Advanced Calculus with Applications in Statistics

Praise for the First Edition
"An enticing approach to the subject. . . . Students contemplating a career in statistics will acquire a valuable understanding of the underlying structure of statistical theory. . . statisticians should consider purchasing it as an additional reference on advanced calculus."
–Journal of the American Statistical Association
"This book is indeed a pleasure to read. It is simple to understand what the author is attempting to accomplish, and to follow him as he proceeds. . . . I would highly recommend the book for one’s personal collection or suggest your librarian purchase a copy."
–Journal of the Operational Research Society
Knowledge of advanced calculus has become imperative to the understanding of the recent advances in statistical methodology. The First Edition of Advanced Calculus with Applications in Statistics has served as a reliable resource for both practicing statisticians and students alike. In light of the tremendous growth of the field of statistics since the book’s publication, André Khuri has reexamined his popular work and substantially expanded it to provide the most up–to–date and comprehensive coverage of the subject.
Retaining the original’s much–appreciated application–oriented approach, Advanced Calculus with Applications in Statistics, Second Edition supplies a rigorous introduction to the central themes of advanced calculus suitable for both statisticians and mathematicians alike. The Second Edition adds significant new material on:Basic topological conceptsOrthogonal polynomialsFourier seriesApproximation of integralsSolutions to selected exercises
The volume’s user–friendly text is notable for its end–of–chapter applications, designed to be flexible enough for both statisticians and mathematicians. Its well thought–out solutions t o exercises encourage independent study and reinforce mastery of the content. Any statistician, mathematician, or student wishing to master advanced calculus and its applications in statistics will find this new edition a welcome resource.

Spis treści:
Preface.
Preface to the First Edition.
1. An Introduction to Set Theory.
2. Basic Concepts in Linear Algebra.
3. Limits and Continuity of Functions.
4. Differentiation.
5. Infinite Sequences and Series.
6. Integration.
7. Multidimensional Calculus.
8. Optimization in Statistics.
9. Approximation of Functions.
10. Orthogonal Polynomials.
11. Fourier Series.
12. Approximation of Integrals.
Appendix. Solutions to Selected Exercises.
General Bibliography.
Index.

Nota biograficzna:
ANDRE I. KHURI, PhD, is a Professor in the Department of Statistics at the University of Florida, Gainesville.

Okładka tylna:
Praise for the First Edition
"An enticing approach to the subject. . . . Students contemplating a career in statistics will acquire a valuable understanding of the underlying structure of statistical theory. . . statisticians should consider purchasing it as an additional reference on advanced calculus."
–Journal of the American Statistical Association
"This book is indeed a pleasure to read. It is simple to understand what the author is attempting to accomplish, and to follow him as he proceeds. . . . I would highly recommend the book for one’s personal collection or suggest your librarian purchase a copy."
–Journal of the Operational Research Society
Knowledge of advanced calculus has become imperative to the understanding of the recent advances in statistical methodology. The First Edition of Advanced Calculus with Applications in Statistics has served as a reliable resource for both practicing statisticians and students alike. In light of the tremendous growth of the field of statistics since the book’s publication, André Khuri has reexamined his popular work and substantially expanded it to provide the most up–to–date and comprehensive coverage of the subject.
Retaining the original’s much–appreciated application–oriented approach, Advanced Calculus with Applications in Statistics, Second Edition supplies a rigorous introduction to the central themes of advanced calculus suitable for both statisticians and mathematicians alike. The Second Edition adds significant new material on:Basic topological conceptsOrthogonal polynomialsFourier seriesApproximation of integralsSolutions to selected exercises
The volume’s user–friendly text is notable for its end–of–chapter applications, designed to be flexible enough for both statisticians and mathematicians. Its well thought–out solutions to exercises encourage independent study and reinforce mastery of the content. Any statistician, mathematician, or student wishing to master advanced calculus and its applications in statistics will find this new edition a welcome resource.