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Precize Computer Oriented Numerical Methods, B.C.A. II, Semester III

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The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner to meet the various needs of all types of learners. Each chapter begins with definitions followed by theorems with complete proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject. Well-planned and exhaustive exercises have been given in each chapter to provide the students with an opportunity of exhaustive practice.

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Introduction to differentiation, integration and matrix algebra.

Data Representation and Computer Arithmetic : Introduction, Concept of Exact and Approximate Numbers, Concept of Significant digits, Representation of Numbers in Memory, Storage of Integer Numbers: Signed Representation, 1’s Complement Representation, 2’s Complement Representation, Floating Point Numbers and their storage, Floating Point Arithmetic, Normalization and their consequences, Errors, Measures of Accuracy: Absolute Error, Relative Error and Percentage Error, Error types: Data Errors, Truncation Errors, Round-Off Errors, Computational Errors, Rules, Relationship between Relative Error and Significant digits and Error Propagation: Error Propagation in Addition Operation, Subtraction Operation, Multiplication Operation and Division Operation.

 

Solution of Non-Linear Equations : Introduction, Types of Non-Linear Equations: Polynomial Equations, Transcendental Equations, Methods of Finding Solutions of Non- Linear equations: Direct Method, Iterative Method.

Iterative Methods : Bisection Method, False-Position Method, Secant Method, Newton – Raphson Methods, Zeros of a polynomial using Birge – Vieta Method. Convergence of Iterative Methods, Comparison between Iterative Methods.

Simultaneous Linear Equations : Solution of Simultaneous Linear Equations using Direct and Iterative Methods: Direct Methods : Gauss – Elimination Method, Gauss-Jordan Method, Concept of Pivoting, Iterative Method : Gauss-Seidal Method.

Interpolation : Introduction, Lagrange Interpolation, Inverse Interpolation, Finite Differences: Forward Differences, Backward Differences, Divided Differences, Difference Tables : Forward Difference Table, Backward Difference Table, Divided Difference Table, Observations regarding Difference Tables, Newton’s Method of Interpolation : Newton’ s Forward Difference Interpolation Formula, Newton’ s Backward Difference Interpolation Formula, Newton’ s Divided Difference Interpolation Formula.

Numerical Integration : Introduction, Newton-Cotes Integration Formulae: Trapezoidal Rule, Simpson’s 1/3rd Rule, Simpson’s 3/8th Rule.

 

Approximation : Approximation of functions: Taylor Series Representation, Chebyshev Polynomials.

Solution of Ordinary Differential Equations : Introduction, Euler’s Method, Runga–Kutta Methods : 2nd order & 4th order, Predictor Corrector Methods: Modified Euler’s Method.