CHAPTER 4 NUMERICAL METHODS Ray C. Johnson, . Higgins Professor of Mechanical Engineering Emeritus Worcester Polytechnic Institute Worcester, Massachusetts NUMBERS/ FUNCTIONS / SERIES / APPROXIMATIONS AND ERROR / FINITE-DIFFERENCE APPROXIMATIONS / NUMERICAL INTEGRATION / CURVE FITTING FOR PRECISION POINTS / CURVE FITTING BY LEAST SQUARES / CURVE FITTING FOR SEVERAL VARIABLES / INTERPOLATION / ROOT FINDING / SYSTEMS OF EQUATIONS / OPTIMIZATION TECHNIQUES / REFERENCES / In this chapter some numerical techniques particularly useful in the field of machine. | __CHAPTER 4_ NUMERICAL METHODS Ray C. Johnson . Higgins Professor of Mechanical Engineering Emeritus Worcester Polytechnic Institute Worcester Massachusetts NUMBERS FUNCTIONS SERIES APPROXIMATIONS AND ERROR I FINITE-DIFFERENCE APPROXIMATIONS NUMERICAL INTEGRATION CURVE FITTING FOR PRECISION POINTS CURVE FITTING BY LEAST SQUARES I CURVE FITTING FOR SEVERAL VARIABLES INTERPOLATION ROOT FINDING SYSTEMS OF EQUATIONS I OPTIMIZATION TECHNIQUES REFERENCES In this chapter some numerical techniques particularly useful in the field of machine design are briefly summarized. The presentations are directed toward automated calculation applications using electronic calculators and digital computers. The sequence of presentation is logically organized in accordance with the preceding table of contents and emphasis is placed on useful equations and methods rather than on the derivation of theory. NUMBERS In the design and analysis of machines it is necessary to obtain quantities for various items of interest such as dimensions material properties area volume weight stress and deflection. Quantities for such items are expressed by numbers accompanied by the units of measure for a meaningful perspective. Also numbers always have an algebraic sign which is assumed to be positive unless clearly designated as negative by a minus sign preceding the number. The various kinds of numbers are defined in Sec. 2-7 which see. Real Numbers Precision and Rounding Any numerical quantity is expressed by a real number which may be classified as an integer a rational number or an irrational number. For practical purposes of calcu- STANDARD HANDBOOK OF MACHINE DESIGN lation or manufacturing it is often necessary to approximate a real number by a specified number of digits. For some cases significant numbers may be useful and the following relates to .
