3rd Edition

Advanced Mathematics and Mechanics Applications Using MATLAB

    696 Pages 138 B/W Illustrations
    by Chapman & Hall

    Since its introduction in 1984, MATLAB's ever-growing popularity and functionality have secured its position as an industry-standard software package. The user-friendly, interactive environment of MATLAB 6.x, which includes a high-level programming language, versatile graphics capabilities, and abundance of intrinsic functions, helps users focus on their applications rather than on programming errors. MATLAB has now leapt far ahead of FORTRAN as the software of choice for engineering applications.

    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

    Biography

    David Halpern, Howard B. Wilson, Louis H. Turcotte

    "Material [in this book] can serve as a valuable resource for the AEM course that provides a brief exposure to numerics. It can also supplement the more heavily numerical course."
    - SIAM Review, Vol. 46, No. 3