Laplace equation
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U02_L2_T2_we2 : Example of solving an absolute value equation.
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Professor Sylvia Ceyer continues her discussion of acid-base equilibrium, diving into buffers. The lecture concludes with the Henderson-Hasselbalch equation and its use in designing a buffer.
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Buffers and the Hendersen-Hasselbalch equation.
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Concepts covered in this lecture include hydrostatics, Archimedes' Principle, fluid dynamics, and Bernoulli's Equation. The buoyant foce of air on a ballon is discussed, and then Professor Lewin demonstrates how a balloon and a pendulum behave in accelerated, closed containers. The lecture ends with some non-intuitive demos shoiing how ping pong balls behave in air streams.
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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 at...more
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After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analog...more
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What happens when the characteristic equation has complex roots?
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This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
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In this lecture, Professor Lewin displays how the conservation of mechanical energy can be used to derive the equation of motion for simple harmonic oscillators (SHO). In doing so he covers gravitational potential energy, equilibrium points where the net force is zero, parabolic potential energy, and circular potential energy.
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