Computers are certainly good at looping, and many computations are iterative. But loops are where errors can build up and overwhelm the chance for any meaningful results.
Chapter 4 shows that even seemingly innocuous operations, such as summing a list of numbers , can get us into trouble. Examples show how running floating-point sums can gradually lose precision and offer some ways to prevent this from happening.
Chapter 5 is about finding the roots of an algebraic equation, which is another way of saying, "Solve for x. " It introduces several iterative algorithms that converge upon solutions: bisection, regula falsi, improved regula falsi, secant , Newton's, and fixed-point. This chapter also discusses how to decide which algorithm is appropriate.
Chapter 6 poses the question, Given a set of points in a plane, can we construct a smooth curve that passes through all the points, or how about a straight line that passes the closest to all the points? This chapter presents algorithms for polynomial interpolation and linear regression.
Chapter 7 tackles some integration problems from freshman calculus, but it solves them numerically . It introduces two basic algorithms, the trapezoidal algorithm and Simpson's algorithm.
Finally, Chapter 8 is about solving differential equations numerically. It covers several popular algorithms, Euler's, predictor -corrector, and Runge-Kutta.
