Things to remember:The study of Absolute Values in Chapter 1 is crucial to a string grasp of basic Calculus concepts. You should always strive to work out the Suggested Homework Problems where they appear in the text.
Not every continuous function is differentiable...remember K. Weierstrass gave an example of a function (over 100 years ago) which is continuous at every point of the real line but does not have a derivative anywhere!. You can imagine the graph of such a function as having many (infinitely many), spikes or corners. If you want to "understand" this example, look at the book by E.C. Titchmarsh entitled Theory of Functions, Oxford University Press (1930's). Fractals also give rise to examples of nowhere differentiable curves. Check out the following URL for a display of the Apple Fractal. Other websites which exhibit fractals include:My modules form the required text for this course as they have been created with you in mind.
