Tutor profile: Alex W.
Subject: Linear Algebra
What is linear algebra?
Linear algebra often involves the use of Matrices in order to solve several simultaneous equations. At school you may have solved two or three simultaneous equations but they quickly become incredibly time consuming when you have more than this. Use of matrices enables n simultaneous equations to be solves for n unknowns (x,y,z etc) with n constraints, such as 3x+2y+5z=20
What is SOHCAHTOA
SOHCAHTOA describes the fundamental relationship between sides and angles in a triangle. What is allows us to do when used is determine several properties of a triangle depending on what we know already. For example, if we know the length of the hypotenuse and adjacent sides of an angle, then we can work out the angle itself using the relationship: cos(angle)=Adjacent/Hypotenuse.
Describe the fundamental theory of differentiation
Differentiation involves working out the gradient of a function at a point on the graph. That is at any x coordinate what is the gradient (slope) of the function here. A gradient (slope) is a measure of how much the graph changes in y value for each change in x value. Think of a road. A steep road has a large gradient and it rises quickly therefore there is a large change in its vertical value (y) for each change in its horizontal value (x). Unlike thinking of average slope, gradient corresponds to a single point on the graph, and can change quite significantly with small changes in x. The notation for a gradient it dy/dx which translates to change in y with each change in x. The 'd' is from the Greek 'Delta' which means 'change in' in maths notation.
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