Courses tagged with "Taking derivatives" (363)

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 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 17th-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 a…

This course is the second installment of Single-Variable Calculus.  In Part I (MA101) [1], we studied limits, derivatives, and basic integrals as a means to understand the behavior of functions.  In this course (Part II), we will extend our differentiation and integration abilities and apply the techniques we have learned. Additional integration techniques, in particular, are a major part of the course.  In Part I, we learned how to integrate by various formulas and by reversing the chain rule through the technique of substitution.  In Part II, we will learn some clever uses of substitution, how to reverse the product rule for differentiation through a technique called integration by parts, and how to rewrite trigonometric and rational integrands that look impossible into simpler forms.  Series, while a major topic in their own right, also serve to extend our integration reach: they culminate in an application that lets you integrate almost any function you’d like. Integration allows us to calculat…

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/…

Organic chemistry is a branch of chemistry that focuses on a single element: carbon!  Carbon bonds strongly with other carbon atoms and with other elements, forming numerous chain and ring structures.  As a result, there are millions of distinct carbon compounds known and classified.  The vast majority of the molecules that contain carbon are considered organic molecules, with few debatable exceptions such as carbon nanotubes, diamonds, carbonate ions, and carbon dioxide.  Carbon is central to the existence of life as it is an essential component of nucleic acids (DNA and RNA), sugars, lipids, and proteins.  A well-rounded student of science must take courses in organic chemistry to understand its application to various topics, such as the study of polymers (plastics and other materials), hydrocarbons, pharmaceuticals, molecular biology, biochemistry, and other life sciences. In the first semester of organic chemistry, you will learn the basic concepts needed to understand the three-dimensional structu…

This course is a continuation of CHEM103 [1]: Organic Chemistry I.  As you progress through the units below, you will continue to learn the different chemical reactions characteristic of each family of organic compounds.  We will focus on the four most important classes of reactions: electrophilic substitution at aromatic rings, nucleophilic addition at carbonyl compounds, hydrolysis of carboxylic acids, and carbon-carbon bond formation using enolates.  The enolate portion of this course will cover the reactivity of functional groups. We will also look at synthetic strategies for making simple, small organic molecules, using the knowledge of organic chemistry accumulated thus far.  At the end of this course, you will possess the tools you need to plan the synthesis of fairly complicated molecules, like those used in pharmaceutics.  From the perspective of a synthetic organic chemist, the two most challenging aspects of synthesizing drug molecules are the incorporation of  "molecular rings" (rings of 5…

Physical Chemistry II is quite different from Physical Chemistry I.  In this second semester of the Physical Chemistry course, you will study the principles and laws of quantum mechanics as well as the interaction between matter and electromagnetic waves.  During the late 19th century and early 20th century, scientists opened new frontiers in the understanding of matter at the molecular, atomic, and sub-atomic scale.  These studies resulted in the development of quantum physics, which nowadays is still considered one of the greatest achievements of human mind.  While present day quantum physics “zooms in” to look at subatomic particles, quantum chemistry “zooms out” to look at large molecular systems in order to theoretically understand their physical and chemical properties.  Quantum chemistry has created certain “tools” (or computational methods) based on the laws of quantum mechanics that make it theoretically possible to understand how electrons and atomic nuclei interact with each other…

Inorganic chemistry is a division of chemistry that studies metals, their compounds, and their reactivity.  Metal atoms can be bound to other metal atoms in alloys or metal clusters, to nonmetal elements in crystalline rocks, or to small organic molecules, such as a cyclopentadienyl anion in ferrocene.  These metal atoms can also be part of large biological molecules, as in the case of iron in hemoglobin (oxygen-carrier protein in the blood). In this course, you should not think of metals as you encounter them in your daily life (i.e., when you pick up a steel knife, a can of soda, or a gold necklace).  Instead, you should think of a metal as the central atom or ion in a molecule surrounded by other ions or small molecules called ligands.  Depending on what these ligands are, the metal-containing compound can acquire very different physical and chemical properties.  For example, when magnesium (in its ionic state) is bound to carbonate ions, it forms solid crystalline rocks, as in the dolomite rocks (c…

