Advanced mathematics and mechanics applications using MATLAB /
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| Format: | eBook |
| Language: | English |
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Boca Raton, Fla. :
CRC Press,
©2003.
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| Edition: | 3rd ed. |
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- INTRODUCTION; MATLAB: A Tool for Engineering Analysis; Use of MATLAB Commands and Related Reference Materials; Example Problem on Financial Analysis; Computer Code and Results; ELEMENTARY ASPECTS OF MATLAB GRAPHICS; Introduction; Overview of Graphics; Example Comparing Polynomial and Spline Interpolation; Conformal Mapping Example; Nonlinear Motion of a Damped Pendulum; A Linear Vibration Model; Example on Waves in an Elastic String; 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; Computing Natural Frequencies for a Rectangular Membrane; Column Space, Null Space, Orthonormal Bases,
- And SVD; Computation Time to Run a MATLAB Program; METHODS FOR INTERPOLATION AND NUMERICAL DIFFERENTIATION; Concepts of Interpolation; Interpolation, Differentiation,
- And Integration by Cubic Splines; Computing the Length and Area Bounded by a Curve; Numerical Differentiation Using Finite Differences; GAUSS INTEGRATION WITH GEOMETRIC PROPERTY APPLICATIONS; Fundamental Concepts and Intrinsic Integration Tools in MATLAB; Concepts of Gauss Integration; Comparing Results from Gauss Integration and Function QUADL; Geometrical Properties of Areas and Volumes; Computing Solid Properties Using Triangular Surface Elements and Using Symbolic Math; Numerical and Symbolic Results for the Example; Geometrical Properties of a Polyhedron; Evaluating Integrals Having Square Root Type Singularities; Gauss Integration of a Multiple Integral; FOURIER SERIES AND THE FAST FOURIER TRANSFORM; 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 ODE 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; Dynamics of an Elastic Chain; BOUNDARY VALUE PROBLEMS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS; Several Important Partial Differential Equations; Solving the Laplace Equation Inside a Rectangular Region; The Vibrating String; Force Moving on an Elastic String; Waves in Rectangular or Circular Membranes; Wave Propagation in a Beam with an Impact Moment Applied to One End; Forced Vibration of a Pile Embedded in an Elastic Medium; Transient Heat Conduction in
- A One-Dimensional Slab; Transient Heat Conduction in a Circular Cylinder with Spatially Varying Boundary Temperature; Torsional Stresses in a Beam of Rectangular Cross Section; EIGENVALUE PROBLEMS AND APPLICATIONS; Introduction; Approximation Accuracy in a Simple Eigenvalue Problem; Stress Transformation and Principal Coordinates; Vibration of Truss Structures; Buckling of Axially Loaded Columns; Accuracy Comparison for Euler Beam Natural Frequencies by Finite Element and Finite Difference Methods; Vibration Modes of an Elliptic Membrane; BENDING ANALYSIS OF BEAMS OF GENERAL CROSS SECTION; Introduction; Analytical Formulation; Program to Analyze Beams of General Cross Section; Program Output and Code; 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; Potential Fluid Flow around 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; Fitting Nonlinear Equations to Data; Nonlinear Deflections of a Cable; Quickest Time Descent Curve (the Brachistochrone); Determining the Closest Points on Two Surfaces; APPENDICES; List of MATLAB Routines with Descriptions; Selected Utility and Application Functions