Numerical Methods (MATLAB Version) [PDF]

Chinese name: Numerical Method (MatLab)

Author: (US) Mathews

Translator: Zhou Lu
Chen Yu
Qian Fang

Book category: Education/Technology

Resource format: PDF

Version: Scan version

Press: Electronic Industry Press

Book No.7121019078

Release Date: March 2005

Region: Mainland China

Language: Simplified Chinese

Introduction:

Introduction:
This book describes the basic knowledge of numerical analysis. It is applicable to undergraduates majoring in mathematics, computer science, physics, and engineering. This book requires readers to be familiar with calculus and have been trained in structured programming. This book provides a wide range of teaching content that can meet the needs of one semester or even one academic year. Teachers can tailor the content as needed ..
For students in various fields, the numerical method is very useful. This guiding ideology runs through each chapter of this book. Therefore, this book provides a wide range of examples and typical problems to help readers improve their numerical analysis skills in both theoretical and practical aspects. This book tries its best to display the computation results in graphs and charts, so that readers can better understand the effect of numerical approximation. This book uses MATLAB programs to implement numerical algorithms.
The focus of this book is to help readers understand how numerical methods work and what restrictions are imposed. It is not easy to achieve this goal because both theory, error analysis, and readability are required. In this book, the derivation of each method based on the basic conclusions of calculus is given, and an appropriate error analysis is conducted to make it easy for readers to understand. Through these learning, readers can better understand calculus knowledge. Computer exercises programmed with MATLAB provide students with the opportunity to exercise their scientific computing programming skills.
In this book, simple numeric exercises can be completed using a calculator or a handheld computer, and more complex exercises need to be performed using Matlab subprograms. How to instruct students to perform numerical calculations on the computer is completed by various instructors who can assign appropriate teaching tasks based on their existing computer resources. This book encourages the use of MATLAB sub-libraries, which can help students implement the numerical analysis components in computer lab questions.
This version of this book adds a section at the end of Chapter 5th to discuss the besell curve. Chapter 8th, which discusses numerical optimization, is also expanded to introduce the Direct Method of Single-variable and multi-variable optimal functions and the derivative-based method. At the author's request, the MATLAB program in the book can be downloaded from the http://math.fullerton.edu/mathews/numerical.html. At the same time, the instructor's exercise answer manual can also be obtained from the publisher (for details, see the "Instruction on teaching support" at the end of this book ").
I previously thought that no matter which programming language I use, I can take this course. However, I found that most students (except computer students) need to learn new programming languages. MATLAB has now become an indispensable tool for engineering and applied mathematics. Its latest version also enhances programming functions. Therefore, I hope that the MATLAB program in this book can make the content of the book easier to grasp and make learning more effective.
Content:

Directory:

