Numerical Techniques Notes

MTC-232 : Numerical Techniques

Semester - III

Chap-1 Algebraic and Transcendental Equations
Chap-2 Calculus of finite differences and interpolation
Chap-3 Numerical integration
Chap-4 Numerical Solution of ordinary differential equation.

Unit 1: Algebraic and Transcendental Equation [04 Lectures]

1.1 Introduction to Errors
1.2 False Position Method
1.3 Newton-Raphson Method

Unit 2: Calculus of Finite Differences and Interpolation [16 Lectures]

2.1 Differences
2.2. Forward Differences
2.3 Backward Differences
2.4 Central Differences
2.5 Other Differences (δ, μ operators)
2.6 Properties of Operators
2.7 Relation between Operators
2.8 Newton’s Gregory Formula for Forward Interpolation
2.9 Newton’s Gregory Formula for Backward Interpolation
2.10 Lagrange’s Interpolation Formula
2.11 Divided Difference
2.12 Newton’s Divided Difference Formula

Unit 3: Numerical Integration [08 Lectures]

3.1 General Quadrature Formula
3.2 Trapezoidal Rule
3.3 Simpson’s one-Third Rule
3.4 Simpson’s Three-Eight Rule

Unit 4: Numerical Solution of Ordinary Differential Equation [08 Lectures]

4.1 Euler’s Method
4.2 Euler’s Modified Method
4.3 Runge-Kutta Methods

Text Book:-

1. A textbook of Computer Based Numerical and Statistical Techniques, by A. K.
Jaiswal and Anju Khandelwal. New Age International Publishers.
Unit 1: Chapter 2: Sec. 2.1, 2.5, 2.7
Unit 2: Chapter 3: Sec. 3.1, 3.2, 3.4, 3.5, Chapter 4: Sec. 4.1, 4.2, 4.3,
Chapter 5: Sec. 5.1, 5.2, 5.4, 5.5
Unit 3: Chapter 6: Sec. 6.1, 6.3, 6.4, 6.5, 6.6, 6.7
Unit 4: Chapter 7: Sec. 7.1, 7.4, 7.5, 7.6

Reference Books:-

1. S.S. Sastry; Introductory Methods of Numerical Analysis, 3rd edition, Prentice Hall of India, 1999.
2. H.C. Saxena; Finite differences and Numerical Analysis, S. Chand and Company.
3. K.E. Atkinson; An Introduction to Numerical Analysis, Wiley Publications.
4. Balguruswamy; Numerical Analysis.










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