Variation Of Parameters
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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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Example in Which Writing Past the End of Array Causes the Return Address of the Function to be Overwritten, Leading to An Infinite Loop, Example in Which Data Is Incorrectly Shared between Two Different Functions, But Can Still be Printed Out Due to the Structure of the Activation Record (Channelling), How Printf's Prototype Uses "...", Which Allows It to Take A Variable Number of Arguments, Why Parameters Are Pushed Onto the Stack From...more
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More Detail about Activation Records - Layout of Memory During a Function Call
Stanford / Computer Science
More Detail about Activation Records - Layout of Memory During a Function Call, How the Return Address of a Function is Stored on the Stack, Example Showing How an Activation Record is Constructed on the Stack, Setting Up Function Parameters on the Stack, Using the Call Instruction to Jump to the Function, Cleaning Up at the End of a Function and Using the RET Instruction and the Saved Return Address to Return to the Original Function,...more
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Similarity between C++ & Java: - syntax - variable types - operators - control structures
Stanford / Computer Science
Similarity between C++ & Java: - syntax - variable types - operators - control structures, Looking at an Example C++ code: - comment, #include Statements, Global Declarations (constant), Declaring a Function Prototype, The main() Function, Decomposed Function Definition, Example Live Coding: To Calculate the Average, for loop - a while : Another Purpose of the Same Code, C++ User Defined Data Types: -enums -records, C++ Parameters...more
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Understanding conformational relationships makes it easy to draw idealized chair structures for cyclohexane and to visualize axial-equatorial interconversion. After quantitative consideration of the conformational energies of ethane, propane, and butane, cyclohexane is used to illustrate the utility of molecular mechanics as an alternative to quantum mechanics for estimating such energies. To give useful accuracy this empirical scheme...more
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Doppler Effect, Binary Stars, Neutron Stars and Black Holes. Doppler shift is introduced with sound waves, then extended to electromagnetic waves (radiation). The Doppler shift of stellar spectral lines and/or pulsar frequencies provides a measure of the line-of-sight (so-called radial) velocity of the source relative to the observer. Combined with Newton's law of universal gravitation, this can lead to the orbital parameters and the mass...more
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Structure of the Atom: A Conundrum. The work of E. Rutherford, 1911, lead to the discovery of the nucleus. In this lecture, Professor Sylvia Ceyer begins by explaining the backscattering experiment that lead to this key discovery in the early 20th century. She then moves on to a classical description of the atom, including coulombic interaction and the classical equation of motion (Newton's Second Law). The lecture ends with discussion...more
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Kepler's Laws, Elliptical Orbits, Change of Orbits, and the famous passing of a Ham Sandwich by astronauts in orbit. Kepler's three Laws summarize the motion of the planets in our solar system. Following Newton's law of universal gravitation, the conservation of angular momentum and mechanical energy allow us to calculate the semimajor axis of the elliptical orbits, the orbital period and other orbital parameters. All we have to know is...more
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August 9, 2007 presentation by Russ Altman for the Stanford University Office of Science Outreach's Summer Science Lecture Series. There are a number of causes for variation in drug response across the population, but differences in genetics are an important factor. Russ Altman, Professor & Chair of Bioengineering and Professor of Genetics and Medicine, discusses how variations in genetics can alter the "typical" response as well as...more
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Mutations are the origin of genetic diversity. Mutations introduce new traits, while selection eliminates most of the reproductively unsuccessful traits. Sexual recombination of alleles can also account for much of the genetic diversity in sexual species. In some instances, population size can affect diversity and rates of evolution and fixation, but in other cases population size does not matter.
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Professor Sylvia Ceyer continues her discussion on chemical equilibrium and external effects such as a change in volume, adding inert gas, and a change in temperature. Parameters are set for maximizing the yield of a reaction, and the Principle of Le Chatelier's is returned to. Hemoglobin is used as an example involved in a series of equilibrium reactions in response to oxygen pressure.
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Homogeneous Transform Interpretations, Compound Transformations, Spatial Descriptions, Rotation Representations, Euler Angles, Fixed Angles, Example - Singularities, Euler Parameters, Example - Rotations
