• What makes a set of objects a vector space? You will no doubt want to refer to notes and the text, but I'd like you to summarize it for starters. • If you have identified a vector space, for example the so-called L2 space of square- integrable functions, what advantages does it give you? • Why do non-linear boundary value problems, i.e., problems with non-linear ODE's or PDE's, fall outside the field of linear spaces? If you can, show by example what the problem is in practice.
• What makes a set of objects a vector space? You will no doubt want to refer to notes and the text, but I'd like you to summarize it for starters. • If you have identified a vector space, for example the so-called L2 space of square- integrable functions, what advantages does it give you? • Why do non-linear boundary value problems, i.e., problems with non-linear ODE's or PDE's, fall outside the field of linear spaces? If you can, show by example what the problem is in practice.
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Transcribed Image Text:• What makes a set of objects a vector space? You
will no doubt want to refer to notes and the
text, but I'd like you to summarize it for starters.
• If you have identified a vector space, for
example the so-called L2 space of square-
integrable functions, what advantages does it
give you?
• Why do non-linear boundary value problems,
i.e., problems with non-linear ODE's or PDE's,
fall outside the field of linear spaces? If you can,
show by example what the problem is in
practice.
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