## Details of MA3105 (Autumn 2019)

 Level: 3 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA3105 Numerical Analysis Rajib Dutta

Syllabus

• Interpolation: Newton's forward, backward and divided difference formulae; Lagrange's method; Gauss, Stirling and Bessel's formulae; spline interpolation.
• Solution of Systems of Linear Equations: Gauss elimination method, Thomas algorithm, Gauss-Jacobi and Gauss-Seidel methods.
• Eigenvalues and Eigenvectors: Power method, Jacobi's method, Given's method, Householder's method.
• Solution of Non-linear Equations: Bisection method, fixed point iteration, Newton-Raphson, secant and regula-falsi methods.
• Solution of System of Non-linear equations: Fixed-point method and Newton's method.
• Numerical Differentiation: Formulae based on Newton's forward, backward, divided difference, and Lagrange's formulae.
• Numerical Integration: Trapezoidal rule, Simpson's 1/3rd and 3/8th rules, Weddle's rule, quadrature formulae based on Stirling's and Bessel's interpolation formulae.
• Solution of Differential Equations: Taylor's series method, Picard's method and Runge-Kutta methods (1st, 2nd and 4th orders) for solving ODEs.

References

1. Atkinson, K., Elementary Numerical Analysis, Wiley.
2. Burden, R.L. and Faires, J.D., Numerical Analysis, Brooks/Cole, International edition.
3. Conte, S.D. and De Boor, C., Elementary Numerical Analysis: An Algorithmic Approach, Tata McGraw-Hill.
4. Froberg, C.E., Introduction to Numerical Analysis, Addison-Wesley.
5. Scarborough, J.B., Numerical Mathematical Analysis, Johns Hopkins University Press.

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Elective
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 5 Core
7 RS 1 Elective
8 RS 2 Not Allowed