomics attempts to explain the role of gover…

This course is designed to provide you with a thorough understanding of the importance of money, banking, and financial markets of a developed economy.  Money, financial institutions, and financial markets have emerged as instruments of payments for the services of factors of production, such as labor and capital.  The use of money facilitates business in a market by acting as a common medium of exchange.  Of course, as that market expands and develops on a national and international level, the importance of money, banking, and other financial markets expands to accommodate innumerable exchanges. This course will allow you to examine not only the origins and nature of money, but also the institutions and markets that have evolved to enable the exchange of goods and services worldwide.  It will provide you with the opportunity to examine the instruments and strategies assisting production, distribution, and consumption.  Also, this course will help you develop an appreciation for important concepts in e…

This course will introduce you to the history of the Atlantic slave trade from 1500 to 1900. You will learn about the slave trade, its causes, and its effects on Africa, Europe, and the Americas. The course will be structured chronologically and geographically; each unit with focus on a particular aspect of the Atlantic slave trade. Each unit will include representative primary-source documents that illustrate important overarching political, economic, and social themes, such as slavery and the slave trade within African societies, the growth of plantation societies in the New World, the advent of European slave dealing in western Africa, the simultaneous growth of European empires and the Atlantic slave trade, the nature of slave trading and the Middle Passage, and the abolition of the Atlantic slave trade in the nineteenth century. By the end of the course, you will understand how the Atlantic slave trade began as a fledgling enterprise of the English, Portuguese, and Spanish in the 1500s and why, by the mi…

The study of Europe, and its role in the world today, is a story of both tragedy and triumph.  From the ashes of centuries of continental conflict through two World Wars and finally into integration by invitation, the European continent has taken what some have deemed the first tentative steps away from the jealously guarded system of sovereign independent states.  With each shaky step away from its near five-hundred-year-old origins in the bosom of Kantian ideals and the Westphalia system (see works cited for Perpetual Peace by Immanuel Kant; the Westphalia system will be discussed in Unit 1), the continent finds itself in conflict with the very nature of its original intent.  Over the past half century, we have seen Europe move away from the world of nation-states and embrace the still largely undefined and constantly evolving idea of member-states. Yet, Europe and the many states within her bounds also guard their position within the realm of international society.  With states flinching away from cu…

Professional Writing is designed to provide adult learners with the basic skills they need to write effective documents in the workplace.  In this course, you will learn how to analyze your audience so that you can write prose that is both clear and persuasive.  You will practice writing common business documents, such as emails, memos, proposals, and presentations.  You will also learn how to effectively edit these documents for maximum impact. This course is part of the Professional Development Program (PRDV), which is designed especially for adult learners who are ready to gain and apply skills demanded by today’s employers.

Please note: Our faculty members have indicated that several important changes need to be made in order to improve the course and your experience as a student. In 2013, we will be re-releasing this course under the simplified title: ARTH101: Art Appreciation and Techniques. Until then, you are welcome to work through this course at your own leisure; there

PURPOSE OF COURSE…

This course provides students with a comprehensive introduction to computers. Students will explore a variety of topics in computing, such as the following: the components of a computer, common computer terminology, an introduction to the Internet, computer security and privacy, computer troubleshooting techniques, and steps to maintain the life of your computer. Through readings and videos, students will learn how to fully understand the basics of computer technology.

This course will introduce you to the field of mechanical engineering and the relationships between physics, mathematics, communications, and sciences which inform the study, design, and manufacture of mechanical products and systems.  The course is divided into four units.  In the first unit, you will learn how mechanical engineering is broadly defined, what mechanical engineers do, and what technical capabilities they have.  We will also review some basic principles from mathematics and physics that you will apply in any discipline of engineering.  In the second unit, you will learn about the ethical considerations and technical communication skills necessary for engineering work.  You will revisit these issues in more detail in several courses within the Mechanical Engineering curriculum.  The third unit focuses on computational tools for engineering problems.  In Unit 3 you will learn about a specific open source computational environment (Scilab) and the application of that environment to some com…

CAD, or computer-aided design, is a powerful modeling tool that technical professionals use.  With CAD, architects can draw up building plans and engineers can develop component and system designs.  Some CAD programs even allow users to perform stress analysis, demonstrating how well a proposed structure will fare when put to use.  For example, when does a load become too big?  How much weight can be put onto a bridge before it becomes structurally unsound?  Using CAD, professionals can create precise engineering drawings in both 2- and 3-D, complete with dimensions and specifications, in a neat and readable format.  This modeling method has taken design to a whole new level of efficiency and accuracy. We are fortunate to be engineers working in the current eraone of computers, technology, and ease of precision.  Without CAD, we would have to draft (or draw up) design blueprints by hand, which can be tedious and time-consuming.  With CAD, however, we can generate accurate 2-D and 3-D drawings, scale…

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.

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.