Exam (elaborations)
Che 505 Final Exam Part 3 (Oral) With Complete Solutions Latest Update
- Course
- CHE 505
- Institution
- Arizona State University
Che 505 Final Exam Part 3 (Oral) With Complete Solutions Latest Update
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Solution 2024/2025Pepper
Che 505 Final Exam Part 3 (Oral) With
Complete Solutions Latest Update
Linear function space ANS✔✔ think of a function as an infinite dimension
vector
function spaves defined by smoothness, continuous nature, differentiability,
integrability over some interval (a,b)
c(0,1) set of all functions that are continuous over interval 0 to 1
l2(a,b) set of all functions whose integral of |f(x)|^2 from a to b exists and is
finite
goal: define linear space that allows us to do things analogous to what we
did in vector space
spectral resolution
projections and orthogonality
null space and solvability condition
inner product in function space and properties ANS✔✔ gives semblance of
orientation between 2 functions
<f,g> = integral from a to b (f*x)g(x)dx
when evaluated gives scalar
, Solution 2024/2025
Pepper
<f,g> = <g,f>*
<f,ag+bh> = a<f,g> + b<f,h> (homogeneity and superposition
<f,f> is greater than or equal to zero, equality only true when f=0
<f,f> = integral from a to b (|f(x)|^2dx
<f,g> = 0 then f and g orthogonal
norms in function space and properties ANS✔✔ gives sembelence of size of
the function in the function space
norm of a function is a scalar
||f(x)||^2 = <f,f>
l2(a,b) - space of all functions that are square integrable from a to b
all functions whose norm exists and is finite
||f|| is greater than or equal to zero, equality only true if f=0
||af|| = |a|||f||
||f+g|| is less than or equal to ||f|| + ||g||
completeness of space ANS✔✔ for us to be able to do the same thing in
function space that we can do in vector space the space needs to be
complete
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