Class Notes 1-5-2010: Difference between revisions

Revision as of 15:39, 17 January 2010

1) Linear Systems

2) Functions as Vectors

Modeling functions as vectors. Using function approximations, the vector path is described.

Function waves with varying periods based on the function x(t) = x(t+T)

v_{x} = \vec{v} \cdot \hat{i}

\hat{v} = v_{x} \hat{i} + v_{y} \hat{j}

\hat{v} = \sum_{i} v_{i} {\hat{a}}_{i}

⟨ v_{x}, v_{y} ⟩

\hat{u} \cdot \hat{v} = | \hat{u} | | \hat{v} | \cos θ

x (t) = \sum_{n = 1}^{\infty} [b_{n} \sin ((\frac{2 π n}{T}) t)]

Colby Fullerton

Brian Roath

@@ Line 16: / Line 16: @@
 :<math> \mathbf{\hat{v}} = v_\mathrm{x} \mathbf{\hat{i}} + v_\mathrm{y} \mathbf{\hat{j}} </math>
 :<math> \mathbf{\hat{v}} = \sum_{i} v_\mathrm{i} \mathbf{\hat{a}}_\mathrm{i} </math>
+:<math> \langle v_x, v_y\rangle</math>
+:<math> \mathbf{\hat{u}} \cdot \mathbf{\hat{v}} = |\mathbf{\hat{u}}| |\mathbf{\hat{v}}| \cos\theta </math>
 :<math> x(t) = \sum^\infty_{n=1} \left[ b_n \sin \left( \left( \frac {2\pi n} {T} \right) t \right) \right] </math>