Advanced Mathematics and Mechanics Applications Using MATLAB

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