TAILIEUCHUNG - Lectures In basic computational numerical analysis: Part 1

Part 1 Lectures In basic computational numerical analysis has contents: Numerical linear algebra, solution of nonlinear equations, approximation theory. | (m) −1 )] ƒ(x ) [J(ƒ (m+1) x =x − (m) (m) D f f 0 i = +1 − f i −1 i 2h LECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS J. M. McDonough University of Kentucky Lexington, KY 40506 E-mail: jmmcd@ ƒ( y′ = y,t) LECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS J. M. McDonough Departments of Mechanical Engineering and Mathematics University of Kentucky c 1984, 1990, 1995, 2001, 2004, 2007 Contents 1 Numerical Linear Algebra Some Basic Facts from Linear Algebra . . . . . . . . . . . . . . . Solution of Linear Systems . . . . . . . . . . . . . . . . . . . . . . Numerical solution of linear systems: direct elimination . Numerical solution of linear systems: iterative methods . Summary of methods for solving linear systems . . . . . . The Algebraic Eigenvalue Problem . . . . . . . . . . . . . . . . . The power method . . . . . . . . . . . . . . . . . . . . . . Inverse iteration with Rayleigh quotient shifts . . . . . . . The QR algorithm . . . . . . . . . . . . . . . . . . . . . . Summary of methods for the algebraic eigenvalue problem Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 5 5 16 24 25 26 29 30 31 32 2 Solution of Nonlinear Equations Fixed-Point Methods for Single Nonlinear Equations . . . . . . . . . Basic fixed-point iteration . . . . . . . . . . . . . . . . . . . . Newton iteration . . . . . . . . . . . . . . . . . . . . . . . . . Modifications to Newton’s Method . . . . . . . . . . . . . . . . . . . The secant method . . . . . . . . . . . . . . . . . . . . . . . . The method of false position . . . . . . . . . . . . . . . . . . Newton’s Method for Systems of Equations . . . . . . . . . . . .

• Toán học
• Introduction to spectroscopy
• Numerical linear algebra
• Solution of nonlinear equations
• Approximation theory
• Molecular formulas
• Infrared spectroscopy
• Nuclear magnetic resonance spectroscopy
• Resonance spectroscopy
• Nuclear magnetic spectroscopy
• Ultraviolet spectroscopy
• Mass spectrometry
• Combined structure problems
• A complete introduction
• Modern NMR spectroscopy
• The 1H and 13C NMR spectra of Toluene
• The study of dynamic processes
• Electron paramagnetic resonance spectroscopy
• Chemically induced dynamic nuclear polarization
• Chemical shift correlation
• An introduction to x ray physics
• Compton scattering
• Photoelectric absorption
• Absorption spectroscopy
• Dimensional diffraction
• Diffraction optics
• Elements of flow visualization
• Flow structure
• Governing equations
• Fluid dynamics
• Analysis of incompressible flow
• Flow in pipes and ducts
• Numerical solution of ODEs
• Numerical solution of PDEs
• Mathematical introduction
• Discretization methods for PDEs
• Elliptic equations
• bioimpedance spectroscopy
• Hilbert transform
• multi frequency BIA
• different non linear
• optimization techniques
• illegal adulterant
• technology petrochemical
• oil and gas transport
• geological drilling
• oil lubrication
• Electroanalytical Chemistry
• ohmic Potential
• Inverse phase transfer catalysis
• Organic synthesis
• Carbon nanotubes in water
• Functional polymers forming complexes
• Oligomerization thermodynamic