Bøger af J.H. Heinbockel

This book is an introduction to tensor calculus and continuum mechanics. i.e. applied mathematics developing basic equations in engineering, physics and science.

Introduction to the Variational Calculus is an introduction to the various mathematical methods needed for determining maximum and/or minimum values associated with functions and functionals. The material presented is suitable for a one semester course in the subject area called calculus of variations. It is written for mathematicians, engineers, physicists, chemistry and science majors and is suitable for upper level college undergraduates or beginning graduate students. It can be used as a reference book for various calculus of variation topics.Chapter one reviews necessary background material from the subject area of calculus and advanced calculus. Chapter two reviews maximum and minimum values associated with functions and functions subject to constraint conditions. Chapter three introduces techniques for finding extreme values associated with functionals. The Euler-Lagrange equations are developed for a variety of functionals. The fourth chapter develops some of the more detailed concepts associated with the subject area of calculus of variations. The fifth and sixth chapters consider various applied engineering applications of the calculus of variations. Selected applied topics are developed together with necessary solution methods.There are three Appendices. The Appendix A contains units of measurements from the Systeme International Unites along with some selected physical constants. The Appendix B contains gives the representation of the gradient, divergence and curl in Cartesian, cylindrical and spherical coordinates. The Appendix C contains solutions to selected exercises. The book is 356 pages with numerous exercises and applications presented at the end of each chapter.For additional information and downloads please visit the web site www.math.odu.edu/~jhh/counter7.html

Numerical Methods for Scientific Computing is an introducion to numerical methods and analysis techniques that can be used to solve a variety of complicated engineering and scientific problems. The materialis suitable for upper level college undergraduates or beginning graduate students. There is more than enough material for a two semester course in numerical methods and analysis for mathematicians, engineers, physicists, chemistry and science majors.Chapter one reviews necessary background prerequisite material. The chapter two illustrates techniques for finding roots of equations. Chapter three studies solution methods applicable for handling linear and nonlinear systems of equations. Chapter four introduces interpolation and approximation techniques. The chapter five investigates curve fitting using least squares and linear reqression. The chapter six presents the topics of difference equations and Z-transforms. The chapter seven concentrates on numerical differentiation and integration methods. Chapter eight examines numerical solution techniques for solving ordinary differential equations and chapter nine considers numerical solution techniques for solving linear partial differential equations. The chapter ten develops Monte Carlo techniques for simulating and analyzing complex systems. The final chapter eleven presents parallel computing considerations together with selected miscellaneous topics.

Mathematical Methods for Partial Differential Equations is an introduction in the use of various mathematical methods needed for solving linear partial differential equations. The material is suitable for a two semester course in partial differential equations for mathematicians, engineers, physicists, chemistry and science majors and is suitable for upper level college undergraduates or beginning graduate students.Chapter one reviews necessary background material from the subject area of ordinary differential equations and then develops solution techniques for some easy to solve partial differential equations. Chapter two introduces orthogonal functions and Sturm-Liouville systems. Chapter three utilizes orthogonal functions to develop Fourier series and Fourier integrals. The fourth, fifth and sixth chapters consider various applied engineering applications of partial differential equations. Selected applied topics are developed together with necessary solution methods associated with parabolic, hyperbolic and elliptic type partial differential equations. Chapter seven introduces transform methods for solving linear partial differential equations. Numerous examples associated with the Laplace, Fourier exponential, Fourier sine, Fourier cosine and selected finite Sturm-Liouville transforms are given. Chapter eight introduces Green's functions for ordinary differential equations and chapter nine finishes with applications of Green function techniques for solving linear partial differential equations.There are four Appendices. The Appendix A contains units of measurementsfrom the Système International d'Unitès along with some selected physical constants. The Appendix B contains solutions to selected exercises. The Appendix C lists mathematicians whose research has contributed to the area of partial differential equations. The Appendix D contains a short listing of integrals. The text has numerous illustrative worked examples and over 340 exercises.