|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910508443603321 |
|
|
Autore |
Allahviranloo Tofigh |
|
|
Titolo |
A Course on Integral Equations with Numerical Analysis : Advanced Numerical Analysis |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham : , : Springer International Publishing AG, , 2021 |
|
©2022 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (222 pages) |
|
|
|
|
|
|
Collana |
|
Mathematical Engineering Ser. |
|
|
|
|
|
|
Altri autori (Persone) |
|
|
|
|
|
|
Soggetti |
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Nota di contenuto |
|
Intro -- Preface -- Contents -- 1 Introduction to Numerical Analysis -- 1.1 Introduction -- 1.2 Error Analysis -- 1.2.1 Errors in an Algorithm -- 1.2.2 Round of Error and Floating Points Arithmetic -- 1.2.3 Algorithm Error Propagation -- 1.3 Interpolation -- 1.3.1 Lagrange Interpolation -- 1.3.2 Newton's Divided Difference Interpolation -- 1.4 A Short Review on Vector Norms and Linear System of Equations -- 1.4.1 Vector Norm -- 1.4.2 Direct Methods -- 1.4.3 Numerical Methods -- 1.5 Numerical Integration -- 1.5.1 Newton-Cotes Integration Method -- 1.5.2 The Peano's Kernel Representation -- 1.5.3 Gauss Integration Method -- 2 Interval Interpolation -- 2.1 Interval Error -- 2.1.1 Interval Calculations -- 2.2 Interval Interpolation -- 2.2.1 Theorem -- 2.2.2 Theorem -- 2.2.3 Theorem -- 2.2.4 Example -- 2.2.5 Example -- 3 Orthogonal Polynomials and Least Square Approximation -- 3.1 Orthogonal Polynomials -- 3.1.1 Definition-Inner Product of Definite Functions -- 3.1.2 Definition-Orthogonal Functions -- 3.1.3 Example -- 3.1.4 Example -- 3.1.5 Example -- 3.1.6 Definition -- 3.1.7 Example -- 3.1.8 Theorem -- 3.1.9 Orthogonal Polynomials and Least Squares Approximation -- 3.1.10 Example -- 3.1.11 Theorem -- 3.1.12 Example -- 4 Integral Equations -- 4.1 Introduction -- 4.1.1 Definition-Integral Equation -- 4.1.2 Example -- 4.1.3 Definition-First Type Integral Equation -- 4.1.4 Definition-Kernel -- 4.1.5 Definition-Homogeneous Integral Equation of the Second Type -- 4.1.6 Definition-Volterra Integral Equation -- |
|
|
|
|