Resonance Phenomena
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This lecture completes the first half of the semester by analyzing three functional groups in terms of the interaction of localized atomic or pairwise orbitals. Many key properties of biological polypeptides derive from the mixing of such localized orbitals that we associate with "resonance" of the amide group. The acidity of carboxylic acids and the aggregation of methyl lithium into solvated tetramers can be understood in analogous...more
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Summary Of Previous Lecture (Analyzing General Periodic Phenomena As A Sum Of Simple Periodic Phenomena), Fourier Coefficients; Discussion Of How General The Fourier Series Can Be (Examples Of Discontinuous Signals), Discontinuity And Its Impact On The Generality Of The Fourier Series, Infinite Sums To Represent More General Periodic Signals, Summary Of Convergence Issues, Convergence: Continuous Case, Smooth Case (Fourier Series...more
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Professor Diamond builds on previously introduced material about the cardiac system and introduces angiology, the study of the blood vessels. To begin, she draws a diagram of the composition of the circulatory system, showing how the arteries, arterioles, capillaries differ from veins and veinules. She also explains what blood vessels are made of and their specific functions. She then details elastic arteries (those more limited in...more
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This lecture brings experiment to bear on the previous theoretical discussion of bonding by focusing on hybridization of the central atom in three XH3 molecules. Because independent electron pairs must not overlap, hybridization can be related to molecular structure by a simple equation. The "Umbrella Vibration" and the associated rehybridization of the central atom is used to illustrate how a competition between strong bonds and stable...more
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Continued Discussion Of Fourier Series And The Heat Equation, Transition From Fourier Series To Fourier Transforms (Periodic To Nonperiodic Phenomena), Fourier Series Analysis And Synthesis; Relation To Fourier Transform And Inverse Fourier Transform, Fourier Series/ Coefficients With Period T, Spectrum Picture For Fourier Series With Period T, Effects Of A Change In T, The Complications Of Finding The Fourier Transform By Letting T Go To...more
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Correction To The End Of The CLT Proof, Discussion Of The Convergence Of Integrals; Approaches To Making A More Robust Definition Of The Fourier Transform, Examples Of Problematic Signals, How To Approach Solving The Problem; Choosing Basic Phenomena To Use To Explain Others, Identifying The Best Class Of Signals For Fourier Transforms; + Their Properties, The Definition Of The Class Of Rapidly Decreasing Functions, Rationale For Why...more
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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 (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's,...more
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Elecromagnetic Waves (Radio), the Speed of Light, Resonance, and Distance Determination using Lasers
MIT / Physics
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Professor McBride begins by following Newton's admonition to search for the force law that describes chemical bonding. Neither direct (Hooke's Law) nor inverse (Coulomb, Gravity) dependence on distance will do - a composite like the Morse potential is needed. G. N. Lewis devised a "cubic-octet" theory based on the newly discovered electron, and developed it into a shared pair model to explain bonding. After discussing Lewis-dot notation...more
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Systems consisting of pendulums and springs can freely oscillate at their natural frequencies (also called normal modes). When we expose a system to a wide spectrum of frequencies, the response will be very large at the normal mode frequencies (resonances) of that system. Examples include musical instruments (standing waves on violin strings and pressure waves in wind instruments), and torsional standing waves on a bridge driven by strong winds.
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Regulation of financial and securities markets is intended to protect investors while still enabling them to make personal investment decisions. Psychological phenomena, such as magical thinking, overconfidence, and representativeness heuristic can cause deviations from rational behavior and distort financial decision-making. However, regulation and regulatory bodies, such as the SEC, FDIC, and SIPC, most of which were created just after...more
