# Courses tagged with " product differentiation and variety" (133)

How do we understand architecture? One way of answering this question is by looking through the lens of history, beginning with First Societies and extending to the 16th century. This course in architectural history is not intended as a linear narrative, but rather aims to provide a more global view, by focusing on different architectural "moments."

How did the introduction of iron in the ninth century BCE impact regional politics and the development of architecture? How did new religious formations, such as Buddhism and Hinduism, produce new architectural understandings? What were the architectural consequences of the changing political landscape in northern Italy in the 14th century? How did rock-cut architecture move across space and time from West Asia to India to Africa? How did the emergence of corn impact the rise of religious and temple construction in Mexico?

Each lecture analyzes a particular architectural transformation arising from a dynamic cultural situation. Material covered in lectures will be supplemented by readings from the textbook *A Global History of Architecture.*

Join us on a journey around the globe and learn how architecture has developed and interacted with the world’s culture, religion, and history.

This college-level, calculus-based Introductory Newtonian Mechanics course covers all of the topics and learning objectives specified in the College Board Course Description for Advanced Placement®Physics C (Mechanics). It covers Newton’s Laws, Kinematics, Energy, Momentum, Rigid Body Rotation, and Angular Momentum. The course covers applications of these basic principles to simple harmonic motion, orbital motion, and to problems that involve more than one basic principle. These principles also underlie the 12 online laboratory activities.

Our emphasis is on helping students learn expert-like ways of solving challenging problems, many of which are similar to problems on previous Advanced Placement Examinations in Mechanics C. We stress a key insight: mechanics is about forces changing motion. We apply this concept to organizing the core knowledge in a way that helps students apply it to sophisticated multi-concept problems. We feel this is the best way to prepare students for success not only on the AP Examination but also in other college-level science, technology, engineering and math courses that emphasize problem-solving.

If you are a teacher looking to learn better ways to teach your students, or are interested in using some of our MOOC materials in your own classroom—possibly as a private online course for your students—we strongly encourage you to sign up for our teacher’s discussion cohort, a “private discussion room” for teachers to share pedagogical ideas and instructional techniques.To join these discussions, verify yourself as a teacher by clicking this link, and we will enroll you in the teacher’s discussion cohort.

**FAQ**

**How long is this course?**

The course consists of 13 weeks of required (graded) material and 2 weeks of optional (ungraded) material. You do not need to complete the optional weeks in order to receive a certificate, but we strongly encourage you to complete these units, especially if you are preparing for the College Board’s AP Physics C: Mechanics exam.

**Is there a required textbook?**

You do not need to buy a textbook. A complete eText, including worked-examples and some video lectures, is included in this edX course and is viewable online. If you would like to use a textbook with the course (for example, as a reference), most calculus-level books are suitable. Introductory physics books by Young and Freedman, Halliday, Resnick, & Walker, or Knight are all appropriate (and older editions are fine).

**My physics is a little rusty. How should I prepare for this course?**

If you would like to brush-up on basic mechanics skills before taking this course, we recommend the brief warm-up course, On-Ramp to AP Physics C: Mechanics.

**What if I take a vacation?**

The course schedule is designed with this in mind! Course content is always released at least 3 weeks ahead of the deadline, providing you with the opportunity for flexibility in scheduling.

**How are grades assigned?**

There are five parts of the course that are worth points: (1) Checkpoint problems are incorporated into the reading; (2) most weeks have an interactive lab component; (3) more involved homework problems occur at the end of each week and (4) quizzes at the end of every 1-2 weeks; (5) the course culminates in a final exam. Each category is worth a varying number of points; and you are allowed several attempts on each problem. A final grade of at least 60% is needed for certification; hence you will not have to do every problem.

**Note: Taking this Course Involves Using Some Experimental Materials**

The RELATE group that authors and administers this course is a physics education research group. We are dedicated to understanding and improving education, especially online. In one of the only published studies measuring learning in a massive open online course (MOOC), we showed that a previous iteration of this course produced slightly more conceptual learning than a traditionally taught on-campus course. Currently, we are working to find just what caused this learning.

