Neuron Communication

Neuron Structure:

There are three main types of neutrons, each with similar but slightly  different structures. These neutron types include Interneurons, sensory neurons, and motor neurons, each shown below. These three neuron diagrams each consist of an axon, dendrites, a cell body, and a nucleus (real neurons also possess a myelin sheath as well as terminal branches/bulbs).

 

Interneuron: 

In this diagram the dendrites are shown in yellow (thinner branch-like projections) at the ends of the axon which is also modelled in yellow and are the longer and thicker arms radiating out of the center.

In the centre is the cell body (soma) shown in pink which contains the nucleus (shown in orange).

 

 

 

Motor Neuron:

In this diagram the dendrites are shown in pink and once again resemble rather thin, branch-like projections. The axon is modelled in pink and is the longer thicker arm that radiates downwards towards the axon terminals at the bottom of the diagram.

The cell body (soma) is shown in orange and the nucleus is shown in yellow.

 

 

Sensory Neuron:

In this diagram, the axon (shown in orange) is the long segment that runs down the middle, the dendrites and axon terminals are shown also in orange ateihter end of the neutron.

The cell body (soma (shown in pink)) is not located along the axon in sensory neurons, it is instead found more outside of the rest of the cell. The nucleus is located within the cell body and is shown in pink.

 

 

 

Neuron Function:

How does an Action Potential (AP) move along the nerve fibre?

Resting Potential– resting potential is the state of the axon before and after and after action potential has passed through. In this state, the inside of the axon has a voltage of approximately -70mV, therefor, the inside of the axon is negatively charged.

Depolarization- when an electrical stimulation travels down the axon in a chain reaction the incoming message triggers depolarization, depolarization is the process of the axon opening channels in its membrane that allow only Na+ to pass through from the outside of the axon to the inside.

Repolarization- repolarization occurs when channels open in the axon membrane to allow K+ ions to leave the axon and replace Na+ on the outside of the axon, here the voltage will drop slightly below typical resting potential voltage but then quickly return to resting potential —> the next segment of the axon is now going to depolarize.

 

Synapse Structure:

provided by the Queensland Brain Institute

 

The Synapse, demonstrated in the diagram to the left is the space or “gap” between the axon terminal of one neuron and the dendrite of another neuron. Other structures present at the synapse include neurotransmitters, synaptic vesicles, and receptor sites. the synapse also has a membrane (synaptic membrane) that allows for optimal diffusion of neurotransmitters.

 

Synapse Function:

the synapse is the name of the tiny space present between the axon terminal buttons and the receiving ends of dendrite from other neurons. At the axon terminal buttons neurotransmitters (NT) are produced and stored within synaptic vesicles. when an action potential (AP) reaches an axon terminal, it causes the synaptic vesicles to release the NT into the synaptic gap, NT’s will then diffuse through the gap where they will bind to receptors on the receiving dendrite of the next neuron. The receptor can be either excitatory or inhibitory and this is what determines whether or not the effects of the NT will be felt. Enzymes are also present in the synaptic gap to recycle NT’s, without the recycling of NT’s the effects of the NT would be everlasting.

 

 

 

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 18- Top 5 Things I Learned

The semester is coming to an end, this class has been one of the most difficult but also rewarding classes I’ve ever taken as into has taught me not only the importance of C, D, P, E, U, but it has also taught me things about myself and my learning. Here are the top 5 things I’ve learned throughout the course of the last semester in Pre-calculus 11.

1. Factoring:

factoring is extremely important! This is possibly the most important skill to have/concept to understand in all of pre-calculus 11. It is by far the most relevent and repeated idea throughout the entire course. Factoring reappears in over half of the chapters as it is necessary for units like inequalities, Quadratics, as well as reciprocal functions etc…

 

2. Geometric vs Arithmetic, Sequence vs Series:

This unit was our very first unit that we completed in the class, I thought this unit was important to add to this post because of how different it is from any of the other units and thus slightly more difficult to remember. An Arithmetic sequence is a constant addition from on term to the next in a predictable pattern. An Arithmetic series is still dealing with addition (as it is Arithmetic) however it focuses on the sum of all of the terms within the pattern. A geometric sequence deals with constant multiplying as opposed to adding, and a geometric series one again focuses on the sum of all of the combined terms within the pattern.

