A partial fractions decomposition can be useful if we want to compute an integral where the functions p(x) and q(x) are polynomials in x. This post explains, how such a decomposition works and how this method helps to simplify such integrals. At first we notice that the problem lies in the polynomial q(x) of theContinue reading “How to integrate by partial fractions”
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How to solve a system of linear equations
This post explains how to find the solutions of any system of linear equations with an arbitrary number of variables, if solutions exist. The method consists of the following three steps:
Using Gauss elimination we write the system in triangular form.
In this format, we see whether the system has either no solution, exactly one solution or infinitely many solutions.
If there are solutions, we determine them by simple insertions.
How to divide by a complex number
When we divide a complex number by another one, say we usually want to obtain the result in standard form. So how do we simplify a quotient such that the result takes the form ? The answer is: We multiply the numerator and the denominator of the quotient by the complex conjugate of theContinue reading “How to divide by a complex number”
math for physicists 