ADVACED CALCULUS WITH APPLICATIONS IN STATISTICS

This edition provides a rather substantial addition to the material covered in the first edition. The principal difference is the inclusion of three new chapters, Chapters 10, 11, and 12, in addition to an appendix of solutions to exercises. Chapter 10 covers orthogonal polynomials, such as Legendre, Chebyshev, Jacobi, Laguerre, and Hermite polynomials, and discusses their applications in statistics. Chapter 11 provides a thorough coverage of Fourier series. The presentation is done in such a way that a reader with no prior knowledge of Fourier series can have a clear understanding of the theory underlying the subject. Several applications of Fouries series in statistics are presented. Chapter 12 deals with approximation of Riemann integrals. It gives an exposition of methods for approximating integrals, including those that are multidimensional. Applications of some of these methods in statistics are discussed. This subject area has recently gained prominence in several fields of science and engineering, and, in particular, Bayesian statistics. The material should be helpful to readers who may be interested in pursuing further studies in this area. taken from preface