# BCS-054:Computer Oriented Numerical Techniques

### Question Papers

### Books

#### IGNOU Study Material in pdf

Download free pdf files of BCS-054 from eGyankosh. Covers all units of all blocks.

### Syllabus

### BLOCK 1: Computer Arithmetic and Solution of Linear and Non-linear Equations

#### Unit 1 : Computer Arithmetic

Floating Point Arithmetic and Errors, Rounding and Chopping of a Number and Associated Errors, Floating Point Representation of Numbers, Truncation errors and Taylor's Series

#### Unit 2 : Solution of Linear Algebraic Equations

Preliminaries, Direct Methods, Gauss Elimination Method (Basic), Gauss Elimination Method (Row Interchanges: Pivotal condensation),Iterative Methods, Gauss Jacobi Iterative Method, The Gauss-Seidel Iteration Method, Comparison of Direct and Iterative Methods

#### Unit 3 : Solution of Non-linear Equations

Non Linear Equations, Solution of Non Linear Equations, Successive Substitution Method(Fixed point method), Bisection Method ,Newton-Raphson Method, Regula-falsi Method, Secant Method

### BLOCK 2: Interpolation

#### Unit 1 : Operator

What is Interpolation, Some Operators and their Properties, Interrelation between operators, Applications of operators on some functions

#### Unit 2 : Interpolation with Equal Intervals

Difference Table, Interpolation Methods, Newton Forward Difference Formula, Newton Backward Difference Formula, Central Difference Formula, Stirling's Formula, Bessle's Formula

#### Unit 3 : Interpolation with Unequal Intervals

Lagrange's Method, Divided Difference Method, Divided Difference Table, Newton's Divided Difference Method

### BLOCK 3: Differentiation, Integration and Differential Equations

#### Unit 1 : Numerical Differentiation

Differentiation by Forward/Backward Difference Formula, Differentiation by Central Difference Formula

#### Unit 2 : Numerical Integration

Methodology's of Numerical Integration, Rectangular Rule, Trapezoidal Rule, Simpsons (1/3) Rule

#### Unit 3 : Ordinary Differential Equation

Initial Value and Boundary Value Problem, Euler's Method, Improved Euler's Method, Runge Kutta (R-K) Methods (of Order 2 and 4)