In this course, the RELATE group will be comparing learning from different types of online activities that will be administered to randomly assigned sub-groups of course participants. At certain points in the course, new vs. more traditional sequences of activities will be assigned to different sub-groups. We will then use common questions to compare the amount of associated learning. Which group receives the new activities will be switched so that all groups will have some new activities and some traditional ones.

Our experimental protocol has been approved by the MIT Committee on Use of Human Subjects. As part of this approval we have the obligation to inform you about these experiments and to assure you that:

- We will not divulge any information about you that may be identified as yours personally (e.g. a discussion post showing your user name).
- The grade for obtaining a certificate will be adjusted downwards (from 60%) to compensate if one group has slightly harder materials.

Note: By clicking on the “Enroll Now” button, you indicate that you understand that everyone who participates in this course is randomly assigned to one of the sub-groups described above.

This computer science course is the second of a two-course sequence on how to write good software using modern software engineering techniques.

This course will dig deeper into what makes for "good" code -- safe from bugs, easy to understand, and ready for change. We will explore two paradigms for modern programming: (1) grammars, parsing, and recursive datatypes; and (2) concurrent programming with threads.

This is a challenging and rigorous course that will help you take the next step on your way to becoming a skilled software engineer.

Photo by raincrystal on Flickr. (CC-BY-SA) 2.0

This is the second of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The second module, 8.421.2x, describes atomic structure, including electronic levels, fine structure, hyperfine structure and Lamb shift. You will then learn about how electric and magnetic fields shift atomic levels. The discussion of time-dependent electric fields prepares you for the interactions of atoms with light and for the dressed atom picture.

At MIT, the content of the five modules makes the first of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these modules you will learn about the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

Completing the two-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

### 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.

*Course image uses graphic by SVG by Indolences. Recoloring and ironing out some glitches done by Rainer Klute. [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons*

This is the last of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

8.421.5x: Coherence

This fifth module, 8.421.5x, looks at a central theme of atomic physics - coherence. This includes coherence of single atoms for two-level systems and three-level systems, and coherence between atoms, which can result in superradiant behavior.

At MIT, the content of the five modules makes the first of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these modules you will learn about the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

Completing the two-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

### 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.

*Course image uses graphic by SVG by Indolences. Recoloring and ironing out some glitches done by Rainer Klute. [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons*

This is the first of five modules to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

8.421.1x: Resonance

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The first module, 8.421.1x, introduces resonance as an overarching theme of the course. You will deepen your understanding of the physics of resonance by examining systems using both classical and quantum techniques. Of special importance is the precession of a magnetic moments in time-dependent magnetic fields.

At MIT, the content of the five modules makes the first of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these modules you will learn about the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

Completing the five-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

**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.

*Course image uses graphic by SVG by Indolences. Recoloring and ironing out some glitches done by Rainer Klute. [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons*

This is the third of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The third module, 8.421.3x, covers how atoms interact with light. First, dipole and higher order couplings are introduced, and concrete examples for selection rules and matrix elements are given. After quantizing the electromagnetic field and introducing photons, the Jaynes-Cummings model and vacuum Rabi oscillations are presented. Coherent and incoherent time evolution are discussed, also in the framework of Einstein's A and B coefficients.

Completing the two-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

### FAQ

Who can register for this course?

This is the fourth of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The fourth module, 8.421.4x, includes a comprehensive discussion of line broadening effects, including Doppler effect, sidebands for trapped particles, power broadening, and effects of interactions and collisions. The concept of two-photon transitions is relevant for Raman processes and light scattering.

### FAQ

Who can register for this course?

In this physics course, you will be introduced to the QED Hamiltonian (Quantum ElectroDynamics), and learn how to construct diagrams for light-atom interactions. Using your new tools you will study Van der Waals and Casimir interactions, resonant scattering and radiative corrections.

