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Numerical analysis is the study of the methods used to solve problems involving continuous variables. It is a highly applied branch of mathematics and computer science, wherein abstract ideas and theories become the quantities describing things we can actually touch and see. The real number line is an abstraction where many interesting and useful ideas live, but to actually realize these ideas, we are forced to employ approximations of the real numbers. For example, consider marking a ruler at sqrt{2}. We know that sqrt{2} approx 1.4142, but if we put the mark there, we know we are in error for there is an infinite sequence of nonzero digits following the 2. Even more: a number doesn’t have any width, yet any mark we make would have a width, and in that width lives an infinite number of real numbers. You may ask yourself: isn’t it sufficient to represent sqrt{2} with 1.414? This is the kind of question that this course will explore. We have been trying to answer such questions for over 2,0… Details:
http://www.saylor.org/courses/ma213/
Categories:
Mathematics
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