Problem set 4

... Due at the beginning of class on Tuesday, August 18. Matrix of discretized derivative In the lecture it was mentioned that Newton’s equation ẍ = f could be written as a matrix equation when discretized. Here you will do this for the simpler problem of the first derivative. Given the position of a p ...

... Due at the beginning of class on Tuesday, August 18. Matrix of discretized derivative In the lecture it was mentioned that Newton’s equation ẍ = f could be written as a matrix equation when discretized. Here you will do this for the simpler problem of the first derivative. Given the position of a p ...

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... Definition Suppose X is a nonempty set. Then a function f : X → C is a bounded function if there exist a C < ∞ such that |f (x)| < C for all x ∈ X. The set of all bounded functions on X is usually denoted by B(X) ([?], pp. 61). Under standard point-wise addition and point-wise multiplication by a sc ...

... Definition Suppose X is a nonempty set. Then a function f : X → C is a bounded function if there exist a C < ∞ such that |f (x)| < C for all x ∈ X. The set of all bounded functions on X is usually denoted by B(X) ([?], pp. 61). Under standard point-wise addition and point-wise multiplication by a sc ...