# CSVTU B.E. IV Semester IT Computational Mathematics Syllabus

CHHATTISGARH SWAMI VIVEKANAND TECHNICAL UNIVERSITY, BHILAI (C. G.)

Semester: B.E. IV Sem. Branch:  Information Technology

Subject: Computational Mathematics

UNIT– 1NUMERICAL SOLUTIONS OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS

Bisection Method, Regula-Falsi Method, Newton-Raphson Method, Secant Method, Birge-Vieta Method,

Bairstow’s Method.

UNIT– 2 NUMERICAL SOLUTIONS OF SIMULTANEOUS LINEAR EQUATIONS

(No. of periods 8+2)

Direct Methods – Gauss Elimination, Gauss-Jordan & Crout’s Triangularisation Method.

Iterative Methods – Jacobi’s, Gauss- Siedal & Successive Over Relaxation Method.

UNIT – 3 INTERPOLATION WITH EQUAL AND UNEQUAL INTERVALS (No. of periods 8+2)

Finite differences, Newton’s Forward & Backward Difference Formulae, Central Difference Formula,

Stirling’s Formula, Bessel’s Formula, Lagrange’s Formula and Newton’s Divided Difference Formula,

UNIT – 4 NUMERICAL DIFFERENTIATION AND INTEGRATION (No. of periods 8+2)

Derivatives using Forward, Backward and Central Difference Formulae.

Newton-Cote’s Quadrature Formula, Trapezoidal rule, Simpson’s rules, Weddle’s rule.

UNIT – 5 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

(No. of periods 8+2)

Picard’s Method, Taylor’s Series Method, Euler’s Method, Euler’s Modified Method, Runge-Kutta Methods,

Predictor-corrector Methods- Milne’s Method, Adams-Bashforth Method.

TEXT BOOKS:

1. Numerical Methods in Engineering and Science by Dr. B.S. Grewal, Khanna Publishers.

2. Numerical Methods for Scientific and Engineering Computation by M .K. Jain, S. R. K. Iyengar & R. K.

Jain, Wiley Eastern Limited.

REFERENCE BOOKS:

1. Numerical Methods for Scientists and Engineers by K. Shankar Rao, Prentice Hall of India.

2. Numerical Methods with C++ Programming, by Somasundaram & Chandrasekar