• Many Mexican-Americans worked as migratory laborers + outside programs
• Indian Reorganization Act of 1934
• Woman were paied less
• Environmental cost of damns and public projects

commentary on the effects of the New Deal

Incorporating aspects of Arthur M. Schlesinger’s Appraisal of the New Deal, William E. Leuchtenburg’s Appraisal of the New Deal, Anthony Badger’s Appraisal of the New Deal.

Through the analysis of the New Deal programs, what was particularly salient was Anthony Badger’s framing of the event as not one that is ultimately “successful” or “failed” but instead one which focuses on its long-term effects in context with the future policies. The equivocal labeling allows nuance that places the Deal properly in its historical content. According to Badger, helping the poor, a significant policy goal of the deals, were left as “unfinished business” when going to war. This idea contrasts with William E. Leuchtenburg’s framing of the same event—that it was never the true intention of the deal to assist in subsidies on a humane level, but that which supported the economy and incidentally those that reaped benefits on it.

For an ODE, eigensolutions of some expression \(x’=Ax\) consists of the class of solutions which remains in a line through the origin, which consists of the family which:

\begin{equation} x(t) = ke^{\lambda t} v \end{equation}

where \(\lambda\) is an eigenvalue of \(A\), and \(v\) its corresponding eigenvector.

motivation

\begin{equation} y’ = F(y) \end{equation}

an autonomous ODE, suppose we have some solution \(y=a\) for which \(y’ = 0\), that is, \(F(a) = 0\), we know that the system will be trapped there.

The eigenspace of \(T, \lambda\) is the set of all eigenvectors of \(T\) corresponding to \(\lambda\), plus the \(0\) vector.

constituents

• \(T \in \mathcal{L}(V)\)
• \(\lambda \in \mathbb{F}\), an eigenvalue of \(T\)

requirements

\begin{equation} E(\lambda, T) = \text{null}\ (T - \lambda I) \end{equation}

i.e. all vectors such that \((T- \lambda I) v = 0\).

where, \(E\) is an eigenspace of \(T\).

additional information

sum of eigenspaces is a direct sum

\(E(\lambda_{1}, T) + … + E(\lambda_{m}, T)\) is a direct sum.

see Extended Kalman Filter

The Elastic Modulus is a measurement of how much deformation takes place given some force on the system. Formally, it is the slope of the stress-strain curve, defined by:

\begin{equation} E = \frac{stress}{strain} \end{equation}

The units in pascals as it is: force per area (pascals) divided by deformation (dimensionless, as it is a fraction of old shape over new shape \(\frac{V}{V}=1\)).

Depending on how its measured, it is called different things:

• Young’s Modulus: tensile elasticity—tendency for object to deform along an axis with force applied (usually that is just called the Elastic Modulus)
• Shear’s Modulus: shear elasticity—tendency of an object to shear (deform in shape with the constant volume) with force applied
• Bulk Modulus: volumetric elasticity—tendency for an object to deform in all directions when uniformly loaded