# Online courses directory (26)

The discovery of exoplanets is one of the greatest revolutions in modern astrophysics. Twenty years ago, we had no idea whether any of the countless stars out there beyond our solar system had planets or not.

Today, things are totally different. Over 1,000 planetary systems have been discovered. The universe is teeming with planets. And what strange planets they are - hot Jupiter-like planets skimming the surfaces of their stars, cold and lonely free-floating planets far from any star, planets made of diamond, planets with rain made of glass, super-Earths and even planets orbiting neutron stars. In this course, we’ll bring you up-to-date with the latest research on exoplanets, and how this research has revolutionised our understanding of the formation of solar systems like our own.

This course is designed for people who would like to get a deeper understanding of these mysteries than that offered by popular science articles and shows. You will need reasonable high-school level mathematics and physics to get the most out of this course.

This is the second of four ANUx courses which together make up the Australian National University's first year astrophysics program. It follows on from the introductory course on the Greatest Unsolved Mysteries of the Universe, and is followed by courses on the violent universe and on cosmology. These courses compromise the Astrophysics XSeries. Learn more about the XSeries program and register for all the courses in the series today!

In this course, we will look at many important aspects of the circulation of the atmosphere and ocean, from length scales of meters to thousands of km and time scales ranging from seconds to years. We will assume familiarity with concepts covered in course 12.003 (Physics of the Fluid Earth). In the early stages of the present course, we will make somewhat greater use of math than did 12.003, but the math we will use is no more than that encountered in elementary electromagnetic field theory, for example. The focus of the course is on the **physics** of the phenomena which we will discuss.

Electromagnetic Theory covers the basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional e.m.f. and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. This is a graduate level subject which uses appropriate mathematics but whose emphasis is on physical phenomena and principles.

This course provides a thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis is placed on problem solving and quantitative reasoning. This course covers Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves.

The fundamental concepts, and approaches of aerospace engineering, are highlighted through lectures on aeronautics, astronautics, and design. Active learning aerospace modules make use of information technology. Student teams are immersed in a hands-on, lighter-than-air (LTA) vehicle design project, where they design, build, and fly radio-controlled LTA vehicles. The connections between theory and practice are realized in the design exercises. Required design reviews precede the LTA race competition. The performance, weight, and principal characteristics of the LTA vehicles are estimated and illustrated using physics, mathematics, and chemistry known to freshmen, the emphasis being on the application of this knowledge to aerospace engineering and design rather than on exposure to new science and mathematics.

This physics course introduces the concept of tensor product states to discuss entanglement and Bell inequalities. You will learn about angular momentum and its representations. This is used to understand the spectrum of central potentials and to introduce hidden symmetries. Lastly, you will learn about the addition of angular momentum and an algebraic approach to the hydrogen atom spectrum.

This is the last of three courses offering a sophisticated view of quantum mechanics and its proper mathematical foundation.

- Part 1: Wave Mechanics
- Part 2: Quantum Dynamics
- Part 3: Entanglement and Angular Momentum

To follow this course you should have taken Part 1: Wave Mechanics, and Part 2: Quantum Dynamics.

Completing the 3-part Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics

The series will follow MIT’s on campus 8.05, the second semester of the three-course sequence on undergraduate quantum mechanics, and will be equally rigorous. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors.

Learner Testimonials

“*I’ve thought long and hard to come up with a better MOOC than this one (I’ve completed 25 of these things over the past 2 years) and can’t do it. 8.05x is #1 and I suspect will stay that way for some time to come.*”

“*Being an engineering student from India trying to shift to Physics, I am often faced with the requirement to study topics on my own. Very often this has led me to feel inadequate. 8.05x was the perfect opportunity for me to both gain knowledge and evaluate my understanding on a high quality international platform. It has really exceeded my expectations. Now, at the end of fifteen weeks, I feel more confident and hopefully I am more knowledgeable.*”

**FAQ**

Who can register for this course?

Unfortunately, learners from Iran, Cuba, Sudan and the Crimea region of Ukraine will not be able to register for this course at the present time. While edX has received a license from the U.S. Office of Foreign Assets Control (OFAC) to offer courses to learners from Iran and Sudan our license does not cover this course.

