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Let's begin by reviewing a fairly simple (linear) equation: (1) y = 2x + 3 (1) describes the relationship between two variables, x and y . Given a value for one, we can use (1) to work out the value of the u...

First, we use the idea that a complex number z can be written in terms of its real and imaginary parts, i.e. z = x+iy, to write our expression as: | x+ iy -5 - 3i | = 3 Next, we can group the real and imagin...

What is first principle? Why does it look nothing like the differentiation I had been doing for the past few years? Differentiation from first principle is the main idea behind differentiation, a technique w...

Take a matrix A=( a c b d ), where a,b,c,d are numbers. First find the determinant. This is a d-b c. Now, rearrange the matrix to become ( d -c -b a ). Divide this by the determinant, to have A -1 = 1 / (ad-...

Take any polynomial, eg/ y=x 3 + 1 / 2 x 2 -3x+9. Then dy / dx =3x , +x-3, in this case. This is because, when deriving in this sense, you take each term in x, multiply it by its index, and reduce that index...