COMPUTER ORIENTED NUMERICAL METHODS
This book is a concise presentation of the basic concepts used in evolving numerical methods with special emphasis on developing computational algorithms for solving problems in algebra and calculus on a computer. It is written for undergraduate science and engineering students who have taken a first course in differential and integral calculus. The approach is to ensure conceptual understanding of the numerical methods by relying on students geometric intuition. The book provides coverage of iterative methods for solving algebraic and transcendental equations, direct and iterative methods of solving simultaneous algebraic equations, numerical methods for differen-tiation and integration, and solution of ordinary differential equations with initial conditions. The formulation of algorithms is illustrated with a number of solved examples and an algorithmic language based on English (and similar to PASCAL) is used to express the logic of the numerical procedures. This approach is thus different from that used in most books which either use a programming language like FORTRAN or use flow charts to express algorithms. The solutions to selected problems have been provided at the end of the book.
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Solution of Simultaneous Algebraic Filiations
Least Squares Approximation of Functions
Approximation of Functions
arithmetic operations assume Bairstow's method bisection method calculated called chapter closed form coefficients computational algorithm convergence cubic splines decimal derivative difference table differential equation digit mantissa endfor evaluated Example executed exponent expressed false position method floating point arithmetic fourth order function Gauss elimination Gauss-Seidel Gauss-Seidel method given as Algorithm gives Heun's method higher order Illustrating initial guess instruction iterative method l)th least squares loop mantissa Newton-Raphson method normalized floating point number of iterations number of points Numerical Analysis Numerical Methods Observe obtained octal order polynomial plot polynomial equation predictor-corrector method problem procedure Read relative error root rounding errors Runge-Kutta method secant method significant digits Simpson's rule simultaneous equations slope solution curve solving starting values steps Stop stored straight line Substituting Subtract successive approximation tabulated values Taylor series technique Trapezoidal rule truncation error variable Write zero
Page 2 - Unlike a schoolboy a computer (as of today) does not have the capability of reading and understanding instructions written in a natural language like English. Thus it is necessary to express the algorithm in a language understood by the computer. An algorithm coded in a computer language is called a program and the language used for coding is called a programming language.