Mastering Statics

Start Date: 09/15/2019

Course Type: Common Course

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Course Syllabus

Understanding Forces and Moments
Equivalent Systems of Forces and Equilibrium
Stability and Static Determinancy

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Course Introduction

Statics is the most fundamental course in Mechanics. In this course, you will learn the conditions under which an object or a structure subjected to

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Article Example
Social Statics Economist Murray Rothbard called "Social Statics" "the greatest single work of libertarian political philosophy ever written."
Comparative statics Comparative statics is commonly used to study changes in supply and demand when analyzing a single market, and to study changes in monetary or fiscal policy when analyzing the whole economy. The term 'comparative statics' itself is more commonly used in relation to microeconomics (including general equilibrium analysis) than to macroeconomics. Comparative statics was formalized by John R. Hicks (1939) and Paul A. Samuelson (1947) (Kehoe, 1987, p. 517) but was presented graphically from at least the 1870s.
Comparative statics One limitation of comparative statics using the implicit function theorem is that results are valid only in a (potentially very small) neighborhood of the optimum—that is, only for very small changes in the exogenous variables. Another limitation is the potentially overly restrictive nature of the assumptions conventionally used to justify comparative statics procedures.
Comparative statics In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter.
Comparative statics Comparative statics asks how this maximizer changes in response to changes in the "m" parameters. The aim is to find formula_67.
Comparative statics For models of stable equilibrium rates of change, such as the neoclassical growth model, comparative dynamics is the counterpart of comparative statics (Eatwell, 1987).
Comparative statics Paul Milgrom and Chris Shannon pointed out in 1994 that the assumptions conventionally used to justify the use of comparative statics on optimization problems are not actually necessary—specifically, the assumptions of convexity of preferred sets or constraint sets, smoothness of their boundaries, first and second derivative conditions, and linearity of budget sets or objective functions. In fact, sometimes a problem meeting these conditions can be monotonically transformed to give a problem with identical comparative statics but violating some or all of these conditions; hence these conditions are not necessary to justify the comparative statics. Stemming from the article by Milgrom and Shannon as well as the results obtained by Veinott and Topkis an important strand of operational research was developed called monotone comparative statics. In particular, this theory concentrates on the comparative statics analysis using only conditions that are independent of order-preserving transformations. The method uses lattice theory and introduces the notions of quasi-supermodularity and the single-crossing condition. The wide application of monotone comparative statics to economics include production theory, consumer theory, game theory with complete and incomplete information, auction theory, and others.
Audio mastering Record mastering became a highly prized and skilled craft, and it was widely recognized that good mastering could make or break a commercial pop recording. As a result, the independent mastering studio was born. Early independent mastering engineers included Doug Sax, Bob Ludwig, Bob Katz and Bernie Grundman and Denny Purcell.
Statics Statics is the branch of mechanics that is concerned with the analysis of loads (force and torque, or "moment") acting on physical systems that do not experience an acceleration ("a"=0), but rather, are in static equilibrium with their environment. When in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mass moves at constant velocity. The application of Newton's second law to a system gives:
Audio mastering Examples of possible actions taken during mastering:
Audio mastering Although there is no "optimum mix level for mastering", the example in the adjacent picture only suggests what mix levels are ideal for the studio engineer to render and for the mastering engineer to process. It is important to allow enough headroom for the mastering engineer's work. Reduction of headroom by the mix or mastering engineer has resulted in a loudness war in commercial recordings.
Monotone comparative statics Monotone comparative statics is a sub-field of comparative statics that focuses on the conditions under which endogenous variables undergo monotone changes (that is, either increasing or decreasing) when there is a change in the exogenous parameters. Traditionally, comparative results in economics are obtained using the Implicit Function Theorem, an approach that requires the concavity and differentiability of the objective function as well as the interiority and uniqueness of the optimal solution. The methods of monotone comparative statics typically dispense with these assumptions. It focuses on the main property underpinning monotone comparative statics, which is a form of complementarity between the endogenous variable and exogenous parameter. Roughly speaking, a maximization problem displays complementarity if a higher value of the exogenous parameter increases the marginal return of the endogenous variable. This guarantees that the set of solutions to the optimization problem is increasing with respect to the exogenous parameter.
Mastering engineer A professional mastering engineer renders mixes that have a good harmonic balance. Harmonic balancing can be accomplished by correcting and removing tonal imbalances. Once corrected or removed, the audio will be much more pleasurable for listening. This is a fundamental aspect to a mastering engineer's job and the reason why many consider mastering to be a form of art as well as an "audio engineering" discipline.
Mastering engineer The mastering engineer is responsible for a final edit of a product and preparation for manufacturing copies. Although there are no official requirements to work as an audio mastering engineer, practitioners often have comprehensive domain knowledge of audio engineering, and in many cases, may hold an audio or acoustic engineering degree. Most audio engineers master music or speech audio material. The best mastering engineers might possess arrangement and record production skills, allowing them to 'trouble-shoot' mix issues and improve the final sound. Generally, good mastering skills are based on experience, resulting from many years of practice.
Audio mastering Mastering has a special significance for house, techno and other styles of electronic dance music:
Statics The static equilibrium of a particle is an important concept in statics. A particle is in equilibrium only if the resultant of all forces acting on the particle is equal to zero. In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations, where the sums of forces in all three directions are equal to zero. An engineering application of this concept is determining the tensions of up to three cables under load, for example the forces exerted on each cable of a hoist lifting an object or of guy wires restraining a hot air balloon to the ground.
Last Drop Mastering Last Drop Mastering is an audio mastering and post-production facility located in San Francisco, California, working with artists online since 1999.
Audio mastering The process of audio mastering varies depending on the specific needs of the audio to be processed. Mastering engineers need to examine the types of input media, the expectations of the source producer or recipient, the limitations of the end medium and process the subject accordingly. General rules of thumb can rarely be applied.
Comparative statics Suppose a firm produces "n" goods in quantities formula_72. The firm's profit is a function "p" of formula_72 and of "m" exogenous parameters formula_74 which may represent, for instance, various tax rates. Provided the profit function satisfies the smoothness and concavity requirements, the comparative statics method above describes the changes in the firm's profit due to small changes in the tax rates.
Audio mastering Mastering requires critical listening; however, software tools exist to facilitate the process. Mastering is a crucial gateway between production and consumption and, as such, it involves technical knowledge as well as specific aesthetics. Results still depend upon the accuracy of speaker monitors and the listening environment. Mastering engineers may also need to apply corrective equalization and dynamic compression in order to optimise sound translation on all playback systems. It is standard practice to make a copy of a master recording, known as a safety copy, in case the master is lost, damaged or stolen.