Analytical chemistry is the branch of chemistry dealing with measurement, both qualitative and quantitative.  This discipline is also concerned with the chemical composition of samples.  In the field, analytical chemistry is applied when detecting the presence and determining the quantities of chemical compounds, such as lead in water samples or arsenic in tissue samples.  It also encompasses many different spectrochemical techniques, all of which are used under various experimental conditions.  This branch of chemistry teaches the general theories behind the use of each instrument as well analysis of experimental data. This course begins with a review of general chemistry and an introduction to analytical terminology.  You will learn terms relevant to the process of measuring chemical compounds, such as sensitivity and detection limit.  The course continues with a unit on common spectrochemical methods, followed by an extension of these methods in a unit on atomic spectroscopy.  These methods allow…

Biochemistry is the study of the chemical processes and compounds, such as cellular makeup, that bring about life in organisms.  It is a combination of multiple science fields; you can think of it as general and cell biology coupled with organic and general chemistry.  Although living organisms are very complex, from a molecular view, the material that constitutes “life” can be broken down into remarkably simple molecules, much like the breakdown of our English language to the English alphabet.  Although there exists thousands upon thousands of molecules, they all breakdown into four core components: nucleic acids, amino acids, lipids, and carbohydrates.  As we can make hundreds of thousands of words from just 26 letters, we can make thousands of different biomolecules from those 4 components.  For example, the human genome, containing the necessary information to create a human being, is really just one very long strand of 4 different nucleotides. This course is structured around that approach, so…

Remember that organic chemistry is the discipline that studies the properties and reactions of organic, carbon-based compounds.  This course is intended to be taken after the first two semesters of organic chemistry.  Many of the topics within this outline have been covered in the first two semesters of organic chemistry; however, this course will explore these topics in much greater depth.  It is important to make sure that you have a good grasp of the concepts from earlier organic chemistry courses before moving on to this course. We begin by studying a unit on ylides, benzyne, and free radicals.  Many free radicals affect life processes.  For example, oxygen-derived radicals may be overproduced in cells, such as white blood cells that try to defend against infection in a living organism.  In the first unit, you will learn about free radicals, including oxygen-containing compounds.  Afterward we move into a comprehensive examination of stereochemistry, as well as the kinetics of substitution and el…

Advanced Inorganic Chemistry is designed to give you the knowledge to explain everyday phenomena of inorganic complexes. You will study the various aspects of their physical and chemical properties and learn how to determine the practical applications that these complexes can have in industrial, analytical, and medicinal chemistry. This course will begin with the discussion of symmetry and point group theory and its applications in the field of vibrational spectroscopy. We will then study molecular orbital (MO) theory specifically applied to metal organic complexes. MO theory will be critical in understanding the following: 1) the relative position of ligands in the spectrochemical series, 2) the electronic transitions and related selection rules, and 3) the application of spectroscopy of metals. The course will then move onto the study of the oxidation states of transition metals and their redox properties. A firm grasp of the chemical redox properties of transition metals is critical to understanding thei…

Spectroscopy is the study of the interaction between matter and electromagnetic radiation.  Molecules respond to different types of radiation in different ways, depending on the frequency (?) or wavelength (?) of the radiation.  In General Chemistry, we studied spectroscopy as a tool for explaining the quantum mechanical model of the atom.  In that course, we learned that light is an electromagnetic radiation of a wavelength that is visible to the human eye.  We also learned that light, which exists in tiny “packets” called photons, exhibits properties of both waves and particles, a characteristic referred to as the wave-particle duality.  The quantized relationship is defined as E = hv, where E is energy, h is Plank’s constant, and v is frequency. Spectroscopy and spectrometry are often used in chemistry for the identification of substances through the spectrum from which they are emitted or by which they are absorbed.  The type of spectroscopic technique is defined by the type of radia…

