numerical analysis5

numerical analysis5 - c ∈ ( a,b ) such that f ( c ) = K ....

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2 1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS Theorem (Extreme Value Theorem) . If f C [ a,b ] , then c 1 ,c 2 [ a,b ] exist with f ( c 1 ) f ( x ) f ( c 2 ) for all x [ a,b ] . In addition, if f is diFerentiable on ( a,b ) , then c 1 and c 2 occur either at the endpoints of [ a,b ] or where f 0 is zero. Theorem (Intermediate Value Theorem) . If f C [ a,b ] and K is any number between f ( a ) and f ( b ) , then there exists
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Unformatted text preview: c ∈ ( a,b ) such that f ( c ) = K . Corollary (Intermediate Value Theorem) . If f ∈ C [ a,b ] and f ( a ) f ( b ) < , then there exists c ∈ ( a,b ) such that f ( c ) = 0 . Note. This corollary is often used in approximating roots of equations....
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This note was uploaded on 04/07/2011 for the course CIVIL 441 taught by Professor Hjjj during the Spring '11 term at Gazi Üniversitesi.

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