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Numerical Techniques

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Specific References

According to New Revised CBCS Syllabus w.e.f. 2020-21

S.Y. B.Sc. (Computer Science)

Semesters-III

A Text book of

Numerical Techniques

Author: Arun Pandhari

ISBN: 978-81-946618-9-4

This book is authored by an eminent Post Graduate Head of Mathematics. He has over four decades of experience. It is written according to the revised curriculum of the University of Pune, which is scheduled to be implemented from June 2020.

It is meant to meet the needs of the student community and of professors teaching mathematics. This book is written according to the curriculum specifications of the university research committee and the text prescribed therein. It includes a systematic expansion of the topic, examples of different types of solutions, comprehensive exercises, and example solutions from real-life surveys.

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Contents

1. Algebraic and Transcendental Equation

1. Introduction to Error

2. Algebraic and Transcendental Equation

3. Regula-Falsi Method (The Method of False Positions)

4. Newton Raphson Method

2. Calculus of Finite Differences and Interpolation

1. Differences

2. Forward Difference

3. Backward Difference Operator

4. Central Differences

5. Other Difference

6. Properties of Operators

7. Relation between Operators

8. Fundamental Theorem on Differences of Polynomial

9. Interpolation

10.Newton-Gregory Formula for Forward Interpolation

11.Newton’s –Gregory Formula for Backward Interpolation

12.Interpolation with Unequal Interval

13.Lagrange’s Interpolation Formula

14.Divided Differences

15.Newton’s Divided Difference Formula (Interpolation with Unequal Intervals)

3. Numerical Integration

1. Introduction

2. General Quadrature Formula (For Equidistant Arguments)

3. Trapezoidal Rule

4. Simpson’s 1/3rd Rule 

5. Simpson’s 3/8th Rule

6. Euler-Maclaurin’s Formula

4. Numerical Solution of Ordinary Differential Equation

1. Introduction

2. Euler’s Method

3. Euler’s Modified Method

4. Runge – Kutta Methods

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