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Possibly this is a slightly old question... An "introduction to control theory" course sounds unlikely to cover this stuff, but one of the control courses in the Masters' year I'm in right now includes topics that might be of interest to you: Convex optimisation Semi-definite programming to guarantee stability Distributed algorithms (most ...


I'm not doing notation for this, it's simple algebra. X = 1,000,000 = 5000 / .1 * ((1.1)^n - 1) 1,000,000 = 50,000(1.1)^n - 50,000 1,050,000 = 50,000(1.1^n) divide both sides by 50,000 21 = 1.1^n etc.


differential derivation The displacement vector is defined as : $$\vec{u} = u_{r}\mathbf{\vec{e}_r} + u_{\theta}\mathbf{\vec{e}_\theta}+u_{z}\mathbf{\vec{e}_z} $$ by derivation you can obtain all the relevant strains. geometrical derivation One way to derive the strain tensor is from geometry. The diagonal (normal) components $\epsilon_{rr}$ , $\epsilon_{...


Taylor is straightforward: $$ \sqrt{1+2x} =\left.\sqrt{1+2x}\right|_0 +\left.{d \over dx}\sqrt{1+2x}\right|_0x +O(x^2) \\ =1 +\left.{d \over dx}{1 \over \sqrt{1+2x}}\right|_0x +O(x^2) \\ =1 +x +O(x^2) \\ $$ Note that Taylor holds for matrices variables under some conditions. ps.If you can handle it, you also have the Generalized Binomial Expansion for ...

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