Separately, EdX has applied for a license to offer courses to learners in the Crimea region of Ukraine, but we are awaiting a determination from OFAC on that application. We are deeply sorry the U.S. government has determined that we have to block these learners, and we are working diligently to rectify this situation as soon as possible.

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. While this end goal remains the same, we will now focus on adapting what we have learned to applications. By the end of this course, you should have a solid understanding of functions and how they behave. You should also be able to apply the concepts we have learned in both Parts I and II of Single-Variable Calculus to a variety of situations. We will begin by revisiting and building upon what we know about the integral. We will then explore the mathematical applications of integration before delving into the second major topic of this course: series. The course will conclude with an introduction to differential equations. [1] http:///courses/ma101/…

Differential equations are, in addition to a topic of study in mathematics, the main language in which the laws and phenomena of science are expressed. In its most basic sense, a differential equation is an expression that describes how a system changes from one moment of time to another, or from one point in space to another. When working with differential equations, the ultimate goal is to move from a microscopic view of relevant physics to a macroscopic view of the behavior of a system as a whole. Let’s look at a simple differential equation. From previous math and physics courses, we know that a car that is constantly accelerating in the x-direction, for example, obeys the equation d2x/dt2 = a, where a is the applied acceleration. This equation has two derivations with respect to time, so it is a second-order differential equation; because it has derivations with respect to only one variable (in this example, time), it is known as an ordinary differential equation, or an ODE. Let’s say t…

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…

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…

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.

À l’École Polytechnique Fédérale de Lausanne, un cours de physique générale fait partie de la formation de tous les futurs ingénieurs et scientifiques. Le présent cours de mécanique en fait partie. Il a pour but de leur apprendre à transcrire sous forme mathématique un phénomène physique, afin de pouvoir en formuler une analyse raisonnée.

Week 1: A first simple neuron model

Week 2: Hodgkin-Huxley models and biophysical modeling

Week 3: Two-dimensional models and phase plane analysis

Week 4: Two-dimensional models (cont.)/ Dendrites

Week 5: Variability of spike trains and the neural code

Week 6: Noise models, noisy neurons and coding

Week 7: Estimating neuron models for coding and decoding

Before your course starts, try the new edX Demo where you can explore the fun, interactive learning environment and virtual labs. Learn more.

A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.

This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

Using vectors to study motion is a fundamental skill to have when studying physics. Vector quantities used to describe the physical world include displacement, velocity, acceleration, and force. In this free online physics course the standard way to represent vectors and their axes as well as unit vector notation are explained in a clear and step-by-step manner. Examples show how to work out the angle or distance necessary to get the desired displacement. Using two known variables you will learn how to work through the process of calculating the remaining value, such as time in air or horizontal displacement using a variety of techniques. This free online physics course will be of great interest to students who are studying physics, chemistry, engineering, mathematics, and to students who wish to pursue a career in any of the sciences or engineering fields, and even the sportsperson who wants to plan for a specific outcome when hitting a golf ball or batting a ball.<br />

Gravity is the force that keeps us on the ground and understanding how gravity works is very important as it has a great influence on the upward and downward movement of objects. This free online course about gravity will explain Newton’s Second Law of Motion, the universal constant, which is used to work out the force of gravity throughout the universe. You will also learn what the effect of the earth's force of gravity, or little g as it is known, has on an object and why mass is not the same as weight. To fully understand gravity this course will take you step-by-step through the relevant formulas, showing you how to calculate velocity or distance based on time and then plot these changes so you will have a visual concept of what is happening. This course will be of great interest to students who are studying physics, chemistry, engineering, mathematics, and to students who wish to pursue a career in any of the sciences or engineering fields.<br />

Calculating change in motion is a very important concept to master in physics. When change happens in one dimension it is relatively easy to calculate the variable. However, change rarely happens in just one direction so you need to learn how to manage more than one variable. This free online physics course explains how to visually represent each change in a dimension as a vector so that it can be easily understood. You will learn how to add two vectors together and calculate all the relevant information for the resulting third vector. Working through various examples, including different elevations and inclines, you will learn how to solve for any variable through the use of the right-angled triangle and then use trigonometry and quadratic equations to calculate the relevant variables. This free online physics course will be of great interest to students who are studying physics, chemistry, engineering and mathematics and to any individual who wants to learn more about the movement of objects in two dimensions.<br />

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