Advanced mathematics and mechanics applications using MATLAB. (©2003)

• Record Type: Book
• Further Information: Note: Howard B. Wilson, Louis H. Turcotte, David Halpern.
• Other Names: Wilson, H. B; Turcotte, Louis H; Halpern, David
• 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 Functions
• Edition: 3rd ed
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2003
• Copyright Date: 2003
• Extent: 1 online resource (xiii, 678 pages), illustrations
• Subjects: 620/.00151; Engineering mathematics -- Data processing; Mechanics, Applied -- Data processing; Engineering -- methods; Mechanics; TECHNOLOGY & ENGINEERING -- Engineering (General); TECHNOLOGY & ENGINEERING -- Reference; Engineering mathematics -- Data processing; Mechanics, Applied -- Data processing; Electronic books; Electronic books
• Languages: English
• ISBNs: 1420035444; 9781420035445; 9781584882626
• Related ISBNs: 158488262X
• Notes: Note: Includes bibliographical references (pages 655-662) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.