3. Special Triangles:

I found special triangles to be quite interesting, I enjoyed their predictability and accuracy. We learned about 2 special triangles one being originally part of a square that had been cut in half diagonally (1:1: \sqrt{2} , the other from an equilateral triangle that had been cut directly down the Center (1:2: \sqrt{3}

 

4. Absolute Value:

At first I found understanding absolute value to be quite difficult, I had this concept explained to me in a few different ways and I think that the easiest way to understand it was to think of it on a number line, the absolute value is telling us how many units away from zero that value is located.

 

5. Completing the Square:

Completing the square is a “technique” used to convert standard equation forms into general (also known as vertex) form, this form of an equation gives you a very clear vertex point which can be very important when graphing. I personally found this completing the square method difficult at first, likely because there are a fair few steps to remember when applying this method.

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 16- Applications of Rational Equations

Applications for Rational Equations are questions relating rational equations to real life situations and circumstances.

Hints/Steps:

1. Read through problem carefully to understand what is being asked

2. Decide where you will need to introduce a variable in place of an unknown number

3. Create an equation based on the given information

4. Solve the equation

5. Express answer in a full sentence and check that the solution makes sense for what was being asked

Note: there are 4 types of applications

1. Problems involving distance, speed, and time

2. Problems involving proportions

3. Problems involving motion

4. Problems involving work

 

Example:

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 17- Trig Summary

GENERALLY

Trigonometry definition:

trigonometry can be defined as simply as the mathematics involving the relationships between side lengths and angles of a triangle.

New vocabulary:

terminal arm: the line found within any of the 4 quadrants, creating an angle

coterminal angles: angles that share the same initial and terminal sides

quadrantal angles: angles that lie directly on the x and/or y axis (ie. 0°, 360°, 90°, 180°, 270°)

Rotational angle: the angle between 0° and the terminal arm

reference angle: the angle measured between the closest seperation of the x-axis and the terminal arm.

 

LESSONS SUMMARY

6.1 General updates-

Calculating the reference angle:      ref angle= 180 – 92= 88°

calculating the coterminal angle: 

hypotenus=radius

sides= x & y

a^2+b^2=c^2 ——> x^2+y^2=r^2

6.2 Exact Trig Values

sin=y/r, cos=x/r, tan=y/x

To remeber in which quadrants each ratio is positive: CAST rule

Special Triangles

originally a square:

originally an equilateral triangle:

The Sine Law

\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}

this formula can be modified so that the variable for which you are solving (either an angle or side) can be solved in fewer steps.

The Cosine Law

To be used if there are no angles with corresponding side lengths given and thus sine law will not work

 

 

 

 

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 15- Fractional Equations

This week in chapter 7.5 we began solving Fractional Equations, when dealing with Fractional equations it’s important to remember that you must SOLVE as opposed to SIMPLIFYING, which is related to expressions as opposed to equations. This also means that after solving you should be left with a value that will be equal to x.

There are two types of Fractional equations, there are “simple” equations and there are “ugly” equations.

Solving Simple Equations:

When you are given two simple fractions you may CROSS MULTIPLY:  this is accomplished by multiplying each numerator by the opposite denominator this will get rid of the fraction and you will be left with a much simpler fraction-free equation, from there, you must isolate x.

 

Solving Ugly Equations:

when solving an “ugly equation, or an equation with either more than one fraction, or polynomial fractions etc… MULTIPLY BY THE DENOMINATOR: First determine the common denominator, then divide the common denominator by the original denominator from each fraction and then multiply the remainder by the numerator. Lastly, solve to isolate x (or any variables in the equation).

this method is suitable for any kind of Fractional equation (ie. it will always work).

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 14- Equivalent Rational Expressions

This week we began chapter 7, the first lesson of chapter 7 was on equivalent rational expressions for example \frac{1}{2},\frac{2}{4},\frac{4}{8} are all equivalent rational expressions, also known as fractions. The definition of a rational number is “the quotient of two integers” whereas a rational expression can be defined as “the quotient of two polynomials”.

Since these are simply expressions as opposed to equations it means that all we can do is SIMPLIFY the expression (ie. reduce the fraction until it’s in its simplest form), if it were an equation we would be able to SOLVE the equation (ie. determine the value of the variable).

steps:

1. Determine the non-permissible values before simplifying. Non-permissible values are the same a son restrictions and will result in an answer that is “undefined”.

