Search over 10,000 free study notes

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-...

For this explanation we will use the following example from a 2013 exam paper: If u 1 = 2 and u n+1 =(5u n -3)/(3u n -1), then prove that u n =(3n+1)/(3n-1) for all n>=1 The first step of any proof by ind...

To differentiate tan(x): Note: Here, we use d/dx f(x) to mean "the derivative of f(x) with respect to x". 1) rewrite tan(x) as sin(x)/cos(x) 2) Apply the quotient rule (or, alternatively, you could...