Analytical chemistry is the branch of chemistry dealing with measurement, both qualitative and quantitative. This discipline is also concerned with the chemical composition of samples. In the field, analytical chemistry is applied when detecting the presence and determining the quantities of chemical compounds, such as lead in water samples or arsenic in tissue samples. It also encompasses many different spectrochemical techniques, all of which are used under various experimental conditions. This branch of chemistry teaches the general theories behind the use of each instrument as well analysis of experimental data. Upon successful completion of this course, the student will be able to: Demonstrate a mastery of various methods of expressing concentration; Use a linear calibration curve to calculate concentration; Describe the various spectrochemical techniques as described within the course; Use sample data obtained from spectrochemical techniques to calculate unknown concentrations or obtain structural information where applicable; Describe the various chromatographies described within this course and analyze a given chromatogram; Demonstrate an understanding of electrochemistry and the methods used to study the response of an electrolyte through current of potential. (Chemistry 108)

" 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."

Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.

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.

We derive the equations for a driven oscillator.

Electromagnetic phenomena are explored 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, and power generation and transmission. Fundamentals 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.

Electromagnetic phenomena are explored 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, and power generation and transmission. Fundamentals 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.

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)

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.

Organic chemistry is the study of the carbon and the bonding patterns that make carbon the central element to life. A well-rounded science student must take courses in organic chemistry to understand its application to various other topics, such as the study of DNA, pharmaceuticals, and plastics. In the first semester of organic chemistry, the student will cover the basics. The student will explore different explanations of how molecules bond and learn about the simplest carbon structures (alkanes) before moving on to more complex carbon structures (alkenes and alkynes) and their reactions. The student will then transition into stereoechemistry (the spatial arrangement of atoms) and spectroscopy (methods of identifying molecules) and will conclude the course by examining the four basic organic chemistry mechanisms. This last section will demonstrate electron movement in chemical reactions. Upon successful completion of this course, students will be able to: Describe organic molecules in terms of bonding, stereochemistry, functional groups, and resonance; Demonstrate proficiency in the nomenclature of organic molecules; Derive the intermolecular force of given molecules based on their chemical structures; Draw and represent organic molecules, using arrow notation to show the movement of electrons; Demonstrate proficiency in identifying various classes of reactions (i.e. addition, elimination, arrangements); Describe the thermodynamics of organic reactions using energy diagrams; Analyze the stereochemistry of simple organic molecules and the stereochemical consequences of reactions; Demonstrate proficiency in Newman projections and conformations of cyclohexanes; Demonstrate proficiency in determining whether alkyl halides will undergo a substitution or elimination reaction for a given set of reaction conditions; Describe the basic reaction mechanisms of alcohols; Demonstrate proficiency in calculating the degree of unsaturation of molecules; Describe the basic reaction mechanisms of alkenes and alkynes; Explain the concept of chirality, optical activity, and stereoisomerism; Explain the concept of a carbocation, which is an ion with a positively-charged carbon; Rank different carbocations according to their stability and/or reactivity; Explain the differences between SN1 and SN2 substitution reactions and between E1 and E2 eliminations reactions. (Chemistry 103; See also: Biology 107)

This 12-minute video lesson looks at resonance in benzene and the carbonate ion. [Organic Chemistry playlist: Lesson 47 of 73].

Mechanical vibrations and waves; simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations and normal modes; vibrations of continuous systems; reflection and refraction; phase and group velocity. Optics; wave solutions to Maxwell's equations; polarization; Snell's Law, interference, Huygens's principle, Fraunhofer diffraction, and gratings.

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.

An introduction to the concept of resonance as it applies to musical instruments.

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.