Advanced Mathematics and Mechanics Applications Using MATLAB, Third Edition

Advanced Mathematics and Mechanics Applications Using MATLAB illustrates the problem-solving capabilities of MATLAB in advanced engineering and the physical sciences. The book covers a wide range of numerical topics and discusses the algorithmic methods that can be used for their solution. 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. Several other diverse topics, such as conformal mapping, heat conduction, and inertial property calculation for areas, are also included. The text has numerous sample programs that can be used to solve complicated applied problems. The programs have extensive comments and are intended for separate study without additional reference. Many of the programs presented in the text treat applications not presented in traditional texts, e.g., spline computation of inertia properties of arbitrary areas. Additionally, all the programs are contained on a diskette accompanying the book. This diskette is organized with directories corresponding to different chapters, and a group of frequently used functions-such as those for spline interpolation and interactive data input-comprises a separate utility library.

Table of Contents:
Introduction Software Tools for Engineering Analysis Use of MATLAB Commands and Related Reference Materials Description of MATLAB Commands and Related Reference Materials Graphics Commands Plotting Functions Polynomial Interpolation Example Conformal Mapping Example String Vibration Example Example on Animation of a Rotating Cube 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 Line Integrals for Geometric Properties of Plane Areas Spline Approximation of General Boundary Shapes 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 ODE23 and ODE45 Integrators 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 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 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 References List of MATLAB Routines with Descriptions MATLAB Utility Functions Index