2. Reduce and Simplify, sometimes you may have to Factor the expression until it’s in simplest form.

3. Verify, You can test the equivalency of two fractions by replacing the variable with any value, if the reduced fractions are the same then the fractions are equivalent.

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 13- Reciprocal Functions

In this lesson (8.3,4,5) we started graphing and understanding reciprocal functions of linear and quadratic equations.

Reciprocal linear functions:

Reciprocals of linear functions will always create a “2 part graph” this is referred to as a hyperbola, a hyperbola of a linear graph will always have two “swooping L” shaped lines exactly opposite each other in opposite quadrants of the graph. Ex. Located in top left and bottom right quadrant.

Reciprocal quadratic functions:

Reciprocals of quadratic functions, similarly to linear functions will also create a hyperbola, however it may sometimes look slightly different, for example you may have two “swooping L’s” each on the same side of the graph (positive or negative), you may even have a third section on your graph if the parabola dips below the X axis and into the negative section of the graph. Reciprocal graphs of quadratic functions may even yield 2 or three asymptotes and as many as 4 invariant points.

New vocabulary:

critical points- the point upon which the line on the graph abruptly changes direction

invariant points- 1, and -1, points that remain the same when’s reciprocated

asymptotes- invisible lines that cross the x and y intercepts And “reorganize/separate” sections of the graph, these are the undefined values.

 

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 12- Absolute value and reciprocal functions

This week we started the “Absolute value and reciprocal functions” unit. This first lesson focused mainly on the shape of the graph that will result from graphing an absolute value of both a line and a parabola.

When you graph the absolute value of an equation, any part of the line or parabola that may drop below the X axis (ie. is a negative value) will “flip up” to the positive section of the graph. When the previously negative section of the graph moves up into the positive section it should be COMPLETELY SYMMETRICAL to its previous position on the negative half of the graph and it resembles a “mirror image”. This is because the values are the same except positive, they are exactly the same distance from zero.


On a linear graph (has only a line, no parabola). There is one singular point where the graphs negative values are “flipped” so that they are positive, this point is referred to as the critical point, this causes the graph to look like a big “V” but this DOES NOT make it the same as a parabola, it is still a linear graph.

 

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 11- Graphing quadratic inequalities in 2 variables

Similarly to graphing linear inequalities in 2 variables, the goal is to determine where on the graph is the solution “true”. When talking about linear 2 variable inequalities, the graph will be shaded one side of the line (the shaded side contains the solutions that make the equation “true”). However, since every quadratic equation will be graphed as a parabola instead of a line, the shaded are where the solutions will be found is the area found inside the curve of the parabola.

Steps:

1. Determine all that can be determined by the given inequality ie. opens up/down, congruent to___, the y intercept etc…

2. if the inequality is presented general form, Factor (to determine the axis of symmetry and thus the vertex), factor to find the zeros, then add the value of the zeros together and divide that number by 2, this is the axis of symmetry.

3. Graph the inequality.

4. Use a Test Point to establish weather the inside or the outside of the graph contains the solutions.

5. Shade the area where the solutions are found.

Example:

Leave a Reply

Your email address will not be published. Required fields are marked *

Week 10- Infinite Geometric Series

In an infinite geometric series, the series gradually and eventually diverges or converges, this means that there may not always be a determinable sum because the values will continue increasing and there will theoretically always be another value in the series; it’s never ending I.e infinite

 

Infinite vs Finite series:

In a Finite series, n will always have a determined or determinable value because it is converging. This value can be calculated using the formula S_n=frac\{a(r^n-1)}{r-1}. In an Infinite geometric series however, n is Infinite due to it’s converging or diverging nature and therefor S_n cannot be determined using the same formula. Instead we use the formula S_infty=frac\{a}{1-r} as demonstrated below.

Converging:

12, 6, 3…

r=o.5

S_infty=frac\{a}{1-r} S_infty=frac\{12}{1-0.5} S_infty=frac\{12}{0.5} S_infty=24

 

diverging:

2, 8, 32…

r=4

NO POSSIBLE SUM

Leave a Reply

Your email address will not be published. Required fields are marked *