Online courses directory (19947)

This course is an introduction to complex analysis, or the theory of the analytic functions of a complex variable.  Put differently, complex analysis is the theory of the differentiation and integration of functions that depend on one complex variable.  Such functions, beautiful on their own, are immediately useful in Physics, Engineering, and Signal Processing.  Because of the algebraic properties of the complex numbers and the inherently geometric flavor of complex analysis, this course will feel quite different from Real Analysis, although many of the same concepts, such as open sets, metrics, and limits will reappear.  Simply put, you will be working with lines and sets and very specific functions on the complex planedrawing pictures of them and teasing out all of their idiosyncrasies.  You will again find yourself calculating line integrals, just as in multivariable calculus.  However, the techniques you learn in this course will help you get past many of the seeming dead-ends you ran up against in…

This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling. Today, the theory of probability has found many applications in science and engineering. Engineers use data from manufacturing processes to sample characteristics of product quality in order to improve the products being produced. Pharmaceutical companies perform experiments to determine the effect of a drug on humans and use the results to make decisions about treatment of illnesses, while economists observe the state of the economy over periods of time and use the information to forecast the economic future. In this course, you will learn the basic terminology and concepts of probability theory, including random experiments, sample spaces, discrete distribution, probability density function, expected values, and conditional probability. You will al…

Mathematics is about structure, about reasoning, and about modeling.  This course braids these three threads together.  Mathematical logic began as the study of the reasoning used in mathematics, but it turns out to be useful in describing the mathematical concept of structure and in modeling automated reasoningthat is, modeling computation. The logical approach to structure gives an alternate perspective on such other mathematical subjects as combinatorics and abstract algebra.  This, for the most part, is described by the area of model theory, which is the focus of Unit 1. In Unit 2, we will look at modeling computation.  The central fact of these models, from a logical standpoint, is that once we can handle a computation as a definable mathematical object, we can prove that certain computations are impossible.  The most famous such proof is Gödel’s Incompleteness Theorem, showing that it is impossible to compute truth in a system sufficiently strong to describe natural number arithmetic.

This course will introduce you to a number of statistical tools and techniques that are routinely used by modern statisticians for a wide variety of applications. First, we will review basic knowledge and skills that you learned in MA121: Introduction to Statistics [1]. Units 2-5 will introduce you to new ways to design experiments and to test hypotheses, including multiple and nonlinear regression and nonparametric statistics. You will learn to apply these methods to building models to analyze complex, multivariate problems. You will also learn to write scripts to carry out these analyses in R, a powerful statistical programming language. The last unit is designed to give you a grand tour of several advanced topics in applied statistics. [1] http://www.saylor.org/courses/ma121/…

This course is designed to provide you with a simple and straightforward introduction to econometrics.  Econometrics is an application of statistical procedures to the testing of hypotheses about economic relationships and to the estimation of parameters.  Regression analysis is the primary procedure commonly used by researchers and managers whether their employments are within the goods or the resources market and/or within the agriculture, the manufacturing, the services, or the information sectors of an economy. Completion of this course in econometrics will help you progress from a student of economics to a practitioner of economics.  By completing this course, you will gain an overview of econometrics, develop your ability to think like an economist, hone your skills building and testing models of consumer and producer behavior, and synthesize the results you find through analyses of data pertaining to market-based economic systems.  In essence, professional economists conduct studies that combine…

This course is a continuation of the first-semester course titled Introduction to Computer Science I (CS101 [1]).  It will introduce you to a number of more advanced Computer Science topics, laying a strong foundation for future academic study in the discipline.  We will begin with a comparison between Javathe programming language utilized last semesterand C++, another popular, industry-standard programming language.  We will then discuss the fundamental building blocks of Object-Oriented Programming, reviewing what we learned last semester and familiarizing ourselves with some more advanced programming concepts.  The remaining course units will be devoted to various advanced Computer Science topics, including the Standard Template Library, Exceptions, Recursion, Searching and Sorting, and Template Classes.  By the end of the class, you will have a solid understanding of Java and C++ programming, as well as a familiarity with the major issues that programmers routinely address in a professional setting.

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…