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### Questions (22)

 6 When is a symmetric matrix invertible? 5 What does it mean for something to be strictly less than $\epsilon$ for an arbitrary $\epsilon$? 4 Is this book implying that elliptic PDE is the only one that can be minimized by calculus of variations? 3 What is the role of the recourse variable in stochastic programming? 3 How is the Jacobian $J_{h(g(x))}=J_f$ of composed function $f(x)=h(g(x))$ a sum of the gradients of g, $\nabla g_i(x)$ weighted by $g_i(x)$?

### Reputation (170)

 +25 What does it mean for something to be strictly less than $\epsilon$ for an arbitrary $\epsilon$? +5 Let $f:[a,b] \rightarrow \mathbb{R}$ is cts with $f(a), f(b) < 0, \int_a^b f(x)dx \ge 0$. Show $\exists c \in (a,b) s.t. \int_c^b f(t) dt \ge 0$. +5 Let $f: D \rightarrow \mathbb{R}$ be strictly increasing. Show that if $f(D)$ is an interval then $f$ is continuous. +5 What is the role of the recourse variable in stochastic programming?

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### Tags (51)

 0 linear-algebra × 7 0 linear-transformations × 3 0 matrices × 5 0 ordinary-differential-equations × 2 0 calculus × 5 0 pde × 2 0 real-analysis × 5 0 symmetric-matrices × 2 0 convex-optimization × 3 0 lebesgue-measure × 2

### Accounts (5)

 Mathematics 170 rep 18 Stack Overflow 18 rep 4 Cross Validated 11 rep 2 The Workplace 1 rep Medical Sciences 1 rep