In the 1960’s, H. Marshall McLuhan, media theorist, critic, and visionary, asserted that societies are changed by the advances of technology, especially communication technologies.  He is well known for his prophecy that communication technology would one day make us one great “global village.”  In the end, the processes and theories regarding communication in our daily lives to exchange information, create meaning, and share understanding remain a critical component of human relationships.  Whether we are chatting with a stranger while waiting for a bus, solving a problem with a group of coworkers, or sharing our dreams and goals with our best friend, principles and practices of human communication are at the foundation of each of these human transactions. This course provides an introduction to the human communication concentration in the communications major.  This course will introduce you to communication principles, common communication practices, and a selection of theories to better unders…

The purpose of this course is to systematically examine the elements and factors which result in an effective speech.  The textbook and associated lectures present an element-by-element examination of the essentials of public speaking while also identifying traits of the individual speaker and how they impact preparation and presentation.  In addition to these resources, a comprehensive series of brief videos demonstrate specific, performance-oriented aspects of public speaking.  Tying each of these course elements together are the themes of information and ethics, emphasized in each resource because they are becoming increasingly important to all communicators.  For example, the textbook constantly returns to the discussion of society’s ever-increasing access to information and the demands on the individual to use it effectively and ethically.  The authors note that “the New York Times has more information in one week than individuals in the 1800s would encounter in a lifetime,” which illustrates…

The purpose of this course, as governed by the textbook at its core, Understanding Media and Culture: An Introduction to Mass Communication, is to complete a fairly comprehensive examination of the evolution and impact of the media, primarily in the United States.  Each of the major media (newspapers, magazines, books, radio, movies, music, and television), as well as new media (electronic entertainment, social media, and the Internet), are examined from their conception to the present and future possibilities.  Emphasis is placed on how each media industry has evolved over time, responding to changes in society, technology, politics, and economics.  The course also explores the cultural impact of the media, from individual media products to entire industries, with particular emphasis on the cultural and ethical factors that influence production, consumption, and also, due to the advent of new media, participation.  Upon completing this course, you should be more conscious of how your viewpoints are shape…

We live in an increasingly globalized world.  Technology enables us to do business just as easily with our neighbors as with a businessperson thousands of miles away from us.  Knowing how to navigate cultural differences is an increasingly valuable skill that will make you a more valuable employee.  Encounters among members of different cultures frequently fail simply because of basic cultural differences, such as the importance of time, proper greetings, or even the use of eye contact.  This course is designed to help you identify how to become a better communicator in these sorts of cross-cultural situations.  You will learn about barriers to successful communication that involve cultural differences.  You will also learn more about your own communication style and how it can be developed to facilitate more successful intercultural encounters. Though some of this course addresses a Western/U.S. perspective, much of the course focuses on characteristics of specific cultures and how generally one cultur…

There is no shortage of quotes in which inspirational business leaders describe the sources of their success. Their reasons are often diverse, but almost everyone comes back to the same thing: people. The people are the company; they create the success. In BUS301: Managing Human Capital, you learned how to find, train, and manage these people. Please keep in mind that there is more to successful business leadership than managing human capital. You must have a suitable structure and culture at your firm in order to achieve success. Imagine the U.S. military; it boasts some of the best-trained soldiers in human history, but that talent would be wasted without a structure designed to appropriately deploy forces. In other words, the military would not be as successful without streamlined organizational behavior. Organizational behavior (OB) is the study of how people interact in organizations. These interactions are governed by a number of factors, including your personal life, the personality of your boss or you…

Scott McLean, formerly the Shadle-Edgecombe Endowed Faculty Chair at Arizona Western College, introduces the textbook used throughout this course by noting that “[E]ffective communication takes preparation, practice, and persistence.  There are many ways to learn communication skills; the school of experience, or ‘hard knocks,’ is one of them.  But in the business environment, a ‘knock’ (or lesson learned) may come at the expense of your credibility through a blown presentation to a client.” Effective communication skills are a prerequisite for succeeding in business.  Communication tools and activities connect people within and beyond the organization in order to establish the business’s place in the corporate community and the social community, and as a result, that communication needs to be consistent, effective, and customized for the business to prosper.  McLean’s textbook provides theories and practical information that represent the heart of this course, while additional resources a…