Numerical Methods
The complete B.Sc syllabus for Numerical Methods (MASE-03), the fifth-semester Discipline-Specific Elective of the Bachelor of Science programme at Chhattisgarh state universities (NEP four-year UG, 2024-28) — numerical solution of algebraic and transcendental equations, interpolation, numerical differentiation and integration, and the numerical solution of differential equations. Available in English and Hindi editions.
Numerical Methods · English
by Dr. H.K. Pathak · ₹370 — covers this full syllabus.
Sankhyatmak Vidhiyan (संख्यात्मक विधियाँ) · Hindi
by Dr. H.K. Pathak · ₹370 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Numerical Methods for Algebraic & Transcendental Equations
Round-off error and computer arithmetic, local and global truncation errors, algorithms and convergence; bisection method, false-position method, fixed-point iteration, Newton's method and secant method for solving equations.
Unit 2 · Interpolation
Lagrange and Newton interpolations, piecewise-linear interpolation, cubic-spline interpolation, finite-difference operators, and Gregory-Newton forward and backward difference interpolations.
Unit 3 · Numerical Differentiation & Integration
First- and higher-order approximation of the first derivative, approximation of the second derivative; numerical integration — trapezoidal rule, Simpson's rule and its error analysis, Bulirsch-Stoer extrapolation, Richardson extrapolation.
Unit 4 · Numerical Solution of Differential Equations
Euler's method, Runge-Kutta methods, higher-order one-step method, multi-step methods; finite-difference method and shooting method; real-life examples — Google search engine, 1D and 2D simulations, weather forecasting.