Numerical Analysis
The complete BCA syllabus for Numerical Analysis (CASE-03), the fifth-semester Discipline-Specific Elective of the Bachelor in Computer Application programme at Chhattisgarh state universities (NEP four-year UG, 2024-28) — numerical solutions of algebraic and transcendental equations, linear systems, interpolation with numerical differentiation and integration, and initial/boundary value problems of differential equations.
Numerical Analysis · English
by Dr. H.K. Pathak · ₹440 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Numerical Methods for Algebraic & Transcendental Equations
Round-off error; cubic and bi-quadratic solutions — Cardan's method, Ferrari method, Descartes method, Graeffe's root-squaring; bisection method, false-position method, fixed-point iteration, Newton's method and secant method for solving equations.
Unit 2 · Numerical Methods for Linear Systems
Determinant method, matrix-inversion method, lower-upper (LU) decomposition of a matrix and its applications, Thomas method for tridiagonal systems; Gauss-Jordan, Jacobi's, Gauss-Seidel and successive over-relaxation (SOR) methods.
Unit 3 · Interpolation, Numerical Differentiation & Integration
Lagrange and Newton interpolations, piecewise-linear interpolation, cubic-spline interpolation, Hermite's interpolation, Gregory-Newton forward and backward difference interpolations. Numerical differentiation — first- and higher-order approximation of the first derivative, approximation of the second derivative; numerical integration — trapezoidal rule, Simpson's rules and error analysis, Bulirsch-Stoer extrapolation, Richardson extrapolation.
Unit 4 · Initial & Boundary Value Problems of Differential Equations
Euler's method, Taylor's method, Runge-Kutta methods, predictor-corrector, higher-order one-step method, multi-step methods — Adams-Bashforth and Adams-Moulton methods; finite-difference method and shooting method.