Mathematical Models and Methods for Real World Systems

K.M. Furati, Abul Hasan Siddiqi

• Publisher: CRC Press
• Year: 2005
• eBook ISBN: 9781420026511
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This volume centers on the links between mathematics and the physical world. It first explores future challenges of mathematical technology, offers a wide-ranging definition of industrial mathematics, and explains the mathematics of type-II superconductors. After lucid discussions on theoretical and applied aspects of wavelets, the book presents classical and fractal methods for physical problems, including a fractal approach to porous media textures and using MATLAB to model chaos in the motion of a satellite. The final section surveys recent trends in variational methods, focusing on areas such as elliptic inverse problems, sweeping processes, and the BBKY hierarchy of quantum kinetic equations.

Table of contents

• COVER
• TITLE
• COPYRIGHT
• CONTENTS
• PREFACE
• CONTRIBUTING AUTHORS
• Part I: Mathematics for Technology
• Chapter 1: MATHEMATICS AS A TECHNOLOGY– CHALLENGES FOR THE NEXT TEN YEARS
• Chapter 2: INDUSTRIAL MATHEMATICS – WHAT IS IT?
• Part II: Wavelet Methods for Real-World Problems
• Chapter 4: WAVELET FRAMES AND MULTIRESOLUTION ANALYSIS
• Chapter 5: COMPARISON OF A WAVELET-GALERKIN PROCEDURE WITH A CRANK-NICOLSONGALERKIN PROCEDURE FOR THE DIFFUSION EQUATION SUBJECT TO THE SPECIFICATION OF MASS
• Chapter 6: TRENDS IN WAVELET APPLICATIONS
• Chapter 7: WAVELET METHODS FOR INDIAN RAINFALL DATA
• Chapter 8: WAVELET ANALYSIS OF TROPOSPHERIC AND LOWER STRATOSPHERIC GRAVITY WAVES
• Chapter 9: ADVANCED DATA PROCESSES OF SOME METEOROLOGICAL PARAMETERS
• Chapter 10: WAVELET METHODS FOR SEISMIC DATA ANALYSIS AND PROCESSING
• Part III: Classical and Fractal Methods for Physical Problems
• Chapter 11: GRADIENT CATASTROPHE IN HEAT PROPAGATION WITH SECOND SOUND
• Chapter 12: ACOUSTIC WAVES IN A PERTURBED LAYERED OCEAN
• Chapter 13: NON-LINEAR PLANAR OSCILLATION OF A SATELLITE LEADING TO CHAOS UNDER THE INFLUENCE OF THIRD-BODY TORQUE
• Chapter 14: CHOAS USING MATLAB IN THE MOTION OF A SATELLITE UNDER THE INFLUENCE OF MAGNETIC TORQUE
• Chapter 15: A NEW ANALYSIS APPROACH TO POROUS MEDIA TEXTURE – MATHEMATICAL TOOLS FOR SIGNAL ANALYSIS IN A CONTEXT OF INCREASING COMPLEXITY
• Part IV: Trends in Variational Methods
• Chapter 16: A CONVEX OBJECTIVE FUNCTIONAL FOR ELLIPTIC INVERSE PROBLEMS
• Chapter 17: THE SOLUTIONS OF BBGKY HIERARCHY OF QUANTUM KINETIC EQUATIONS FOR DENSE SYSTEMS
• Chapter 18: CONVERGENCE AND THE OPTIMAL CHOICE OF THE RELAXATION PARAMETER FOR A CLASS OF ITERATIVE METHODS
• Chapter 19: ON A SPECIAL CLASS OF SWEEPING PROCESS
• Index