Advanced Mathematics and Mechanics Applications Using Matlab, Third Edition
, by Wilson, Howard B.; Halpern, David; Turcotte, Louis H.
- ISBN: 9781420035445 | 1420035444
- Cover:
- Copyright: 9/17/2002
| 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 | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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