This course is a part of a series of courses to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

- 8.422.1x: Quantum States and Dynamics of Photons
**8.422.2x: Atom-photon Interactions**- 8.422.3x: Optical Bloch Equations and Open System Dynamics
- 8.422.4x: Light Forces and Laser Cooling
- 8.422.5x: Ultracold Atoms and Ions for Many-body Physics and Quantum Information Science

At MIT, the content of the five courses makes the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

Completing the series allows you to pursue advanced study and research in cold atoms, as well as in specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- Quantum states and dynamics of photons
- Photon-atom interactions: basics and semiclassical approximations
- Open system dynamics
- Optical Bloch equations
- Applications and limits of the optical Bloch equations
- Dressed atoms
- Light force
- Laser cooling
- Cold atoms
- Evaporative cooling
- Bose-Einstein condensation
- Quantum algorithms and protocols
- Ion traps and magnetic traps

In this physics course, you will learn about the spontaneous and stimulated light force and friction force in molasses and optical standing waves. You will also study light forces in the dressed atom picture. The course will discuss the techniques of magneto-optical traps and sub-Doppler and sub-recoil cooling.

This course is a part of a series of courses to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

- 8.422.1x: Quantum states and dynamics of photons
- 8.422.2x: Atom-photon interactions
- 8.422.3x: Optical Bloch equations and open system dynamics
**8.422.4x: Light forces and laser cooling**- 8.422.5x: Ultracold atoms and ions for many-body physics and quantum information science

At MIT, the content of the five courses makes the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

Completing the series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- quantum states and dynamics of photons
- photon-atom interactions: basics and semiclassical approximations
- open system dynamics
- optical Bloch equations
- applications and limits of the optical Bloch equations
- dressed atoms
- light force
- laser cooling
- cold atoms
- evaporative cooling
- Bose-Einstein condensation
- quantum algorithms and protocols
- ion traps and magnetic traps

This physics course presents a general derivation of the master equation and the optical Bloch equations. You will learn about various solutions of the optical Bloch equations, and you will discuss the quantum Monte Carlo wavefunction approach. The course will conclude with a discussion of unraveling open system quantum dynamics.

This course is a part of a series of courses to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

- 8.422.1x: Quantum states and dynamics of photons
- 8.422.2x: Atom-photon interactions
**8.422.3x: Optical Bloch equations and open system dynamics**- 8.422.4x: Light forces and laser cooling
- 8.422.5x: Ultracold atoms and ions for many-body physics and quantum information science

At MIT, the content of the five courses makes the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

Completing the series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- quantum states and dynamics of photons
- photon-atom interactions: basics and semiclassical approximations
- open system dynamics
- optical Bloch equations
- applications and limits of the optical Bloch equations
- dressed atoms
- light force
- laser cooling
- cold atoms
- evaporative cooling
- Bose-Einstein condensationquantum algorithms and protocols
- ion traps and magnetic traps.

In this physics course, you will learn about the quantum description of light with applications to squeezed states of light and teleportation as well as the non-classical states of light and single photons. You will learn how to do metrology with light. You will also learn about correlations with photons as well as atom correlation functions.

This course is a part of a series of courses to introduce fundamental concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

**8.422.1x: Quantum States and Dynamics of Photons**- 8.422.2x: Atom-photon Interactions
- 8.422.3x: Optical Bloch Equations and Open System Dynamics
- 8.422.4x: Light Forces and Laser Cooling
- 8.422.5x: Ultracold Atoms and Ions for Many-body Physics and Quantum Information Science

At MIT, the content of these five courses makes up the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these five courses you will learn about the following topics: quantum states and dynamics of photons, photon-atom interactions: basics and semiclassical approximations, open system dynamics, optical Bloch equations, applications and limits of the optical Bloch equations, dressed atoms, light force, laser cooling, cold atoms, evaporative cooling, Bose-Einstein condensation, quantum algorithms and protocols, ion traps and magnetic traps.

