constant coefficients
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Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
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This lecture is all about motion of projectiles (if air drag can be ignored). The objects experience a constant vertical acceleration due to the acceleration of gravity (see also Lecture 12). Professor Lewin reviews the equations for projectile motion, showing that the trajectory is a parabola. He continues with a demonstration that shows how to measure the initial speed of a projectile and how to reach maximum horizontal distance shooting...more
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This lecture is about uniform circular motion. There is a constant radial acceleration (centripetal acceleration) but constant tangential speed. Professor Lewin uses himself as an example, sitting on a chair bolted to a fast rotating turntable feeling the push and pull of centripetal force. He continues with discussion of the motion of the planets around the sun, with respect to gravitational pull, and the idea behind a centrifuge and ...more
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Angular momentum is constant when there is no net torque.
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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, especial...more
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Professor Sylvia Ceyer explains the standard Gibbs free energy of formation and its relationship to thermodynamic stability. The Second Law of Thermodynamics is defined as it relates to controlling spontaneity with temperature. The lecture concludes by defining the thermodynamic equilibrium constant and the reaction quotient/direction of change in a chemical equilibrium.
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In this lecture, Professor Paul Fry turns his attention to the relationship between authorship and the psyche. Freud's meditations on the fundamental drives governing human behavior are read through the lens of literary critic Peter Brooks. The origins of Freud's work on the "pleasure principle" and his subsequent revision of it are charted, and the immediate and constant influence of Freudian thought on literary production is asserted. Br...more
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Ignoring the solution or the solid state molecules when calculating the equilibrium constant.
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PV/T is a constant. Figuring out the volume of an ideal gas at standard temperature and pressure (STP).
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Finding the coefficients of a third degree polynomial given 2 roots and the y-intercept.
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A probabilistic look at how molecules react to develop the intuition behind the equilibrium constant formula.
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Professor Sylvia Ceyer covers radioactive decay and its various uses in modern medicine. Second order half-life, as a second order integrated rate law, is then discussed. The lecture concludes with the overlap of kinetics and chemical equilibrium: the equilibrium constant, elementary reactions, and an example, the decomposition of ozone.
