Numerical Analysis for Applied Science 2nd by Allen Iii Isaacson 1119245656 9781119245469
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Numerical Analysis for Applied Science 2nd by Myron B. Allen Iii Isaacson – Ebook Instant Download/Delivery ISBN:1119245656 9781119245469
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Numerical analysis is a core subject in data science and an essential tool for applied mathematicians, engineers, and physical and biological scientists. This updated and expanded edition of Numerical Analysis for Applied Science follows the tradition of its precursor by providing a modern, flexible approach to the theory and practical applications of the field. As before, the authors emphasize the motivation, construction, and practical considerations before presenting rigorous theoretical analysis. This approach allows instructors to adapt the textbook to a spectrum of uses, ranging from one-semester, methods-oriented courses to multi-semester theoretical courses.
The book includes an expanded first chapter reviewing useful tools from analysis and linear algebra. Subsequent chapters include clearly structured expositions covering the motivation, practical considerations, and theory for each class of methods. The book includes over 250 problems exploring practical and theoretical questions and 32 pseudocodes to help students implement the methods. Other notable features include:
- A preface providing advice for instructors on using the text for a single semester course or multiple-semester sequence of courses
- Discussion of topics covered infrequently by other texts at this level, such as multidimensional interpolation, quasi-Newton methods in several variables, multigrid methods, preconditioned conjugate-gradient methods, finite-difference methods for partial differential equations, and an introduction to finite-element theory
- New topics and expanded treatment of existing topics to address developments in the field since publication of the first edition
- More than twice as many computational and theoretical exercises as the first edition.
Numerical Analysis for Applied Science, Second Edition provides an excellent foundation for graduate and advanced undergraduate courses in numerical methods and numerical analysis. It is also an accessible introduction to the subject for students pursuing independent study in applied mathematics, engineering, and the physical and life sciences and a valuable reference for professionals in these areas.
Table of contents:
Chapter 1: Some Useful Tools
1.1 Introduction
1.2 Bounded Sets
1.3 Normed Vector Spaces
1.4 Eigenvalues and Matrix Norms
1.5 Results from Calculus
1.6 Problems
Chapter 2: Approximation of Functions
2.1 Introduction
2.2 Polynomial Interpolation
2.3 Piecewise Polynomial Interpolation
2.4 Hermite Interpolation
2.5 Interpolation in Two Dimensions
2.6 Splines
2.7 Least‐squares Methods
2.8 Trigonometric Interpolation
2.9 Problems
Chapter 3: Direct Methods for Linear Systems
3.1 Introduction
3.2 The Condition Number of a Linear System
3.3 Gauss Elimination
3.4 Variants of Gauss Elimination
3.5 Band Matrices
3.6 Iterative Improvement
3.7 Problems
Chapter 4: Solution of Nonlinear Equations
4.1 Introduction
4.2 Bisection
4.3 Successive Substitution in One Variable
4.4 Newton’s Method in One Variable
4.5 The Secant Method
4.6 Successive Substitution: Several Variables
4.7 Newton’s Method: Several Variables
4.8 Problems
Chapter 5: Iterative Methods for Linear Systems
5.1 Introduction
5.2 Conceptual Foundations
5.3 Matrix‐Splitting Techniques
5.4 Successive Overrelaxation
5.5 Multigrid Methods
5.6 The Conjugate‐Gradient Method
5.7 Problems
Chapter 6: Eigenvalue Problems
6.1 More About Eigenvalues
6.2 Power Methods
6.3 The QR Decomposition
6.4 The QR Algorithm for Eigenvalues
6.5 Singular Value Decomposition
6.6 Problems
Chapter 7: Numerical Integration
7.1 Introduction
7.2 Newton–Cotes Formulas
7.3 Romberg and Adaptive Quadrature
7.4 Gauss Quadrature
7.5 Problems
Chapter 8: Ordinary Differential Equations
8.1 Introduction
8.2 One‐Step Methods
8.3 Multistep Methods: Consistency and Stability
8.4 Multistep Methods: Convergence
8.5 Problems
Chapter 9: Difference Methods for PDEs
9.1 Introduction
9.2 The Poisson Equation
9.3 The Advection Equation
9.4 Other Time‐Dependent Equations
9.5 Problems
Chapter 10: Introduction to Finite Elements
10.1 Introduction and Background
10.2 A Steady‐State Problem
10.3 A Transient Problem
10.4 Problems
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