Numerical Methods

Numerical Methods by V. Murthy is a comprehensive, student-friendly textbook designed to equip undergraduate students with practical algorithmic strategies, numerical techniques, and quantitative problem-solving tools. 

This textbook is extensively prescribed across BS Mathematics, BS Computer Science, Software Engineering, BS Information Technology, and various engineering disciplines (Civil, Mechanical, Electrical) at leading Pakistani universities and colleges. 

The book thoroughly covers the complete spectrum of core numerical computing and approximation methods. It begins with errors and computer arithmetic, addressing floating-point representation, round-off errors, truncation errors, and error propagation analysis. It then presents solutions for algebraic and transcendental equations using the Bisection method, Regula-Falsi method, Secant method, and Newton-Raphson method. For linear systems of equations, it detailedly explains direct techniques like Gauss elimination and Gauss-Jordan alongside iterative options like Jacobi and Gauss-Seidel iteration. Interpolation and polynomial approximation are comprehensively covered through finite differences, Newton’s forward and backward formulas, Lagrange interpolation, and Newton’s divided differences. Furthermore, numerical differentiation and integration are analyzed using the Trapezoidal rule, Simpson’s 1/3 and 3/8 rules, and Gaussian quadrature. Finally, it provides complete strategies for numerical solutions of ordinary differential equations through Euler’s method, modified Euler’s method, Taylor’s series method, and 4th-order Runge-Kutta (RK-4) methods.

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