Courses tagged with "Taking derivatives" (363)

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…

Mechanics studies how forces affect bodies in motionhow, for example, a bullet is fired from a gun or a top is set in motion by the flick of a wrist.  As an engineer, you will find mechanics of vital importance to any field you choose to pursue.  Whether you are designing a bridge or implementing an electrical power unit for an elevator, you will need to know how to determine which forces can be applied to a body without causing it to break, what happens when bodies collide, how an object moves when different forces are applied to it, and so on.  This course will introduce you to the core concepts of mechanics that will enable you to answer these questions as you strive to design, test, and manufacture safe and reliable products. While most universities split introductory mechanics into two courses, with one devoted to statics and the other to solids, this course will introduce you to both areas.  You will begin by learning about staticsobjects that are not accelerating (in other words, objects that are…

There are many different ways that you can go about solving engineering problems.  One of the most important methods is energy analysis.  Energy is a physical property that allows work of any kind to be done; without it, there would be no motion, no heat, and no life.  You wouldn’t be able to get out of bed in the morning, but it wouldn’t matter, because there would be no sun.  Without energy, our world would not exist as it does. Thermodynamics is the study of energy and its transfers though work.  It is the link between heat and mechanical exertion.  Once you have a solid grasp on thermodynamic concepts, you should be able to understand why certain mechanisms (such as engines and boilers) work the way they do, determine how much work they can put out, and know how to optimize these power systems.   A thorough understanding of thermodynamics is crucial to any career that focuses on HVAC systems, car engines, or renewable energy technology. This course will focus on the fundamentals of thermod…

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…

You may think at first that the words “fluid” and “mechanics” should not go together.  However, the ways in which fluids (gases and liquids and a few other materials) respond to forces, exert forces, and move from one place to another (their mechanics) are crucially important to many aspects of our experience and our ability to build tools. Consider, for example, the following areas in which fluid mechanics play an important, if not fundamental, role: Meteorology and ocean dynamics (tsunamis, hurricanes, and tornados) Fluid flow within living systems (blood flow, lymph flow, air flow) Hydraulic machinery (jacks, pumps, lifts, steering mechanisms) Chemical processing and piping (pumps, reactors, separators, pipelines) Turbomachinery (jet engines, power plants) Aeronautical and ship machinery (airplanes, helicopters, boats and ships) In this course you will first learn about the definition of a fluid and the properties of a fluid, such as density, compressibility, and viscosity.  You wil…

Dynamics is a sub-branch of the general field of study known as Mechanics.  It is very closely related toand often combined withthe study of Statics, which you encountered in ME102: Mechanics I [1]. In both Statics and Dynamics, we use Newton’s 2nd Law: F = ma.  In Statics, the sum of the applied forces is always zero, thus making the acceleration zero.  This was very important to the structures studied in Statics.  Catastrophe generally results when structures (like bridges and buildings) accelerate.  Very likely you are quite pleasedeven if you do not realize it every timewhen you cross a bridge that does not accelerate while you are on it, and we have Newton’s First Law to thank for it.  Newton’s First Law states that objects will continue to do what they are doing unless unbalanced forces make them do otherwise.  This law includes the law equilibrium condition that the moments will also sum to zero, and that there will thus be no rotational acceleration.  In Dynamics, the sum of the forces…

This self-contained course presents a sampling of the fields of Materials Engineering and Materials Science. This course is intended primarily for engineering students who are not planning to major in either Materials Engineering or Materials Science. We will focus primarily on the concerns of the materials engineerthe person interested in choosing materials to make a finished product. This selection is determined by compromises among material properties, ease of fabrication, and cost. In contrast, the materials scientist is concerned with understanding the relationships between material properties and the internal structure of a materialthat is, atomic bonding, arrangements of atoms, grain structure, and other microscopically observable features. We leave most of these associations to advanced courses, which will use more chemistry and physics than needed for this course. The course is divided into four units: Unit 1: Ways That Materials Can Fail  What Can Go Wrong? Unit 2: Classes of Engineering Mate…

