summation

Examples of summation in the following topics:

• Summation Notation

  • Use summation notation to express the sum of a subset of numbers
  • Fortunately there is a convenient notation for expressing summation.
  • This section covers the basics of this summation notation.
  • The Greek letter Σ indicates summation.
  • The "i = 1" at the bottom indicates that the summation is to start with X1 and the 4 at the top indicates that the summation will end with X4.The "Xi" indicates that X is the variable to be summed as i goes from 1 to 4.

• Signal Summation

  • Signal summation occurs when impulses add together to reach the threshold of excitation to fire a neuron.
  • Summation, either spatial or temporal, is the addition of these impulses at the axon hillock .
  • Together, synaptic summation and the threshold for excitation act as a filter so that random "noise" in the system is not transmitted as important information.
  • Spatial summation means that the effects of impulses received at different places on the neuron add up so that the neuron may fire when such impulses are received simultaneously, even if each impulse on its own would not be sufficient to cause firing.
  • Temporal summation means that the effects of impulses received at the same place can add up if the impulses are received in close temporal succession.

• Summation Notation

  • Fortunately there is a convenient notation for expressing summation.
  • This section covers the basics of this summation notation.
  • For finite sequences of such elements, summation always produces a well-defined sum.
  • This can be achieved by using the summation notation "$\Sigma$ " Using this sigma notation, the above summation is written as:
  • In this notation, $i$ represents the index of summation, $a_i$ is an indexed variable representing each successive term in the series, $m$ is the lower bound of summation, and $n$ is the upper bound of summation.

• Interactions of Skeletal Muscles

  • Skeletal muscles interact to produce movements by way of anatomical positioning and the coordinated summation of innervation signals.
  • This addition is termed summation.
  • Within a muscle summation can occur across motor units to recruit more muscle fibers, and also within motor units by increasing the frequency of contraction.
  • Repeated twitch contractions, where the previous twitch has not relaxed completely are called a summation.
  • Explain the summation interactions of skeletal muscles and how they affect movement

• Series and Sigma Notation

  • Summation is the operation of adding a sequence of numbers, resulting in a sum or total.
  • For finite sequences of such elements, summation always produces a well-defined sum.
  • One way to compactly represent a series is with sigma notation, or summation notation, which looks like this:
  • In this formula, i represents the index of summation, $x_i$ is an indexed variable representing each successive term in the series, $m$ is the lower bound of summation, and $n$ is the upper bound of summation.
  • The "$i = m$" under the summation symbol means that the index $i$ starts out equal to $m$.

• Sums and Series

  • The summation of all the terms of a sequence is called a series, and many formulae are available for easily calculating large series.
  • Summation is the operation of adding a sequence of numbers; the result is their sum or total.
  • If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.
  • where $i$ represents the index of summation; $x_i$ is an indexed variable representing each successive term in the series; $m$ is the lower bound of summation, and $n$ is the upper bound of summation.
  • The "$i=m$" under the summation symbol means that the index $i$ starts out equal to $m$.

• Building the commitment for change (a summation)

• Market Supply

  • Market supply is the summation of the individual supply curves within a specific market where the market is characterized as being perfectly competitive.
  • Market supply is the summation of the individual supply curves within a specific market.

• Oscillator Strengths

  • There are several summation rules that restrict the values of the oscillator strengths,
  • where $N $ is the total number of electrons in the atom and the summation is over all the states.
  • One must include transitions to the continuum in this summation.

• Postsynaptic Potentials and Their Integration at the Synapse

  • Postsynaptic potentials are subject to spatial and temporal summation.
  • This figure depicts the mechanism of temporal summation in which multiple action potentials in the presynaptic cell cause a threshold depolarization in the postsynaptic cell.