mca Syllabus

Code: M(CS) 312
Contacts: 3L
Credits: 3
Computer Number Systems; Overflow and underflow;
Approximation in numerical computation; Truncation and round off errors; Propagation and control of round off errors; Chopping and rounding off errors; Pitfalls (hazards) in numerical computations (ill conditioned and well conditioned problems).                       2L

Algorithmic Approach in C Language to all the Numerical Problems Discussed below must be followed:

Interpolation:
Lagrange’s Interpolation, Newton’s forward & backward Interpolation Formula. Extrapolation; Newton’s Divided Difference Formula; Error; Problems.                         4L

Numerical Differentiation:
Use of Newton’s forward and backward interpolation formula only.                       1L

Numerical Integration:
Trapezoidal formula (composite); Simson’s 1/3rd formula (composite); Romberg Integration (statement only); Problems.                                                                    2L

Numerical Solution of System of Linear Equations:
Gauss elimination method; Matrix Inversion; Operations Count; LU Factorization Method (Crout’s Method); Gauss-Jordan Method; Gauss-Seidel Method; Sufficient Condition of Convergence.                                                                                            6L

Numerical Solution of Algebraic and Transcendental Equations:
Iteration Method: Bisection Method; Secant Method; Regula-Falsi Method; Newton-Raphson Method.                                                                                                   4L

Numerical solution of Initial Value Problems of First Order Ordinary Differential Equations:
Taylor’s Series Method; Euler’s Method; Runge-Kutta Method (4th order); Modified Euler’s Method and Adams-Moulton Method.                                                        6L

C Language Overview:
Loop; Recursion; Function; Array; Pointers; Structures and Unions; Various types of File Access Methods: Sequential, Indexed Sequential, Random; Binary. Various types of Files in C and Various types of File Handling Statements in C                                               11L

Total 36L

Implementation above Numerical & Statistical Problems in C Language;

Text Books:
1 Numerical Analysis & Algorithms, Pradeep Niyogi, TMH, 1st ed.
2 C Language and Numerical Methods by C.Xavier
3 Introductory Numerical Analysis by Dutta & Jana
4 Numerical Method:Balagurusamy
5 Numerical Mathematical Analysis by J.B.Scarborough
6 Numerical Methods (Problems and Solution) by Jain, Iyengar , & Jain
7 Numerical Methods In Computer Applications – P.U.Wayse. EPH
8 Computer Oreinted Numerical Method- Dutta,N. ,Vikas
9 Numerical Methods with Programs in Basic Fortran Pascal & C++ - S.B.Rao, Universities Press
10 Computer Programming & Numerical Analysis – N.Dutta, Universities Press
11 Numerical Methods for Engineers – Gupta, New Age International
12 Numerical Solutions of Differential Equations – Jain M.K.,New Age International
13 Numerical Methods for Scientific & Engg Computation – Jain M.K.,New Age International
14 Numerical Analysis – Rao G.S.,New Age International
15 Discrete Mathematical Structures – Rao G.S., New Age International
16 Foundations of Discrete Mathematics – Joshi K.D., New Age International
17 Applied Discrete Structures – Joshi, New Age International
18 Groups, Rings & Modules with Applications – Adhikari, M.R.,Universities Press