Elementary numerical computing with Mathematica
著者
書誌事項
Elementary numerical computing with Mathematica
（McGraw-Hill computer science series）
McGraw-Hill, c1993
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注記
On t.p. the registered trademark symbol "R" appears after the word Mathematica
Includes bibliographical references (p. 428) and indexes
内容説明・目次
内容説明
A practical introduction to numerical methods at an elementary level. It exposes students to a range of possibilities to scientific computing. Although oriented towards Mathematica, the book can be used with other programming languages. It contains lessons on Mathematica but also assumes reasonable access to the Mathematica manual. Avoiding partial derivatives which many students study but fail to master, it covers systems of ordinary differential equations to give the student an accurate picture of scientific computing. The main purpose of the book is to teach the principles of numerical analysis. In addition, it sets out to teach some simple and useful numerical methods; to indicate the sort of techniques that are used in actual numerical software and thereby suggest what kind of performance migh be expected; to give practical advice on the assessment and enhancement of accuracy; and to show how problems requiring numerical computation arise in application. Also available is an instructor's manual (0-07-057821-4).
目次
- Applications
- computational errors
- algorithms
- error
- error propagation
- floating-point computation
- positional number systems
- floating-point numbers
- rounding
- basic operations
- numerical instability
- other difficulties
- rootfinding
- roots
- bisection method
- Newton's method
- functional interaction
- secant method
- systems of linear equations
- matrices
- norms and sensitivity
- Gaussian elimination
- accuracy of partial pivoting
- linear equation solvers
- large sparse systems
- LU factorization
- interpolation
- Taylor's series
- big-oh notation
- existence and uniqueness
- Lagrange form
- inverse interpolation
- least squares approximation
- the least squares problem
- orthogonality
- the normal equations
- numerical differentiation and integration
- numerical differentiation
- simple quadrature rates
- Gaussian quadrature rules
- numerical error estimates
- global adaptive quadrature
- ordinary differential equators
- a single ODE
- Euler's method
- systems of ODE's
- Taylor series methods
- Runge-Kutta methods
- overview. Appendices: Getting started with Mathematica
- exact and approximate numerical calculations
- algebraic calculations
- lists
- defining functions
- procedural programming
- expressions
- defining rules
- how evaluation works
- delayed evaluation.
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