Completing this series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

In this physics course you will learn about ultracold bosons and fermions, and you will hear from Prof. Ketterle about Bose-Einstein condensation (BEC). Prof. Ketterle was among the first to achive BEC in the lab and was awarded the Nobel prize in 2001 for his work along with Eric Cornell and Carl Wieman. You will also learn about weakly interacting Bose gases, as well as superfluid to Mott insulator transition, BEC-BCS crossover, trapped ions and quantum gates with ions.

- 8.422.1x: Quantum states and dynamics of photons
- 8.422.2x: Atom-photon interactions
- 8.422.3x: Optical Bloch equations and open system dynamics
- 8.422.4x: Light forces and laser cooling
**8.422.5x: Ultracold atoms and ions for many-body physics and quantum information science**

Completing the series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- quantum states and dynamics of photons
- photon-atom interactions: basics and semiclassical approximations
- open system dynamics
- optical Bloch equations
- applications and limits of the optical Bloch equations
- dressed atoms
- light force
- laser cooling
- cold atoms
- evaporative cooling
- Bose-Einstein condensation
- quantum algorithms and protocols
- ion traps and magnetic traps.

Curious about entrepreneurship, but not sure where to start? Learn from MIT’s premier program for aspiring entrepreneurs, MIT Launch.

Becoming an Entrepreneur is an innovation and business course designed for aspiring entrepreneurs who want to explore an entrepreneurial path and overcome some of the initial challenges in taking those first steps.

From developing new business ideas and doing market research to entrepreneurial strategy and pitching, this course follows MIT’s successful approach to entrepreneurship. There will be a combination of short videos, thought-provoking case studies, and activities that will challenge you to get you away from your computer screen and into the community to make a real impact.

No previous business or entrepreneurship experience needed. Join us to embark on your entrepreneurial journey.

Social physics is a big data science that models how networks of people behave and uses these network models to create actionable intelligence. It is a quantitative science that can accurately predict patterns of human behavior and guide how to influence those patterns to (for instance) increase decision making accuracy or productivity within an organization. Included in this course is a survey of methods for increasing communication quality within an organization, approaches to providing greater protection for personal privacy, and general strategies for increasing resistance to cyber attack.

How does the final velocity on a zip line change when the starting point is raised or lowered by a matter of centimeters? What is the accuracy of a GPS position measurement? How fast should an airplane travel to minimize fuel consumption? The answers to all of these questions involve the derivative.

But what is the derivative? You will learn its mathematical notation, physical meaning, geometric interpretation, and be able to move fluently between these representations of the derivative. You will discover how to differentiate any function you can think up, and develop a powerful intuition to be able to sketch the graph of many functions. You will make linear and quadratic approximations of functions to simplify computations and gain intuition for system behavior. You will learn to maximize and minimize functions to optimize properties like cost, efficiency, energy, and power.

Learn more about our High School and AP* Exam Preparation Courses

Calculus 1C: Coordinate Systems & Infinite Series

This course was funded in part by the Wertheimer Fund.

**Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.*

How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.

But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.

1. Modeling the Integral

- Differentials and Antiderivatives
- Differential Equations
- Separation of Variables

2. Theory of Integration

- Mean Value Theorem
- Definition of the Integral and the First Fundamental Theorem
- Second Fundamental Theorem

3. Applications

- Areas and Volumes
- Average Value and Probability
- Arc Length and Surface Area

4. Techniques of Integration

- Numerical Integration
- Trigonometric Powers, Trig Substitutions, Completing the Square
- Partial Fractions, Integration by Parts

This course, in combination with Part 1, covers the AP* Calculus AB curriculum.

This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.

This course was funded in part by the Wertheimer Fund.

Learn more about our High School and AP* Exam Preparation Courses

Calculus 1C: Coordinate Systems & Infinite Series

**Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.*

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