Advanced Mathematics and Mechanics Applications Using MATLAB

Advanced Mathematics and Mechanics Applications Using MATLAB

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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 more

Product details

  • Hardback | 696 pages
  • 190.5 x 233.68 x 25.4mm | 1,270.05g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 3rd Revised edition
  • 138 black & white illustrations, 2 black & white tables
  • 158488262X
  • 9781584882626

Review quote

"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. 3show more

Table of contents

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 Functionsshow more