Calculus for Dummies

The main part of Calculus is the discussion of functions (mathematical models of real world phenomena), i.e., the relation between differentiation and integration, techniques of integration, differential equations and their solution, and functions of several variables. The basic ideas in calculus are both simple and beautiful - the technicalities, however, can be quite horrendous. We shall try to avoid those in this course as much as possible.

A very good everyday life example is the odometer and speedometer in a car. At any given time the odometer reading gives us the number of miles traveled. The rate of change of this reading is given by the speed at which the car travels. The faster you drive, the quicker the odometer reading will change. The speedometer reading is nothing but the derivative of the odometer reading! If the car stands still (speed = 0) the odometer will remain constant - the rate of change is zero - or, in mathematical terms, the derivative of a constant is zero! If you drive for 15 minutes at the constant speed of 80 mph, the odometer reading will change by 20 miles (and you are likely to get a ticket). So, knowing the speed at all times we should have a good chance to be able to compute the odometer reading. Mathematically: if you know the derivative of a function, you can compute the function itself by integration. (The most important result in calculus is the connection between differentiation and integration - these operations turn out to be inverse to each other, just like subtraction and addition.) Calculus is really no more difficult than obtaining a driver's licence.




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