The current text is Rowgawski, Jon, Calculus: Early Transcendentals, W.H. Freeman, New York, 1st edition (2008) ISBN-13:978-4292-1073-7.
These pages contain short videos that are directly related to topics in Ma 125 at the University of South Alabama. All the videos here have been produced by either Kent Murdick (Lutemann) or Scott Carter (Professor Elvis Zap). The videos are available at youtube under Lutemann or ProfessorElvisZap. Most of the videos were prepared in 1 or 2 takes. When errors were discovered, some graphical editing was performed. If glaring errors exist, then please let us know and we will correct them.
Students should be aware that by clicking on the video to open the associated youtube window, related videos as sorted by youtube appear. You might also find these helpful.
Most importantly, the department wishes to emphasize that watching videos is
no substitute for attending class!
In addition, the most effective way of learning mathematics is to attempt to work problems and to continue attempting until you obtain a solutions. Professional mathematicians employ a variety of problem solving strategies:
try to understand a more simple problem;
read the associated text;
ask an expert (your professor or a peer tutor);
rework the problem independently;
when you use a formula, write the formula down before you use it --- doing so will help you remember the formula;
keep a notebook of solved problems;
throw away techniques and solutions that don't work.
In this video Kent Murdick introduces a car traveling at a constant speed of 50 Miles per hour. He uses this to motivate the rate of change of a function.
The video below is a sequel. In this distance is no longer a linear function of time, but in the example it is quadratic. Kent demonstrates that the rate of change of the function depends upon the time.
These two videos together summarize a great deal of calculus. After you get into the depth of the course, we suggest that you review this introductory material.
Now the video below might be considered a bit silly (but not nearly as silly as this ); however, a careful listen will show that it describes the fundamental rules for computing limits, and it is a list of the standard rules for differentiation. You won't learn calculus simply by singing, but at least the lyrics contain lists of the fundamental rules.
This video was made for the sake of precalculus, but it also applied to calculus. Notation for various number systems are introduced: those for the natural numbers, the integers , the rational numbers, and the real numbers. Ultimately calculus is the study of the real number system. However, the study occurs from an arcane point of view: we study the real number line and its underlying differentiable structure by looking at functions that preserve this structure.
On several occasions you will wish to review a topic from Precalculus. The precalculus video pages are arranged in much the same way that these are.
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