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Numerical Methods by Iyengar S.R.K. and Jain R.K.



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Numerical Methods by Iyengar S.R.K. and written by Iyengar S.R.K. Department of Mathematics IIT, New Dehli, India and Jain R.K. Department of Mathematics IIT, New Dehli, India. This comprehensive textbook covers material for one semester course on Numerical Methods (MA 1251) for B.E./ B. Tech. students of Anna University. The emphasis in the book is on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner. The book is written as a textbook rather than as a problem/guide book. The textbook offers a logical presentation of both the theory and techniques for problem solving to motivate the students in the study and application of Numerical Methods. Examples and Problems in Exercises are used to explain.

Numerical Methods by Iyengar S.R.K. and written by Iyengar S.R.K. and Jain R.K. cover the following topics.

  • 1. SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS
    1.1 Solution of Algebraic and Transcendental Equations
    1.1.1 Introduction
    1.1.2 Initial Approximation for an Iterative Procedure
    1.1.3 Method of False Position
    1.1.4 Newton-Raphson Method
    1.1.5 General Iteration Method
    1.1.6 Convergence of Iteration Methods
    1.2 Linear System of Algebraic Equations
    1.2.1 Introduction
    1.2.2 Direct Methods
    1.2.2.1 Gauss Elimination Method
    1.2.2.2 Gauss-Jordan Method
    1.2.2.3 Inverse of a Matrix by Gauss-Jordan Method
    1.2.3 Iterative Methods
    1.2.3.1 Gauss-Jacobi Iteration Method
    1.2.3.2 Gauss-Seidel Iteration Method
    1.3 Eigen Value Problems
    1.3.1 Introduction
    1.3.2 Power Method
    1.4 Answers and Hints

  • 2. INTERPOLATION AND APPROXIMATION
    2.1 Introduction
    2.2 Interpolation with Unevenly Spaced Points
    2.2.1 Lagrange Interpolation
    2.2.2 Newton’s Divided Difference Interpolation
    2.3 Interpolation with Evenly Spaced Points
    2.3.1 Newton’s Forward Difference Interpolation Formula
    2.3.2 Newton’s Backward Difference Interpolation Formula
    2.4 Spline Interpolation and Cubic Splines
    2.5 Answers and Hints

  • 3. NUMERICAL DIFFERENTIATION AND INTEGRATION
    3.1 Introduction
    3.2 Numerical Differentiation
    3.2.1 Methods Based on Finite Differences
    3.2.1.1 Derivatives Using Newton’s Forward Difference Formula
    3.2.1.2 Derivatives Using Newton’s Backward Difference Formula
    3.2.1.3 Derivatives Using Newton’s Divided Difference Formula
    3.3 Numerical Integration
    3.3.1 Introduction
    3.3.2 Integration Rules Based on Uniform Mesh Spacing
    3.3.2.1 Trapezium Rule
    3.3.2.2 Simpson’s 1/3 Rule
    3.3.2.3 Simpson’s 3/8 Rule
    3.3.2.4 Romberg Method
    3.3.3 Integration Rules Based on Non-uniform Mesh Spacing
    3.3.3.1 Gauss-Legendre Integration Rules
    3.3.4 Evaluation of Double Integrals
    3.3.4.1 Evaluation of Double Integrals Using Trapezium Rule
    3.3.4.2 Evaluation of Double Integrals by Simpson’s Rule
    3.4 Answers and Hints

  • 4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
    4.1 Introduction
    4.2 Single Step and Multi Step Methods
    4.3 Taylor Series Method
    4.3.1 Modified Euler and Heun’s Methods
    4.4 Runge-Kutta Methods
    4.5 System of First Order Initial Value Problems
    4.5.1 Taylor Series Method
    4.5.2 Runge-Kutta Fourth Order Method
    4.6 Multi Step Methods and Predictor-Corrector Methods
    4.6.1 Predictor Methods (Adams-Bashforth Methods)
    4.6.2 Corrector Methods
    4.6.2.1 Adams-Moulton Methods
    4.6.2.2 Milne-Simpson Methods
    4.6.2.3 Predictor-Corrector Methods
    4.7 Stability of Numerical Methods
    4.8 Answers and Hints

  • 5. BOUNDARY VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS AND INITIAL & BOUNDARY VALUE PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS
    5.1 Introduction
    5.2 Boundary Value Problems Governed by Second Order Ordinary Differential Equations,
    5.3 Classification of Linear Second Order Partial Differential Equations
    5.4 Finite Difference Methods for Laplace and Poisson Equations
    5.5 Finite Difference Method for Heat Conduction Equation
    5.6 Finite Difference Method for Wave Equation
    5.7 Answers and Hints
    Bibliography
    Index

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