Das A. Numerical Analysis with Elements of Computer Science

Revised Edition, NCBA, 2020. — 257 p. — ISBN 9788173817557.The book has been minutely planned keeping in mind the requirements of the students of various universities. The treatment is simple and logical. It should ideally be an irreplaceable text for the forward looking students with futuristic ideas.Preface
NUMERICAL ANALYSIS
Numerical ApproximationsError
Significant Digits and Rounding-off
Loss of Significance due to Subtraction
Floating Point Representation of Real Numbers
Addition and Subtraction
Multiplication and Divisio'n
Error Propagation and Generation
General Formula
Inherent Errors
Truncation Error
OperatorForward Difference Table
Backward Difference Table
Relation of Operators
Interpolation
Definition
Polynomial Interpolation
Error and Uniquenessjn Polynomial Interpolation
Newton's Forward Difference Polynomial for Equispaced Points
Newton's Backward Difference Polynomial for Equispaced Points
Gauss's Forward Difference Formula
Gauss's Backward Difference Formula
Stirling Interpolation Formula
Bessel's Interpolation Formula
Lagrange's Interpolation Formula
Aitken's Interpolation Formula
Divided Difference
Definition
Divided Difference Table
Relation between Divided Difference and Derivatives
Relation between Divided Difference and Finite Difference
Newton's Interpolation Formula with Divided Difference
Non-linear EquationIterative Methods
Method of Tabulation
Bisection Method
Regula Falsi Method
Secant Method
Method of Iteration
Aitken's ~2-Method
Newton-Raphson Method
Condition of Convergence of Newton-Raphson Method
Order of Convergence of Secant Method and Newton-Raphson Method
Numerical DifferentiationError in Numerical Differentiation
Numerical Integration
Newton Cotes Formula (Closed Type)
Newton Cotes Formula (Open Type)
General Formula for Numerical Integration
Trapezoidal Rule
Simpson's l/3 Rule
Simpson's 3/8 Rule
Weddle's Rule
Computational Table for Trapezoidal and Simpson's l/3 Rule
Computational Table for Weddle's Rule
Gaussian Integration
System of Linear EquationsGaussian Elimination Method
Gauss-Jordan Method
Iterative Methods
Gauss-Jacobi Method
Gauss-Seidel Method
Gauss-Seidel Method in Matrix Notation
Numerical Solution of Ordinary Differential EquationPicard's Method
Euler's Method
Modified Euler's Method
Runge-Kutta Method
Algorithm of Runge-Kutta Method of Order 2
Algorithm of Runge-Kutta Method of Order 4
A Few Short Questions on Numerical Analysis
ELEMENTS OF COMPUTER SCIENCE
Computer: An Introductory ConceptHistory of Computers
Computer Generations
Classification of Computers
Computer Characteristics
Hardware and Software
Computer Units
Operating System
Programming Languages
Number SystemDecimal Number System
Binary Number System
Octal Number System
Hexadecimal Number System
Conversion
Binary Arithmetic
l's Compliment and 2's Compliment Methods
Algorithm and FlowchartIntroduction to FORTRAN 77Characters
Constants and Variables
Arithmetic Operations and Expressions
Built-In-Functions
Examples of Arithmetic Expressions
Relational Expression
FORTRAN Statements
Type Statement
Data Statement
Parameter Statement
Arithmetic Assignment Statement
Read and Write Statements
FORMAT Statement
Control Statement
The Do-Continue Statement
The Dimension Statement
Implied Do-loop
The STOP Statement
The END Statement
Subprogram
FUNCTION Subprogram
SUBROUTINE Subprogram
Programming Technique
Miscellaneous Examples
Boolean Algebra and Logic Gates
Definition
Principle of Duality
Fundamental Theorems on Boolean Algebra
Boolean Function
Disjunctive Normal Form
Conjunctive Normal Form
Conversion
Switching Circuit
Switching and Boolean Function
Logic Gates
To Express Basic Gates Using Universal Gates