Heat transfer is the thermal energy in transit due to a spatial temperature difference. The topic of heat transfer has enormous applications in mechanical engineering, ranging from cooling of microelectronics to design of jet engines and operations of nuclear power plants. In this course, you will learn about what heat transfer is, what governs the rate of heat transfer, and why heat transfer is so important. You will also learn about the three major modes of heat transfer: conduction, convection, and radiation.  Heat conduction is the transport of heat through a solid body, by vibrations of molecules or in the case of electrical conductors, by movement of electrons from one molecule to another. Heat convection is a process by which heat is transferred through a fluid by motion of fluid. Thermal radiation is the transport of energy between two bodies by electromagnetic waves. In addition to the three main modes of heat transfer, you will also learn about heat transfer during phase changes (boiling and conden…

Numerical methods have been used to solve mathematical expressions of engineering and scientific problems for at least 4000 years (for some historical discussion you may wish to browse the Ethnomathematics Digital Library [1] or the MacTutor History of Mathematics Archive [2] from St. Andrews University).*  Such methods apply numerical approximation in order to convert continuous mathematical problems (for example, determining the mechanical stress throughout a loaded truss) into systems of discrete equations that can be solved with sufficient accuracy by machine. Numerical methods provide a way for the engineer to translate the language of mathematics and physics into information that may be used to make engineering decisions. Often, this translation is implemented so that calculations may be done by machines (computers). The types of problems that you encounter as an engineer may involve a wide variety of mathematical phenomena, and hence it will benefit you to have an equally wide range of numerical met…

This course will serve as your introduction to working in an engineering laboratory.  You will learn to gather, analyze, interpret, and explain physical measurements for simple engineering systems in which only a few factors need be considered.  This experience will be crucial to your success in analyzing more complicated systems in subsequent coursework and in the practice of mechanical engineering. We frequently encounter measurement systems in our everyday lives.  Consider the following examples: 1.      The many gauges found on the control panel of a motor vehicle indicate vehicle speed, engine coolant temperature, transmission setting, cabin temperature, engine speed, and oil pressureamongst many other measurements. 2.      A routine visit to a physician often entails several measurements of varying complexityinternal temperature, blood pressure, internal appearance, heart rate, respiration rate, and tissue texture, amongst many, many more. 3.      The experienced cook may use s…

Most mechanical engineering systems today involve significant amounts of electrical and electronic control systems. Effectively, most modern mechanical engineering systems are mechatronic systems. Mechatronics is the discipline that results from the synergetic application of electrical, electronic, computer, and control engineering in mechanical engineering systems. Thus, it is essential for the mechanical engineer to have a strong understanding of the composition and design of mechatronic systems, which is the goal of this course. Mechatronic systems are around us everywhere. A car contains many mechatronic systems, such as anti-lock braking systems, traction control, the engine control unit and cruise control, to name a few. A satellite dish position control unit is another example of a mechatronic system. Modern industrial automated processes would not be possible without the discipline of mechatronics, covering areas such as vehicle manufacturing, pharmaceutical industries, and food processing plants. R…

This course deals with the transfer of work, energy, and material via gases and liquids.  These fluids may undergo changes in temperature, pressure, density, and chemical composition during the transfer process and may act on or be acted on by external systems.  You must fully understand these processes if you are an engineer working to analyze, troubleshoot, or improve existing processes and/or innovate and design new ones. In your everyday life, you will likely encounter examples of the thermal-fluid systems we will study in this course.  Consider the following scenarios: Read this recent report [1] by Gary Goettling for the Georgia Tech Alumni Association.*  In it, Goettling describes a refrigeration system with no moving parts based on improvements to a patent filed by Einstein and Szilard in 1930.  As an engineer, how would you go about evaluating this design for energy efficiency, safety, reliability, and manufacturing, operating, and installation costs? Have you ever wondered how the level se…

