Advanced mathematics and mechanics applications using MATLAB

著者

書誌事項

Advanced mathematics and mechanics applications using MATLAB

by Howard B. Wilson, Louis H. Turcotte

CRC Press, c1997

2nd ed

大学図書館所蔵 件 / 全19件

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注記

Includes bibliographical references p. 617-625

Includes index p. 627-632

内容説明・目次

内容説明

The second edition of this bestselling book by Drs. Wilson and Turcotte uses MATLAB to analyze various applications in mathematics and mechanics. This modern programming environment is an excellent alternative to FORTRAN. It is an interactive environment for technical computing, and includes a high level programming language and simple graphics commands facilitating two- and three-dimensional data presentation. The applications emphasize solutions of linear and nonlinear differential equations. Linear partial differential equations and linear matrix differential equations are analyzed using eigenfunctions and series solutions. All the programs are contained on an accompanying diskette, which is organized with directories corresponding to different chapters. A group of repeatedly used functions, such as those for spline interpolation and interactive data input, comprises a separate utility library.

目次

Introduction MATLAB: A Tool for Engineering Analysis Use Of MATLAB Commands and Related Reference Materials Elementary Aspects of MATLAB Graphics Introduction Overview of Graphics Polynomial Interpolation Example Conformal Mapping Example String Vibration Example Properties of Curves and Surfaces Summary of Concepts from Linear Algebra Introduction Vectors, Norms, Linear Independence, and Rank Systems of Linear Equations, Consistency, and Least Square Approximation Applications of Least Square Approximation Eigenvalue Problems Column Space, Null Space, Orthonormal Bases, and SVD Program Comparing FLOP Counts for Various Matrix Operations Methods for Interpolation and Numerical Differentiation Concepts of Interpolation Interpolation, Differentiation, and Integration by Cubic Splines Numerical Differentiation Using Finite Differences Gaussian Integration with Applications to Geometric Properties Fundamental Concepts and Intrinsic Integration Tools Provided in MATLAB Concepts of Gauss Integration Examples Comparing Different Integration Methods Evaluating a Multiple Integral Line Integrals for Geometric Properties of Plane Areas Spline Approximation of General Boundary Shapes Geometrical Properties for a Volume of Revolution Geometrical Properties of a Polyhedron Fourier Series and the FFT Definitions and Computation of Fourier Coefficients Some Applications Dynamic Response of Linear Second Order Systems Solving the Structural Dynamics Equations for Periodic Applied Forces Direct Integration Methods Integration of Nonlinear Initial Value Problems General Concepts on Numerical Integration of Nonlinear Matrix Differential Equations Runge-Kutta Methods and the ODE45 Integrator Provided in MATLAB Step-Size Limits Necessary to Maintain Numerical Stability Discussion of Procedures to Maintain Accuracy by Varying Integration Step-Size Example on Forced Oscillations of an Inverted Pendulum Dynamics of a Spinning Top Motion of a Projectile Example on Dynamics of a Chain with Specified End Motion Boundary Value Problems for Linear Partial Differential Equations Several Important Partial Differential Equations Solving the Laplace Equation Inside a Rectangular Region The Vibrating String Forced Vibration of a Pile Embedded in an Elastic Medium Transient Heat Conduction in a One-Dimensional Slab Wave Propagation in a Beam with an Impact Moment Applied to One End Torsional Stresses in a Beam of Rectangular Cross Section Accuracy Comparison for Euler Beam Natural Frequencies Obtained by Finite Element and Finite Difference Methods Stress Analysis and Eigenvalue Analysis Introduction Stress Transformation and Principal Coordinates Principal Axes of the Inertia Tensor Vibration of Truss Structures Buckling of Axially Loaded Columns Bending Analysis of Beams of General Cross Section Introduction Applications of Analytic Functions Properties of Analytic Functions Definition of Analyticity Series Expansions Integral Properties Physical Problems Leading to Analytic Functions Branch Points and Multivalued Behavior Conformal Mapping and Harmonic Functions Mapping onto the Exterior or the Interior of an Ellipse Linear Fractional Transformations Schwarz-Christoffel Mapping onto a Square Determining Harmonic Functions in a Circular Disk Fluid Flow about an Elliptic Cylinder Torsional Stresses in a Beam Mapped onto a Unit Disk Stress Analysis by the Kolosov-Muskhelishvili Method Nonlinear Optimization Applications Basic Concepts Initial Angle for a Projectile Closest Point on a Surface Fitting Equations to Data Nonlinear Deflections of a Cable Quickest Time Descent Curve (the Brachistochrone) A. List of MATLAB Routines with Descriptions B. MATLAB Utility Functions Bibliography Index

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