Methods in Approximation: Techniques for Mathematical Modelling

Paperback (Softcover reprint of the original 1st ed. 1986)
$174.56 price
(Save 20%)$219.00 List Price
Other sellers (Paperback)
  • All (3) from $203.73   
  • New (2) from $203.73   
  • Used (1) from $264.32   
Sending request ...

More About This Book

Product Details

  • ISBN-13: 9789401085441
  • Publisher: Springer Netherlands
  • Publication date: 12/31/2013
  • Series: Mathematics and Its Applications (closed) Series , #26
  • Edition description: Softcover reprint of the original 1st ed. 1986
  • Pages: 224
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.51 (d)

Table of Contents

Basic Concepts.- Integral Domains, Fields and Vector Spaces.- Subspaces, Bases and Inner Products.- Spaces, Subspaces and Approximation.- The Continuous Function.- Polynomial Subspaces.- Spaces Generated by Differential Equations.- The Piecewise Linear Function.- Discussion.- Bibliograpy and Comments.- Polynomial Approximation.- Piecewise Linear Functions.- Curve Fitting by Straight Lines.- A One Dimensional Process in Dynamic Programming.- The Functional Equation.- The Principle of Optimality.- A Direct Derivation.- Curve Fitting by Segmented Straight Lines.- A Dynamic Programming Approach.- A Computational Procedure.- Three Dimensional Polygonal Approximation.- The Orthogonal Polynomials.- The Approximation Technique.- Discussion.- Bibliography and Comments.- Polynomial Splines.- The Cubic Spline I.- Construction of the Cubic Spline.- Existence and Uniqueness.- A Computational Algorithm — Potter’s Method.- Splines via Dynamic Programming.- Derivation of Splines by Dynamic Programming.- Equivalence of the Recursive Relations obtained by Dynamic Programming and the Usual results.- Cardinal Splines.- Polynomial Splines.- Generalized Splines.- Mean Square Spline Approximation.- The Cubic Spline II.- The Minimization Procedure.- The Functional Equation.- Recursion Relations.- Bibliography and Comments.- Quasilinearization.- Quasilinearization I.- The Newton Raphson Method.- Quasilinearization II.- Existence.- Convergence.- An Example, Parameter Identification.- Unknown Initial Conditions.- Damped Oscillations.- Segmental Differential Approximation.- Differential Systems with Time Varying Coefficients.- A Method of Solution.- An Interesting Case.- Discussion.- Bibliography and Comments.- Differential Approximation.- Differential Approximation.- Linear Differential Operators.- Degree of Approximation.- Improving the Approximation.- An Example.- Differential-Difference Equations.- A Useful Approximation to g(t).- Discussion.- An Example.- Functional Differential Equations.- The Nonlinear Spring.- The Van der Pol Equation.- Bibliography and Comments.- Differential Quadrature.- Differential Quadrature.- Determination Of the Weighting Coefficients.- A First Order Problem.- A Nonlinear Wave Equation.- Systems of Nonlinear Partial Differential Equations.- Higher Order Systems.- Long Term Integration.- G(y) Linear.- G(y) Nonlinear.- A Mathematical Problem.- Systems with Partial Information.- Bibliography and Comments.- Exponential Approximation.- Approximation in Function Space.- An Example — Pharmacokinetics.- Other Physical Processes.- Proney’s Method.- The Renewal Equation.- The Fredholm Integral Equation.- Bibliography and Comments.- The Riccati Equation.- The Linear Differential Equation.- Differential Inequalities.- Solution of the Riccati Equation in terms of the Maximum Operation.- Upper and Lower Bounds.- Successive Approximations via Quasilinearization.- An Illustrative Example.- Higher Order Approximations.- Multidimensional Riccati Equation.- Variational Problems and the Riccati Equation.- Bibliography and Comments.- Solution of Approximate Equations.- First Order Differential Equations.- The Second Order Differential Equation.- Discussion.- Linear Perturbations.- The Van der Pol Equation I.- The Van der Pol Equation II.- The Riccati Equation.- u? + a(t)u = 0.- Another Approach.- Discussion.- Bibliography and Comments.- Magnetic Field Determination.- The Theoretical Problem.- Maxwell’s Equations.- A Variational Principle.- The Finite Element Method.- Computational Aspects.- Analytical Considerations.- Boundary Conditions.- Discussion.- Bibliography and Comments.

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)