Numerical Methods In Biomedical Engineering

E-Book Overview

Numerical Modeling in Biomedical Engineering brings together the integrative set of computational problem solving tools important to biomedical engineers. Through the use of comprehensive homework exercises, relevant examples and extensive case studies, this book integrates principles and techniques of numerical analysis. Covering biomechanical phenomena and physiologic, cell and molecular systems, this is an essential tool for students and all those studying biomedical transport, biomedical thermodynamics & kinetics and biomechanics. ?· Supported by Whitaker Foundation Teaching Materials Program; ABET-oriented pedagogical layout?· MATLAB problem sets and examples available electronically; UNIX, Windows, Mac OS compatible?· Extensive hands-on homework exercises

E-Book Content

Preface The purpose of this textbook is to serve as an introductory overview of computational tools to solve numerical problems in the rapidly emerging discipline of biomedical engineering. Despite the popularity of bioengineering as a major in engineering, only a handful of textbooks have been written primarily for the instruction of undergraduates in bioengineering, none of which are in the area of numerical methods in biomedical engineering. Addressing this void was one of the driving forces for the current effort. This book is intended as the primary text for an undergraduate course in biomedical engineering. The authors have adopted the book for the Fall semester junior course on Numerical Methods in the Department of Biomedical Engineering at Rutgers University~the book could be easily adopted for either semester of the junior year as well as for the senior year in BME. If the bioengineering concepts are somewhat de-emphasized and the calculus offerings are adjusted, it could also be adopted in the sophomore class. The book assumes that students have prerequisite xiii xiv PREFACE skills in Calculus (I-IV), freshman Chemistry and Physics, General Biology, and an Introduction to Biomedical Engineering. The Numerical Methods course using this book may be offered in parallel with the treatment of junior topics such as Biomedical Transport Phenomena, Biomedical Thermodynamics/Kinetics, Biomechanics, and Bioinstrumentation. This book is well suited to train bioengineers interested in all major subfields within biomedical engineering, because it addresses a wide range of biosystems topics. The book can additionally be used as a text for quantitative biology curriculum aimed at life scientists (cell biologists, biomaterials scientists, and biochemists). Fig. 1 illustrates our philosophy of the role that computing and numerical methods plays in the education of modem-day biomedical engineers. Placed early in the junior year, the course serves as a focal point for integrating fundamentals and problem-solving skills in the context of biomedical applications. The course satisfies two major goals: assimilating computing tools within the student's tool-kit, and applying these tools to a wide range of numerical models encountered in modem biomedical engineering. t,~ "11 0 "1 qD :3" :3" 0 3 3 ""1 - Engineering Core / P s,cs\ /Chemistry ~ > x=l'lO0; >> plot(sin(x/3)) ; 32 CHAPTER 2 INTRODUCTIONTO COMPUTING i / 0.8 1 r / 1 , 11 0.6~ i i '/ I i ' iI I i f i 0.4 / i '/ ] i 0.2 [ I O~ j, -0.2~ , 4]. 4 "/i ,' ,, r i -0.6, ,, , , ,, , J -0.8 ! ,, I ',' -1' 0 10
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