Advanced Calculus with Applications in Statistics / Edition 2

Hardcover (Print)
Buy New
Buy New from
Buy Used
Buy Used from
(Save 40%)
Item is in good condition but packaging may have signs of shelf wear/aging or torn packaging.
Condition: Used – Good details
Used and New from Other Sellers
Used and New from Other Sellers
from $89.50
Usually ships in 1-2 business days
(Save 50%)
Other sellers (Hardcover)
  • All (10) from $89.50   
  • New (2) from $152.66   
  • Used (8) from $89.50   


Designed to help motivate the learning of advanced calculus by demonstrating its relevance in the field of statistics, this successful text features detailed coverage of optimization techniques and their applications in statistics while introducing the reader to approximation theory. The Second Edition provides substantial new coverage of the material, including three new chapters and a large appendix that contains solutions to almost all of the exercises in the book. Applications of some of these methods in statistics are discusses. 

Read More Show Less

Editorial Reviews

From the Publisher
"This is an exceptional book, which I would recommend for anyone beginning a career in statistical research." (Journal of the American Statistical Association, September 2004)
An application-oriented and highly rigorous introduction to the central themes of advanced calculus for statistics students, with enough theoretical explanation to be suitable for mathematics students. Topics include an introduction to set theory, linear algebra, limits and continuity, differentiation, infinite sequences and series, integration, multidimensional calculus, optimization in statistics, and approximation of functions. Exercises and an annotated bibliography are included. Annotation c. Book News, Inc., Portland, OR (
Read More Show Less

Product Details

Meet the Author

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

Read More Show Less

Read an Excerpt

Click to read or download

Read More Show Less

Table of Contents


Preface to the First Edition.

1. An Introduction to Set Theory.

1.1. The Concept of a Set.

1.2. Set Operations.

1.3. Relations and Functions.

1.4. Finite, Countable, and Uncountable Sets.

1.5. Bounded Sets.

1.6. Some Basic Topological Concepts.

1.7. Examples in Probability and Statistics.

2. Basic Concepts in Linear Algebra.

2.1. Vector Spaces and Subspaces.

2.2. Linear Transformations.

2.3. Matrices and Determinants.

2.4. Applications of Matrices in Statistics.

3. Limits and Continuity of Functions.

3.1. Limits of a Function.

3.2. Some Properties Associated with Limits of Functions.

3.3. The o, O Notation.

3.4. Continuous Functions.

3.5. Inverse Functions.

3.6. Convex Functions.

3.7. Continuous and Convex Functions in Statistics.

4. Differentiation.

4.1. The Derivative of a Function.

4.2. The Mean Value Theorem.

4.3. Taylor's Theorem.

4.4. Maxima and Minima of a Function.

4.5. Applications in Statistics.

5. Infinite Sequences and Series.

5.1. Infinite Sequences.

5.2. Infinite Series.

5.3. Sequences and Series of Functions.

5.4. Power Series.

5.5. Sequences and Series of Matrices.

5.6. Applications in Statistics.

6. Integration.

6.1. Some Basic Definitions.

6.2. The Existence of the Riemann Integral.

6.3. Some Classes of Functions That Are Riemann Integrable.

6.4. Properties of the Riemann Integral.

6.5. Improper Riemann Integrals.

6.6. Convergence of a Sequence of Riemann Integrals.

6.7. Some Fundamental Inequalities.

6.8. RiemannStieltjes Integral.

6.9. Applications in Statistics.

7. Multidimensional Calculus.

7.1. Some Basic Definitions.

7.2. Limits of a Multivariable Function.

7.3. Continuity of a Multivariable Function.

7.4. Derivatives of a Multivariable Function.

7.5. Taylor's Theorem for a Multivariable Function.

7.6. Inverse and Implicit Function Theorems.

7.7. Optima of a Multivariable Function.

7.8. The Method of Lagrange Multipliers.

7.9. The Riemann Integral of a Multivariable Function.

7.10. Differentiation under the Integral Sign.

7.11. Applications in Statistics.

8. Optimization in Statistics.

8.1. The Gradient Methods.

8.2. The Direct Search Methods.

8.3. Optimization Techniques in Response Surface Methodology.

8.4. Response Surface Designs.

8.5. Alphabetic Optimality of Designs.

8.6. Designs for Nonlinear Models.

8.7. Multiresponse Optimization.

8.8. Maximum Likelihood Estimation and the EM Algorithm.

8.9. Minimum Norm Quadratic Unbiased Estimation of Variance Components.

8.10. Scheffé's Confidence Intervals.

9. Approximation of Functions.

9.1. Weierstrass Approximation.

9.2. Approximation by Polynomial Interpolation.

9.3. Approximation by Spline Functions.

9.4. Applications in Statistics.

10. Orthogonal Polynomials.

10.1. Introduction.

10.2. Legendre Polynomials.

10.3. Jacobi Polynomials.

10.4. Chebyshev Polynomials.

10.5. Hermite Polynomials.

10.6. Laguerre Polynomials.

10.7. Least-Squares Approximation with Orthogonal Polynomials.

10.8. Orthogonal Polynomials Defined on a Finite Set.

10.9. Applications in Statistics.

11. Fourier Series.

11.1. Introduction.

11.2. Convergence of Fourier Series.

11.3. Differentiation and Integration of Fourier Series.

11.4. The Fourier Integral.

11.5. Approximation of Functions by Trigonometric Polynomials.

11.6. The Fourier Transform.

11.7. Applications in Statistics.

12. Approximation of Integrals.

12.1. The Trapezoidal Method.

12.2. Simpson’s Method.

12.3. NewtonCotes Methods.

12.4. Gaussian Quadrature.

12.5. Approximation over an Infinite Interval.

12.6. The Method of Laplace.

12.7. Multiple Integrals.

12.8. The Monte Carlo Method.

12.9. Applications in Statistics.

Appendix. Solutions to Selected Exercises.

General Bibliography.


Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)