Monday, 17 February 2014

Differentiation - what is it?

Okay so in Maths we learn about differentiation and what to do, the formulas etc, but what is differentiation???

Differentiation is finding the slope of a curve at a particular point on the curve.

Eg:



But how do we find slopes?

First consider a straight line:



We get the slope of a straight line by taking two points on the line and using their co-ordinates (x1, y1) and (x2, y2) in a slope formula:



From functions, we know that a point x has a height of f(x), (i.e. y = f(x) ) :





 Something else to consider is that the slope at a point on a curve is the same slope as the tangent at that point





So if we know two points on the tangent we can work out the tangent slope and thus the curve slope.


Next we require some limits and some imagination.


Picture our curve and tangent:
 


Now zoom in on our point:





And again:


And again... It's getting hard to distinguish between the two lines.

We can soom in infintely until they appear as practically the same line! so we can now say that two points on the curve are now alone on the tangent, a distance of  'h' apart.



The second point becomes (x+h, f(x+h) )

If we make the distance 'h' between the two points as small as possible t will appear as if they are the same point.


Beacause we have two points we can use our slope formula

  

Using our co-ordinates (x, f(x) ) and (x+h, f(x+h) ) this formula becomes:

f(x+h) - f(x) 
(x+h) - x

Subtracting the 'x' on the bottom lines makes this:

f(x+h) - f(x) 
h

Now we wat to make the 'h' as small as possible so we limit h - 0



  Slope = lim  f(x+h) - f(x) 
       h-0           h

This is our differentiation formula!


We can apply this to any curve:

Example:




Sunday, 16 February 2014

Home Ec notes - Carbohydrates

Here are some notes on Carbohydrates, just like the protein ones I have up. There will also be fat notes up in the next week or two when i get the chance to write them out. Hope these help.Any questions/comments/requests feel free to comment :)












Home Ec - Protein notes

I know I have already put up notes on protein but these are the actual notes I have I dont know if I typed all of it when I put them up before. hope they are a help. I will have carbohydrate notes up in the next half an hour. 











Tuesday, 27 August 2013

Home Ec - Protein

Protein

Elemental Composition:
  • Carbon (C)
  • Hyrdrogen (H)
  • Oxygen (O)
  • Nitrogen (N)
 And sometimes:
  • Sulpher (S)
  • Phosphorous (P)
  • Iron (fe)

Chemical Composition:
                                       
                           H                                                         H = hydrogen
                            |                                                          NH2 = Amino Group
                            |                                                          C = Carbon
         NH2------ C -------COOH                                  COOH = Carboxyl group 
                            |                                                          R = variable eg is H in Glycine
                            |
                           R


Essential amino acids are the amino acids that cannot be synthesised (made) by the bosy and must be obtained from food.
                    Eg. Threonine, Methionine, Lysine, Valine

Non-essential amino acids are the amino acids that can be synthesised by the body.
                    Eg. Serine, Alanine






Formation of a peptide link:




 


·        The H from the amino group of amino acid number 1 joins with the OH from the Carboxyl group of the second amino acid

·     This makes H2O

·     Results in formation of peptide link and a water molecule

·     Condensation reaction





The reverse of this is Hydrolysis

Where water is added back into the protein to break the bonds

Eg digestion of food






Structures:
Three Types:      1. Primary structure

                             2. Secondary Structure

                             3. Tertiary structure



Primary Structure

·        The Number and order of amino acids on a polypeptide/protein chain.

Eg Insulin is mad up of 50 amino acids arranged in a definite            order





Secondary Structure

·        The further folding of the primary structure to give a definite shape



·        The folding is caused by links or bridges:

o   Di-sulphide link

o   Hydrogen bond



Di-sulphide link

·        Amino acid cysteine contains sulphur

·        Two Cysteine units on the same chain, or chains side by side, join and a di-sulphide link is formed



Hydrogen bond

·        Hydrogen from one amino acid joins with oxygen from another amino acid. Eg collagen 





Tertiary structure

·        The further folding of the secondary structure to give a 3-D shape.

·        Can be fibrous or globular



Fibrous – straight, curved or zigzag

E.g. elastin in meat



Globular – spherical in shape

E.g. ovalbumin in egg white







Classification of proteins:



1.   Simple Proteins -       From animals and plants

Contains only protein



2.   Conjugated Protein -          Contains a protein and a non-protein



3.   Derived Protein -        made by chemical or  enzymic action

From another protein

E.g. Caesinogen in milk to caesin











Sources of protein

Animal                                             Plant
Meat                                                 Pulse veg – peas, beans, lentils
Fish                                                  Nuts
Milk                                                 Cereals
Eggs                                                 Seeds
Cheese                                                          

                                                                                     Pulse veg – a veg that
                                                                                      grows in a pod