MATH 115 ACTIVITY 1:
... To extend our graphing techniques from last semester (intervals where f is increasing, inrevals where f is decreasing, etc.] to use with sine & cosine, we'd need to be able to solve equations like 3sin(2x) = 0. How many solutions are there to the equation sin(2x) = 0? What do they look like? ...
... To extend our graphing techniques from last semester (intervals where f is increasing, inrevals where f is decreasing, etc.] to use with sine & cosine, we'd need to be able to solve equations like 3sin(2x) = 0. How many solutions are there to the equation sin(2x) = 0? What do they look like? ...
Densities and derivatives - Department of Statistics, Yale
... using the assumption νX < ∞, gives ν A = limn ν supi≥n Ai ≥ . Thus ν is not absolutely continuous with respect to µ. In other words, the –δ property is equivalent to absolute continuity, at least when ν is a finite measure. The equivalence can fail if ν is not a finite measure. ...
... using the assumption νX < ∞, gives ν A = limn ν supi≥n Ai ≥ . Thus ν is not absolutely continuous with respect to µ. In other words, the –δ property is equivalent to absolute continuity, at least when ν is a finite measure. The equivalence can fail if ν is not a finite measure. ...
Convex Programming - Santa Fe Institute
... is denoted ∂ f (x), and is called the subdifferential of f at x. Subdifferentials share many of the derivative’s properties. For instance, if 0 ∈ ∂ f (x), then x is a global maximum of f . In fact, if ∂ f (x) contains only one subgradient p x , then f is differentiable at x and D f (x) = p x . The s ...
... is denoted ∂ f (x), and is called the subdifferential of f at x. Subdifferentials share many of the derivative’s properties. For instance, if 0 ∈ ∂ f (x), then x is a global maximum of f . In fact, if ∂ f (x) contains only one subgradient p x , then f is differentiable at x and D f (x) = p x . The s ...
Math 55b Lecture Notes Contents
... This subsection is copied from my Napkin project. Definition 1.1. A metric space is a pair (M, d) consisting of a set of points M and a metric d : M × M → R≥0 . The distance function must obey the following axioms. • For any x, y ∈ M , we have d(x, y) = d(y, x); i.e. d is symmetric. • The function d ...
... This subsection is copied from my Napkin project. Definition 1.1. A metric space is a pair (M, d) consisting of a set of points M and a metric d : M × M → R≥0 . The distance function must obey the following axioms. • For any x, y ∈ M , we have d(x, y) = d(y, x); i.e. d is symmetric. • The function d ...
Functional analysis - locally convex spaces
... S is an irreducible family of seminorms on the former. If S is a family of seminorms which separates E, then the space (E, S̃) is the locally convex space generated by S. If (E, S) is a locally convex space, we define a topology τS on E as follows: a set U is said to be a neighbourhood of a in E if ...
... S is an irreducible family of seminorms on the former. If S is a family of seminorms which separates E, then the space (E, S̃) is the locally convex space generated by S. If (E, S) is a locally convex space, we define a topology τS on E as follows: a set U is said to be a neighbourhood of a in E if ...