So in this course you will learn a mathematical calculus, enabling you to formalize intuition you already possess concerning how quantities change in relation to one another. You will learn how to use mathematical tools to describe and measure these changes in quantifiable fashion. In short, you will learn a set of formal rules and procedures which will empower you to analyze a wide variety of evolutionary processes ... that is, processes in which there is continual change, over time, in some quantity you wish to track.
What is meant by a "mathematical tool"? Well, consider the mathematics you have already learned ... algebra, for example. If you think about it, algebra is just "abstract arithmetic". When you see an equation such as y - 2 = x + 3, you realize that the letters x and y represent numbers, but unlike the numbers 2 and 3 in the equation, the numbers x and y are not fixed in value. They are variables. The concept of a variable quantity comprises a mathematical tool. You can use this tool to deduce certain information. For example, in this case, since the equation y - 2 = x + 3 is algebraically equivalent to y = x + 5, we can assert that the only way one can subtract 2 from one number, and add 3 to another number, and get the same result, is if the two unknown numbers are 5 units apart. This is true no matter what the two unknown numbers are; their values can vary, but their values must be 5 units apart for the given relationship to hold.
In calculus, the basic mathematical tool at the root of all we do is the function. Basically, a function is a rule for obtaining a numerical value from another given numerical value. Once we have studied the many different ways to "give birth" to a function, we will need to classify functions by type. We will need to develop a very large repertoire of methods for depicting functions graphically/geometrically.
We then study how to apply the tool of the function to measure quantities. The mathematical calculus can then be applied to answer questions such as, Will the quantity be increasing three seconds from now? Was the quantity decreasing or increasing ten seconds ago? How much accumulation will this quantity exhibit over the next minute? Does this quantity reach some maximum rate of increase, and if so, when? Will this quantity accumulate to some maximum level, and then begin to diminish ... and if so, when does the transition occur?
Calculus gives you the tools you need to measure change both qualitatively and quantitatively. And knowing how one quantity changes in relation to another can be of great importance in any endeavor for which optimization is a key goal. Calculus enables a business to determine the maximum price that may be charged for a commodity without adverse effects on demand. Calculus enables a medical examiner performing an autopsy to determine the minimum amount of time that could have elapsed since the person died. Calculus enables ballistics experts to measure the maximum range of a projectile. Calculus enables an engineer to determine the minimum amount of propellant needed for an emergency landing of a spacecraft. And calculus enables a fish hatchery to determine the maximum rate at which fish may be harvested without depleting the population.
Any application in which a quantity changes continuously (that is, by small amounts over small time periods) lends itself to the tools and techniques of the calculus.
So are you ready? Let's have a great course!