This is the first of a two-semester subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical physics. Topics covered include 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.

We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.
We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overlap and transition to chaos; properties of chaotic motion.
Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis.

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.
Course Format
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

Lecture Videos by Professor Arthur Mattuck.
Course Notes on every topic.
Practice Problems with Solutions.
Problem Solving Videos taught by experienced MIT Recitation Instructors.
Problem Sets to do on your own with Solutions to check your answers against when you're done.
A selection of Interactive Java® Demonstrations called Mathlets to illustrate key concepts.
A full set of Exams with Solutions, including practice exams to help you prepare.

Content Development
Haynes Miller 
Jeremy Orloff 
Dr. John Lewis 
Arthur Mattuck

Drums are more than just a collection of natural elements. The art and science of drum making have been part of Indigenous cultures throughout the world for millennia. Drums have a deep spiritual resonance, but also have a necessary understanding of physics, in order to achieve the correct sound.

This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.
Acknowledgments
The instructors would like to thank Robert Haussman for transcribing into LaTeX the problem set and Quiz 2 solutions.

Through three teacher-led demonstrations, students are shown samplers of real-world nanotechnology applications involving ferrofluids, quantum dots and gold nanoparticles. This nanomaterials engineering lesson introduces practical applications for nanotechnology and some scientific principles related to such applications. It provides students with a first-hand understanding of how nanotechnology and nanomaterials really work. Through the interactive demos, their interest is piqued about the odd and intriguing nano-materials behaviors they witness, which engages them to next conduct the three fun associated nanoscale technologies activities. The demos use materials readily available if supplies are handy for the three associated activities.

In this video adapted from the Encyclopedia of Physics Demonstrations, learn how a glass beaker vibrates at a specific frequency and how resonance can force it to shatter.

In this course, the student will first learn about waves and oscillations in extended objects using classical mechanics. The course will then examine the sources and laws that govern static electricity and magnetism. A brief look at electrical measurements and circuits will help establish how electromagnetic effects are observed, measured, and applied. These topics lead to an examination of how Maxwell's equations unify electric and magnetic effects and how the solutions to Maxwell's equations describe electromagnetic radiation, which will serve as the basis for understanding all electromagnetic radiation, from very low frequency radiation emitted by power transmission lines to the most powerful astrophysical gamma rays. The course also investigates optics and launches a brief overview of Einstein's special theory of relativity. A basic knowledge of calculus is assumed. (Physics 102; See also: Biology 110, Chemistry 002, Mechanical Engineering 006)

Students learn about frequency and period, particularly natural frequency using springs. They learn that the natural frequency of a system depends on two things: the stiffness and mass of the system. Students see how the natural frequency of a structure plays a big role in the building surviving an earthquake or high winds.

Explore an active area of research in optical physics: producing designer pulse shapes to achieve specific purposes, such as breaking apart a molecule. Carefully create the perfect shaped pulse to break apart a molecule by individually manipulating the colors of light that make up a pulse.

Vibrations and waves are everywhere. If you take any system and disturb it from a stable equilibrium, the resultant motion will be waves and vibrations. Think of a guitar string—pluck the string, and it vibrates. The sound waves generated make their way to our ears, and we hear the string’s sound. Our eyes see what’s happening because they receive the electromagnetic waves of the light reflected from the guitar string, so that we can recognize the beautiful sinusoidal waves on the string. In fact, without vibrations and waves, we could not recognize the universe around us at all!

The amazing thing is that we can describe many fascinating phenomena arising from very different physical systems with mathematics. This course will provide you with the concepts and mathematical tools necessary to understand and explain a broad range of vibrations and waves. You will learn that waves come from many interconnected (coupled) objects when they are vibrating together. We will discuss many of these phenomena, along with related topics, including mechanical vibrations and waves, sound waves, electromagnetic waves, optics, and gravitational waves.

For advanced undergraduate students: Observe resonance in a collection of driven, damped harmonic oscillators. Vary the driving frequency and amplitude, the damping constant, and the mass and spring constant of each resonator. Notice the long-lived transients when damping is small, and observe the phase change for resonators above and below resonance.

Is it a tumor? Magnetic Resonance Imaging (MRI) can tell. Your head is full of tiny radio transmitters (the nuclear spins of the hydrogen nuclei of your water molecules). In an MRI unit, these little radios can be made to broadcast their positions, giving a detailed picture of the inside of your head.

Student teams conduct an experiment that uses gold nanoparticles as sensors of chemical agents to determine which of four sports drinks has the most electrolytes. In this way, students are introduced to gold nanoparticles and their influence on particle or cluster size and fluorescence. They also learn about surface plasmon resonance phenomena and how it applies to gold nanoparticle technologies, which touches on the basics of the electromagnetic radiation spectrum, electrolyte chemistry and nanoscience. Using some basic chemistry and physics principles, students develop a conceptual understanding of how gold nanoparticles function. They also learn of important practical applications in biosensing.

This learning activity is designed to be used in a large introductory chemistry course, as part of a larger module of learning activities that includes prior viewing of an interactive instructional video. Instructional videos are to be viewed before class meetings. During class time, students work in small groups and discuss the presented information and question prompts, and will build upon the concepts discussed in that video in order to develop a new, extended concept.Students should be tasked with working together to complete the prompts in each section of the activity by a set time limit. After each section is completed, the entire class can share their answers via a personal response system, and the instructor can review and explain the correct responses, using the accompanying slide deck, which translates the problems into multiple-choice prompts.Instructional resources include 1) interactive instructional videos (these can be embedded directly into the learning management system) 2) the learning activity (.docx and .pdf) 3) the learning objectives (.docx and .pdf) and 4) the slide deck (.pptx). - Chemical Bonding- Resonance - Intermolecular Forces- Collision Theory- Equilibrium- Nucleophiles and Electrophiles

Watch a string vibrate in slow motion. Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator. Adjust the damping and tension. The end can be fixed, loose, or open.