Chapter 4 prerequisites
1.1 calculus review.
1.1.1 limits and continuity
1.1.2 micro Functions
1.1.3 points
1.1.4 Series
1.1.5 polynomial Evaluation
1.1.6 exercise
1.2 binary
1.2.1 binary number
1.2.2 sequence and Series
1.2.3 binary score
1.2.4 binary shift
1.2.5 scientific notation
1.2.6 machine count
1.2.7 computer precision
1.2.8 computer floating point number
1.2.9 exercise
Error Analysis of 1.3
1.3.1 truncation error
. 1.3.2 rounding error
1.3.3 rounding and rounding
1.3.4 loss of Precision
1.3.5 O (HN) approximation
Order of sequence 1.3.6
1.3.7 Error Propagation
1.3.8 data uncertainty
1.3.9 exercise
1.3.10 algorithms and programs
Chapter 2 solutions to nonlinear equations f (x) = 0
2.1 Iteration Method for Solving x = g (x)
2.1.1 searching for Fixed Points
2.1.2 graphic interpretation of Fixed Point Iteration
2.1.3 consideration of absolute and relative errors
2.1.4 exercise
2.1.5 algorithms and programs
2.2 root Classification Method
2.2.1 polzano bipartite Method
2.2.2 convergence of the Trial Value Method
2.2.3 exercise
2.2.4 algorithms and programs
2.3 determination criteria for initial approximation and Convergence
2.3.1 detection convergence
2.3.2 problematic Functions
2.3.3 exercise
2.3.4 algorithms and programs
2.4 Newton-aferson method and cut-Line Method
2.4.1 root Slope Method
2.4.2 zero Division Error
2.4.3 convergence speed
2.4.4 Defects
2.4.5 cut Line Method
2.4.6 accelerated convergence
2.4.7 exercises
2.4.8 algorithms and programs
2.5 Etkin process, Stephenson law and Miller Law (optional)
2.5.1 Etkin Process
2.5.2 Miller's Law
2.5.3 Comparison Between Methods
2.5.4 exercise
2.5.5 algorithms and programs
Chapter 2 Numerical Solution of Linear Equations AX = B
3.1 Introduction to vectors and Matrices
3.1.1 matrix and two-dimensional array
3.1.2 exercise
3.2 properties of vectors and Matrices
3.2.1 Matrix Multiplication
3.2.2 Special Matrix
3.2.3 inverse of non-singular matrices
3.2.4 determining factor
3.2.5 plane rotation
3.2.6 MATLAB implementation
3.2.7 exercise
3.2.8 algorithms and programs
3.3 upper triangle Linear Equations
3.3.1 exercise
3.3.2 algorithms and programs
3.4 Gaussian elimination and principal component selection
3.4.1 select the principal component to avoid a (p) pp = 0
3.4.2 select the principal component to reduce the error
3.4.3 pathological conditions
3.4.4 MATLAB implementation
3.4.5 exercise
3.4.6 algorithms and procedures
3.5 triangle Decomposition Method
3.5.1 solutions to Linear Equations
3.5.2 triangle Decomposition Method
3.5.3 computing complexity
3.5.4 replacement Matrix
3.5.5 expanded Gaussian elimination process
3.5.6 MATLAB implementation
3.5.7 exercise
3.5.8 algorithms and programs
3.6 Iteration Method for Solving Linear Equations
3.6.1 Yahoo Iteration
3.6.2 Gaussian-sadel Iteration Method
3.6.3 convergence
3.6.4 exercise
3.6.5 algorithms and programs
3.7 Iterative Methods of nonlinear equations: Sader method and Newton method (optional read)
3.7.1 Theory
3.7.2 generalized Differentiation
3.7.3 convergence near fixed point
3.7.4 sadel Iteration
3.7.5 Newton Method for Solving Nonlinear Equations
3.7.6 Newton method Overview
3.7.7 MATLAB implementation
3.7.8 exercise
3.7.9 algorithms and programs
Chapter 2 interpolation and polynomial approximation
4.1 Taylor series and function compute
4.1.1 polynomial calculation method
4.1.2 exercise
4.1.3 algorithms and procedures
4.2 Introduction to Interpolation
4.2.1 exercise
4.2.2 algorithms and procedures
4.3 Laplace Approximation
4.3.1 error items and Error Bounds
4.3.2 accuracy and O (hN + 1)
4.3.3 MATLAB implementation
4.3.4 exercise
4.3.5 algorithms and procedures
4.4 Newton Polynomials
4.4.1 nested Multiplication
4.4.2 polynomial approximation, node and center
4.4.3 exercise
4.4.4 algorithms and procedures
4.5 cherbihov polynomial (optional read)
4.5.1 copifier polynomial Properties
4.5.2 minimum upper bound
4.5.3 same distance Node
4.5.4 kipev Node
4.5.5 long Ge Phenomenon
4.5.6 interval Transformation
4.5.7 orthogonal
4.5.8 MATLAB implementation
4.5.9 exercise
4.5.10 algorithms and procedures
4.6 Pa German Approximation
4.6.1 Continued Fraction
4.6.2 exercises ..
4.6.3 algorithms and procedures
Chapter 1 Curve Fitting
5.1 Least Squares Fitting Curve
5.1.1 Least Squares
5.1.2 power function fitting y = AxM
5.1.3 exercise
5.1.4 algorithms and programs
5.2 Curve Fitting
5.2.1 Linearity method of y = CeAx
5.2.2 Nonlinear Least Square Method for Solving y = CeAx
5.2.3 data linear transformation
5.2.4 Linear Least Square Method
5.2.5 Matrix Formula
5.2.6 polynomial fitting
5.2.7 polynomial swing
5.2.8 exercise
5.2.9 algorithms and programs
5.3 spline function interpolation
5.3.1 piecewise linear interpolation
5.3.2 piecewise cubic spline
5.3.3 existence of cubic Splines
5.3.4 Construct Cubic Spline
