NM1_introduction_s02

NM1_introduction_s02 - CGN 3421 - Computer Methods Gurley...

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CGN 3421 - Computer Methods Gurley Numerical Methods - Lecture 1 page 47 of 53 Numerical Methods - Lecture 1 Topics: Numerical Methods Introduction WHY ARE WE STUDYING THIS??? matrix methods curve fitting root finding optimization statistical analysis probability analysis integration / differentiation ordinary differential equations signal processing NUMERICAL METHODS (why?) Our creations are based on mathematical models of what occurs in nature. Structural response to wind/waves/earthquakes Airplane performance Chemical reactions Automobile suspensions Steel bridge deformation under heavy railroad loads Traffic patterns for infrastructure design Maximum capacity of piles holding up foundations Waste water treatment plants The betting line on Florida vs. Florida State Insurance premiums ...... These mathematical models of physical processes allow us to design and build new creations that account for the various stresses they will see. Without numerical methods (the creation and application of mathematical models), there would be no aircraft, tall buildings, long bridges, etc. We’ll look at a brief introduction of each of the topics to be covered.
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CGN 3421 - Computer Methods Gurley Numerical Methods - Lecture 1 page 48 of 53 Matrix methods - solving simultaneous equations We’re familiar with the equation relating force and displacement for a spring as . We’ve also learned how to analyze a simple truss structure in statics All a truss is permitted to do is stretch or compress. So one way of analyzing truss type structures is to visualize the structure as a group of attached springs. For example, the simple truss below can be repre- sented as springs. Usually engineers know what the constant is for each spring, and the forces acting on the structure.
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NM1_introduction_s02 - CGN 3421 - Computer Methods Gurley...

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