Chemical Engineering Hand Written_Notes_Part_22

Chemical Engineering Hand Written_Notes_Part_22 - 46 2....

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Unformatted text preview: 46 2. FUNDAMENTALS OF FUNCTIONAL ANALYSIS Original Problem Transformed Problem in Standard Format Transformation Taylor Series / Weierstrass Theorem Tool 2: Solutions of ODE- IVP Tool 3: Numerical Optimization Numerical Solution Tool 1: Solutions of Linear Algebraic Equations Original Problem Transformed Problem in Standard Format Transformation Taylor Series / Weierstrass Theorem Tool 2: Solutions of ODE- IVP Tool 3: Numerical Optimization Numerical Solution Tool 1: Solutions of Linear Algebraic Equations Figure 2 where in such a way that the solution x of equation ( 6.5 ), i.e. (5.15) x = G [ x ] satis f es (5.16) F ( x ) = Key to such transformations is approximation of continuous functions using polynomials. The following two important results from functional analysis play pivotal role in the development of many iterative numerical schemes. The Tay- lor series expansion helps us develop local linear or quadratic approximations of a function vector in the neighborhood of a point in a vector space. The Weier-a function vector in the neighborhood of a point in a vector space....
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Chemical Engineering Hand Written_Notes_Part_22 - 46 2....

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