The Science of Life Lecture Series

Hello internet, and welcome to the Algebra Lecture Series from the Science of Life.  This time, we are focusing on an introduction to the algebra of functions, or taking two or more functions and applying the algebraic functions in order to combine these functions. If we have two functions $f(x)$ and $g(x)$ which have the same domain, then applying the same x-value to them and performing a mathematical operation on them yields a single value.  It is important that they either have the same domain or have overlapping domain, since this is the only way that there would be a non-zero value for each function.  For example, a florist cannot physically store a negative quantity of flowers nor an amount of flowers greater than the physical space available.  Therefor, the domain is from 0 to some finite number determined by the physical space.  The same applies for other plants.  So flowers and plants have the same domain. One mechanism for applying an oper...

Hello internet, and welcome to the Algebra Lecture Series from The Science of Life.  This entry is an introduction to Linear Functions in both graphs and models. There are two situations where the slope would not be stated in the slope-intercept form.  These are cases where the line crosses only one of the 2 (or more) axes. First, let's consider the horizontal line.  If we have a line which has a y-intercept but does not have an x-intercept (does not cross the x-axis), it is called a horizontal line.  Let's look at it from the point of view of the slope-intercept form we developed last time, $y=mx+b$.  We know that the slope is the change in the y-value per change in the x-value.  If we have two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$, the slope is mathematically defined as $m=\frac{y2-y1}{x2-x1}$.  The denominator, the $ dx=x2-x1$, is never going to be zero when there's a y-intercept, since we can go from the left of the y-intercept to th...

Hello internet, and welcome to the introduction to Chapter 1 of General Chemistry.  This chapter is going to set you up for success in chemistry in general, as it will be well used in all chemistry courses.  Most of this chapter will also be used in all of science, but there will be parts which are chem-centric. Chemistry is the study of the materials of the universe and the changes which those materials undergo.  One of the joys of chemistry is seeing how the principles of chemistry applies to all aspects of everyday life, from cooking and burning of gasoline (petrol for my European readers) on the individual level to the development of medications and the growing of crops on the far-reaching end. This first chapter lays down the foundation required for success in any science in general and chemistry in particular.  This includes fundamentals of chemistry, matter, and scientific measurements.  Keep in mind that the information in this lecture series ...