New Left

Examples of New Left in the following topics:

• Student Rebellions and the New Left

  • The New Left drew inspiration from black radicalism, particularly the Black Power movement and the left-wing Black Panther Party.
  • By 1962, the SDS had emerged as the most important of the new campus radical groups; soon it would be regarded as virtually synonymous with the New Left.
  • The media began to cover the organization and the New Left.
  • The fall of 1967 saw a great escalation of the anti-war actions of the New Left.
  • Outline the course of New Left politics, especially the Students for Democratic Society

• Solving Systems of Equations in Three Variables

• Transformation of Radiative Transfer

  • $\displaystyle p'_t = \gamma \left ( p_t - \beta p_x \right ) \\ p'_x = \gamma \left ( p_x - \beta p_t \right ) \\ p'_y = p_y \\ p'_z = p_z .$
  • $\displaystyle \gamma \left ( 1 - \beta \frac{p_x}{p_t} \right ) = \frac{\gamma \left ( p_t - \beta p_x \right )}{p_t} = \frac{p_t'}{p_t}.$
  • $\displaystyle \gamma \left (x_A - \beta t_A \right ) = v' \gamma \left (t_A - \beta x_A\right ) + x_A(0)$
  • Notice how the particle travels at a different velocity in the new frame and the relativistic addition of velocities.Now we find that
  • $\displaystyle \displaystyle \gamma \left ( 1 + \beta v' \right ) = \frac{\gamma\left ( p'_t + \beta p'_x \right ) }{p'_t} = \frac{p_t}{p'_t}$

• A few examples

  • $A = \left[ \begin{array}{cc} 3 & 1 \\ 0 & 3 \\ \end{array} \right]$
  • $\left[ \begin{array}{ccc} -2 & 1& 0 \\ 1 &-2& 1 \\ 0 &1& -2 \end{array} \right] \left[ \begin{array}{c} a \\ b \\ c \end{array} \right] = \left[ \begin{array}{c} 0 \\ 0 \\ 0 \end{array} \right]$
  • $\left[ \begin{array}{cc} a & b\\ b & d \end{array} \right] \left[ \begin{array}{c} x \\ y \end{array} \right] = \left[ \begin{array}{c} 0 \\ 0 \end{array} \right]$
  • and apply it to the two unit vectors, we get two new vectors that form a different box.
  • $\left[ \begin{array}{cc} 1 & -1 \\ 0 & 0 \end{array} \right] \mbox{ and } \left[ \begin{array}{ccc} 0 & 0 & 0\\ 0 & 0 & 0 \end{array} \right]$

• Equations with Absolute Value

  • Set up two separate equations: For the first, keep the new equation you found in step 1, but remove the absolute value signs; for the second, keep the equation you found in step 1, remove the absolute value signs, and multiply one side by -1.
  • $\begin{aligned} 3 \left| 2x+1 \right| -7 +7 &=5 +7 \\ 3 \left| 2x+1 \right| &= 12 \\ \dfrac{3 \left| 2x+1 \right|}{3} &= \dfrac{12}{3} \\ \left| 2x+1 \right| &=4 \end{aligned} $
  • In this image, for example, $\left | -3 \right |=3$.

• Quebec, New York, and New Jersey

  • In the early stages of the American Revolution, battles over Quebec, New York, and New Jersey played an important role in the war.
  • A simultaneous expedition left Cambridge, Massachusetts under Benedict Arnold and traveled with great difficulty through the wilderness of Maine to Quebec City.
  • This arduous trek left Arnold's surviving troops starving and lacking in basic supplies and equipment.
  • News of the capture of New York was favorably received in London, and General Howe was awarded the Order of the Bath for his work.
  • That night, Washington stealthily moved his troops again, intending to attack the garrison Cornwallis left at Princeton.

• Introduction to Ellipses

  • The general equation of an ellipse centered at $\left(h,k\right)$ is:
  • For simplicity, we will choose that center to be $\left(0,0\right)$, the origin of the $x$-$y$ plane.
  • Every $x$-value that solved the old equation must now be multiplied by $a$ in order to solve the new equation.
  • The ellipse $x^2 +\left( \frac{y}{3} \right)^2 = 1$ has been stretched along the $y$-axis by a factor of 3 as compared to the circle $x^2 + y^2 = 1$.
  • The ellipse $\left( \frac{x}{3} \right)^2 +y^2 = 1$ has been stretched along the $x$-axis by a factor of 3 as compared to the circle $x^2 + y^2 = 1$.

• Tensors

  • Let's use the Lorentz matrix to transform to a new frame
  • $\displaystyle \Delta f = f \left (x^{\mu} + \Delta x^\mu \right) - f \left (x^{\mu}\right) \label{eq:300}$
  • $\displaystyle A^\mu = \left [ \begin{array}{c} \phi \\ {\bf A} \end{array} \right ],$
  • $\displaystyle J^\mu = \left [ \begin{array}{c} c \rho \\ {\bf J} \end{array} \right ].$
  • $\displaystyle {\bf p}{t} = q \left ( {\bf E} + \frac{\bf v}{c} \times {\bf B} \right )$

• Inverse Trigonometric Functions

  • As with other functions that are not one-to-one, we will need to restrict the domain of each function to yield a new function that is one-to-one.
  • $\displaystyle{y = \sin^{-1}x \quad \text{has domain} \quad \left[-1, 1\right] \quad \text{and range} \quad \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]}$
  • $\displaystyle{y = \cos^{-1}x \quad \text{has domain} \quad \left[-1, 1\right] \quad \text{and range} \quad \left[0, \pi\right]}$
  • $\displaystyle{y = \tan^{-1}x \quad \text{has domain} \quad \left(-\infty, \infty\right) \quad \text{and range} \quad \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)}$
  • (a) The sine function shown on a restricted domain of $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$; (b) The cosine function shown on a restricted domain of $\left[0, \pi\right]$.

• Thinking Politically

  • Similarly, the American Revolution brought an end to British sovereignty over its American colonies in the New World.
  • The result was the Declaration of Independence and the birth of a new state, The United States of America.
  • Similarly, the American Revolution brought an end to British sovereignty over its American colonies in the New World.
  • Their function is to enforce existing laws, legislate new ones, and arbitrate conflicts via their monopoly on violence.
  • Left-wing politics and right-wing politics are often presented as opposed, and although a particular individual or party may take a left-wing stance on one matter and a right-wing stance on another, the terms left and right are used to refer to two globally opposed political families.