Krishna’s Calculus of Finite Differences & Numerical Analysis

by Dr. G S Malik, Dr. P P Gupta, J P Chauhan

Length: 917 pages
Edition: 4
Language: English
Publisher: Krishna Prakashan Media Pvt Ltd (A Unit of THE KRISHNA GROUP)
Publication Date: 2020-07-10
ISBN-10: B08CSTNHCJ
Sales Rank: #2645480 (See Top 100 Books)

SYLLABUS – CALCULUS OF FINITE DIFFERENCE & NUMERICAL ANALYSIS. PROGRAMMING IN C
Programmer’s Model of a Computer, Algorithms, Flow Charts, Data Types, Arithmetic and Input/Output Instructions, Decisions Control Structures, Decision Statements, Logical and Conditional Operators, Loop, Case Control tructures, Functions, Recursions, Preprocessors, Arrays, Puppetting of Strings, Structures, Pointers, File Formating.

NUMERICAL ANALYSIS

Solution of Equations: Bisection, Secant, Regula Falsi, Newton’s Method, Roots of Polynomials.
Interpolation: Lagrange and Hermite Interpolation, Divided Differences, Difference Schemes Interpolation Formulas using Differences.
Numerical Differentiation
Numerical Quadrature: Newton-Cote‘s Formulas, Gauss Quadrature Formulas, Chebychev’s Formulas.
Linear Equations: Direct Methods for Solving Systems of Linear Equations (Guass Elimination, LU Decomposition, Cholesky Decomposition), Iterative Methods (Jacobi, Gauss-Seidel, Relaxation Methods).
The Algebraic Eigen Value Problem: Jacobi’s Method, Given’s Method, Householder’s Method, Power Method, QR Method, Lanczos’ Method.
Ordinary Differential Equations: Euler Method, Single-step Methods, Runge-Kutta’s
Method, Multi-Step Methods, Milne-Simpson Method, Methods Based on Numerical
Integration, Methods Based on Numerical Differentiation, Boundary Value Problems, Eigen Value Problems.
Approximation: Different Types of Approximation, Least Square Polynomial Approximation, Polynomial Approximation using Orthogonal Polynomials, Approximation with Trigonometric Functions, Exponential Functions, Chebychew Polynomials, Rational Functions.

Calculus of Finite Differences and Numberrical Analysis
Dedication
About the Book
Acknowledgement
Preface to the Last Edition
Preface to the First Edition
Syllabus UGC Curriculum
Syllabus CCS (Meerut)
Brief Contents
Detailed Contents 1
Detailed Contents 2
Detailed Contents 3
Detailed Contents 4
Detailed Contents 5
Detailed Contents 6
Detailed Contents 7
To, The Facility/Students
Chapter 1: The Calculus of Finite Differences
Chapter 2: Interpolation with Equal Intervals
Chapter 3: Interpolation with Unequal Intervals
Chapter 4: Central Difference Interpolation Formulae
Chapter 5: Numerical Differentiation
Chapter 6: Numerical Integration
Chapter 7: Inverse Interpolation
Chapter 8: Summation of Series
Chapter 9: Difference Equations
Chapter 10: Approximations and Errors in Computation
Chapter 11: Numerical Solutions of Ordinary Differential Equations of First and Second Order
Chapter 12: Solution of Algebraic and Transcendental Equations
Chapter 13: Solution of Simultaneous Linear Algebraic Equations
Chapter 14: Matrix Inversion
Chapter 15: Eigen Values and Eigen Vectors
Chapter 16: Bernoulli and Euler Polynomials
Chapter 17: Curve Fitting and Principle of Least Squares
Chapter 18: Numerical Solution of Partial Differential Equations
Chapter 19: Computer Fundamentals with Programming in C
Logarithms 1
Logarithms 2
Antilogarithms 1
Antilogarithms 2
Powers, Roots and Reciprocals 1
Powers, Roots and Reciprocals 2
Natural Tangents 1
Natural Tangents 2
Natural Sines 1
Natural Sines 2
Natural Cosines 1
Natural Cosines 2
Weights and Abscissae of Legendre-Gauss Quadrature Formula
Natural Secants 1
Natural Secants 2
Exponential and Hyperbolic Functions