(BQ) Part 2 book "Fundamental numerical methods and data analys" has contents: Numerical solution of differential and integral equations; least squares, fourier analysis, and related approximation norms; probability theory and statistics; sampling distributions of moments, statistical tests, and procedures. | 5 Numerical Solution of Differential and Integral Equations • • • The aspect of the calculus of Newton and Leibnitz that allowed the mathematical description of the physical world is the ability to incorporate derivatives and integrals into equations that relate various properties of the world to one another. Thus, much of the theory that describes the world in which we live is contained in what are known as differential and integral equations. Such equations appear not only in the physical sciences, but in biology, sociology, and all scientific disciplines that attempt to understand the world in which we live. Innumerable books and entire courses of study are devoted to the study of the solution of such equations and most college majors in science and engineering require at least one such course of their students. These courses generally cover the analytic closed form solution of such equations. But many of the equations that govern the physical world have no solution in closed form. Therefore, to find the answer to questions about the world in which we live, we must resort to solving these equations numerically. Again, the literature on this subject is voluminous, so we can only hope to provide a brief introduction to some of the basic methods widely employed in finding these solutions. Also, the subject is by no means closed so the student should be on the lookout for new techniques that prove increasingly efficient and accurate. 121 Numerical Methods and Data Analysis The Numerical Integration of Differential Equations When we speak of a differential equation, we simply mean any equation where the dependent variable appears as well as one or more of its derivatives. The highest derivative that is present determines the order of the differential equation while the highest power of the dependent variable or its derivative appearing in the equation sets its degree. Theories which employ differential equations usually will not be limited to single .
