INTRODUCTIONMATLAB: A Tool for Engineering Analysis Use of MATLAB Commands and Related Reference MaterialsExample Problem on Financial AnalysisComputer Code and ResultsELEMENTARY ASPECTS OF MATLAB GRAPHICS Introduction Overview of Graphics Example Comparing Polynomial and Spline InterpolationConformal Mapping Example Nonlinear Motion of a Damped Pendulum A Linear Vibration Model Example on Waves in an Elastic StringProperties 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 ApproximationApplications of Least Square Approximation Eigenvalue ProblemsComputing Natural Frequencies for a Rectangular MembraneColumn Space, Null Space, Orthonormal Bases, and SVDComputation 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 DifferencesGAUSS INTEGRATION WITH GEOMETRIC PROPERTY APPLICATIONS Fundamental Concepts and Intrinsic Integration Tools in MATLAB Concepts of Gauss Integration Comparing Results from Gauss Integration and Function QUADLGeometrical 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 PolyhedronEvaluating Integrals Having Square Root Type Singularities Gauss Integration of a Multiple IntegralFOURIER 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 ForcesDirect 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 MATLABStep-Size Limits Necessary to Maintain Numerical Stability Discussion of Procedures to Maintain Accuracy by Varying Integration Step-sizeExample on Forced Oscillations of an Inverted PendulumDynamics of a Spinning TopMotion of a Projectile Example on Dynamics of a Chain with Specified End MotionDynamics of an Elastic Chain BOUNDARY VALUE PROBLEMS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS Several Important Partial Differential EquationsSolving the Laplace Equation Inside a Rectangular RegionThe Vibrating StringForce Moving on an Elastic String Waves in Rectangular or Circular Membranes Wave Propagation in a Beam with an Impact Moment Applied to One EndForced Vibration of a Pile Embedded in an Elastic Medium Transient Heat Conduction in a One-Dimensional SlabTransient Heat Conduction in a Circular Cylinder with Spatially Varying Boundary TemperatureTorsional Stresses in a Beam of Rectangular Cross SectionEIGENVALUE PROBLEMS AND APPLICATIONS Introduction Approximation Accuracy in a Simple Eigenvalue ProblemStress Transformation and Principal Coordinates Vibration of Truss StructuresBuckling 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 FunctionsDefinition of AnalyticitySeries 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 EllipseLinear Fractional Transformations Schwarz-Christoffel Mapping onto a SquareDetermining Harmonic Functions in a Circular Disk Potential Fluid Flow around an Elliptic Cylinder Torsional Stresses in a Beam Mapped onto a Unit DiskStress Analysis by the Kolosov-Muskhelishvili MethodNONLINEAR OPTIMIZATION APPLICATIONS Basic Concepts Initial Angle for a ProjectileFitting Nonlinear Equations to DataNonlinear Deflections of a CableQuickest Time Descent Curve (the Brachistochrone) Determining the Closest Points on Two Surfaces APPENDICESList of MATLAB Routines with Descriptions Selected Utility and Application Functions