Effective communication is essential to teamwork, and teamwork is essential to accomplishing complex engineering work.  In this course, you will learn several aspects of effective technical communication that will help prepare you to work successfully on an engineering team.  The strategies and techniques learned here are also applicable to other situationsfor example, preparing a résumé and cover letter, conducting a successful job interview, negotiating to make a major purchase or sale, and navigating through legal situations that you might encounter. As an example, consider the following situation.  You arrive home after a week-long vacation and find a note on your door saying: Dude My plumber’s cut your phone cord.  I reckon they’ll fix it soon. On the other hand, consider that you find a note resembling:   From: John Atkins      October 24, 2015 2828 Fairlane Rd. Tel: 703-555-4800   To:       Occupant 2824 Fairlane Rd.   I regret to inform you that my plumbing contractor…

The study of dynamic systems focuses on the behavior of physical systems as well as the physics of individual components and the interactions between them.  Control systems are designed to enable dynamic systems to respond in a specific manner.  In this course, we will learn about the mathematical modeling, analysis, and control of physical systems that are in rest, in motion, or acted upon by a force. Dynamic systems can be mechanical, electrical, thermal, hydraulic, pneumatic, or any combination thereof.  An electrical motor is a good example of a dynamic system in which electricity is used to drive the motor’s mechanical movement.  The operation of the motor is controlled by altering the electric current or voltage.  Another good example is a car’s suspension system, which is designed to curb abnormal vibrations while riding on a bumpy road.  In order to design a suspension system, you must analyze the mathematical equations of the physics of the suspension and its response (i.e. how effectivel…

Engineering design is the process of creating solutions to satisfy certain requirements given all the constraints.   This course will focus on the decision-making process that affects various stages of design, including resource allocation, scheduling, facilities management, material procurement, inspection, and quality control.  You will be introduced to the basic theoretical framework and several practical tools you can use to support decision making in the future.  The first two units provide an overview of engineering design process and theories and methods for making decisions, including Analytic Hierarchy Process, Lean Six Sigma, and Quality Function Deployment.  In Unit 3, you will learn about the basic principles of computerized decision support systems.  Unit 4 discusses several advanced mathematical methods used for support decision making, including linear and dynamic programming, decision tree, and Bayesian inference.

This course will ask you to apply the knowledge you have acquired over the course of the entire mechanical engineering curriculum.  It draws upon what you have learned in your courses in mechanics, CAD, materials and processing, thermal and fluid systems, and dynamics and control, just to name a few.  This course is equivalent to the capstone course or senior design project that you would need to complete as a senior in a mechanical engineering program in a traditional American university setting. This course begins in Unit 1 by introducing you to the stages of the design process.  We will then focus on tools and skill sets that are particularly important for succeeding in a design project, including design planning, teamwork skills, project management, and design reporting. Unit 2 covers important design principles and considerations.  You will learn about economic implications (you must keep cost in mind while designing!), the ethical, societal, and environmental impacts of design decisions, and pro…

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…

This course will introduce you to the major topics, problems, and methods of philosophy and surveys the writings of a number of major historical figures in the field. Philosophy can be - and has been - defined in many different ways by many different thinkers. In a scholarly sense, philosophy is the study of the history of human thought. It requires familiarity with great ideas understood through the various major thinkers in world history. In its most general sense, philosophy is simply the investigation of life’s “big questions.” We will explore such fundamental questions in several of the core areas of philosophy, including metaphysics, epistemology, political philosophy, ethics, and the philosophy of religion. With the help of commentaries and discussions from a number of contemporary philosophers, we will read and reflect on texts by major Western and non-Western thinkers including Lao Tzu, Buddha, Confucius, Plato, Aristotle, Saint Anselm, René Descartes, Blaise Pascal, John Locke, Immanuel…

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…