The norm defined on the space of2 pointscontinuous function defined of theclosed interval [a,b] is given byIIf|=\sqrt=\int |f(t)|^2 dt, t in [a,b],where \sqrt is the square root||f||==\sum |f(t)| , for all t in [a,b], where\sqrt is the square root|lf|l=\sqrt=\sum |f(ti)|^2, for some ti in[a,b], i=1,2,3,.., where \sqrt is the squareroot

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The norm defined on the space of 2 points continuous function defined of the closed interval [a,b] is given by ||F||=\sqrt=\int |f(t)|^2 dt, t in [a,b], where \sqrt is the square root IIf||==\sum |f(t)| , for all t in [a,b], where \sqrt is the square root ||f||=\sqrt=\sum |f(ti)|^2, for some ti in O [a,b], i=1,2,3,..., where \sqrt is the square root

The norm defined on the space of 2 points continuous function defined of the closed interval [a,b] is given by ||F||=\sqrt=\int |f(t)|^2 dt, t in [a,b], where \sqrt is the square root IIf||==\sum |f(t)| , for all t in [a,b], where \sqrt is the square root ||f||=\sqrt=\sum |f(ti)|^2, for some ti in O [a,b], i=1,2,3,..., where \sqrt is the square root

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Question

The norm defined on the space of
2 points
continuous function defined of the
closed interval [a,b] is given by
IIf|=\sqrt<f,f>=\int |f(t)|^2 dt, t in [a,b],
where \sqrt is the square root
||f||=<f,f>=\sum |f(t)| , for all t in [a,b], where
\sqrt is the square root
|lf|l=\sqrt<f,f>=\sum |f(ti)|^2, for some ti in
[a,b], i=1,2,3,.., where \sqrt is the square
root

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