5.3.5 endpoint Constraints
5.3.6 suitability of Cubic Spline
5.3.7 exercise
5.3.8 algorithms and programs
5.4 Fourier series and triangular Polynomials
5.4.1 triangular polynomial approximation
5.4.2 exercise
5.4.3 algorithms and programs
5.5 besell Curve
5.5.1 properties of the bernstan Polynomial
5.5.2 nature of the besell Curve
5.5.3 exercise
5.5.4 algorithms and programs
Chapter 2 numerical differentiation
6.1 Derivative Approximation
6.1.1 limit of difference providers
6.1.2 central difference formula
6.1.3 Error Analysis and Step Size Optimization
6.1.4 Richard's external push Method
6.1.5 exercise
6.1.6 algorithms and programs
6.2 numerical difference formula
6.2.1 more central difference Formulas
6.2.2 Error Analysis
6.2.3 Laplace polynomial Differentiation
6.2.4 Newton polynomial Differentiation
6.2.5 exercise
6.2.6 algorithms and programs
Chapter 2 numerical points
7.1 points Introduction
7.1.1 exercise
7.2 combination of trapezoid and Simpson Formulas
7.2.1 Error Analysis
7.2.2 exercise
7.2.3 algorithms and programs
7.3 recursive formula and longberger points
7.3.1 longberger points
7.3.2 exercise
7.3.2 algorithms and programs
7.4 adaptive points
7.4.1 interval subdivision
7.4.2 Accuracy Test
7.4.3 algorithms and programs
7.5 Gaussian-lepete points (optional)
7.5.1 exercises
7.5.2 algorithms and programs
Chapter 2 Numerical Optimization
8.1 minimum value of A Single Variable Function
8.1.1 classification Search Method
8.1.2 use derivative to obtain the minimum value
8.1.3 exercise
8.1.4 algorithms and programs
8.2 Neide-meide method and Powell Method
8.2.1 nede-meide Method
8.2.2 POWELL method
8.2.3 exercise
8.2.4 algorithms and programs
8.3 gradient and Newton Method
8.3.1 The shortest descent method (gradient method)
8.3.2 Newton Method
8.3.3 exercise
8.3.4 algorithms and programs
Chapter 2 solving differential equations
9.1 Introduction to Differential Equations
9.1.1 initial value problems
9.1.2 GEOMETRIC INTERPRETATION
9.1.3 exercise
9.2 Euler's Method
9.2.1 geometric description
9.2.2 step size and error
9.2.3 exercise
9.2.4 algorithms and programs
9.3 sheun Method
9.3.1 step size and error
9.3.2 exercise
9.3.3 algorithms and programs
9.4 Taylor series method
9.4.1 exercise
9.4.2 algorithms and programs
9.5 longge-Kuta method
9.5.1 discussion of this method
9.5.2 step size and error
9.5.3 The long-box-Kuta method of N = 2
9.5.4 long Ge-Kuta-fairberg Method
9.5.5 exercise
9.5.6 algorithms and programs
9.6 prediction-correction method
9.6.1 Adams-bashforth-Morton Method
9.6.2 Error Estimation and correction
9.6.3 considerations
9.6.4 Milne-Simpson method
9.6.5 Error Estimation and correction
9.6.6 correct step size
9.6.7 exercise
9.6.8 algorithms and programs
9.7 Differential Equations
9.7.1 Numerical Solution
9.7.2 high-level differential equations
9.7.3 exercise
9.7.4 algorithms and programs
9.8 edge Value Problems
9.8.1 is divided into two initial values: linear target hitting Method
9.8.2 exercise
9.8.3 algorithms and programs
9.9 Finite Difference Method
9.9.1 exercise
9.9.2 algorithms and programs
Chapter 2 Partial Differential Equations
10.1 Hyperbolic Equation
10.1.1 fluctuation Equation
10.1.2 difference formula
10.1.3 Initial Value
10.1.4 Dalong's Method
10.1.5 two definite rows
10.1.6 exercise
10.1.7 algorithms and programs
10.2 Parabolic Equation
10.2.1 Heat Conduction Equation
10.2.2 difference formula
10.2.3 cranky-Nickerson Method
10.2.4 exercise
10.2.5 algorithms and programs
10.3 Elliptic Equation
10.3.1 Laplace Difference Equation
10.3.2 Linear Equations
10.3.3 Derivative Boundary Condition
10.3.4 Iteration Method
10.3.5 Poisson equation and hamkot Equation
10.3.6 Improvement
10.3.7 exercise
10.3.8 algorithms and programs
Chapter 2 feature values and feature vectors
11.1 homogeneous equations: feature Problems
11.1.1 background
11.1.2 feature value
11.1.3 keratin
11.1.4 advantages of symmetry
11.1.5 feature value range estimation
11.1.6 method Overview
11.1.7 exercise
Power 11.2 Method
11.2.1 convergence speed
11.2.2 shift inverse idempotence
11.2.3 exercise
11.2.4 algorithms and programs
11.3 jakits Method
11.3.1 plane Rotation Transformation
11.3.2 similarity and Orthogonal Transformation
11.3.3 kV conversion Sequence
11.3.4 general steps
11.3.5 make dpq and dqp zero
11.3.6 general steps
11.3.7 correction of matrix feature values
11.3.8 policy for removing apq
11.3.9 exercise
11.3.10 algorithms and programs
11.4 feature value of symmetric matrix
11.4.1 Householder Method Numerical Method (MATLAB)
11.4.2 Householder transformation
11.4.3 triangular reduction
11.4.4 QR method
11.4.5 accelerated shift
11.4.6 exercise
11.4.7 algorithms and programs
Appendix a matlab Introduction
Some Exercise answers...
Comparison of Chinese and English terms

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