Numerical Analysis

 

Unit 1: Computations and Errors   (3)

1.1.      Significant digits

1.2.      Errors

1.3.      General error formula

1.4.      Error in a series approximation

Unit 2: Solution of Algebraic and Transcendental Equations     (8)

2.1.      Linear equations

2.2.      Graphical solution of equations

2.3.      Bisection method

2.4.      The method of false position

2.5.      Iteration method

2.6.      Newton – Raphson method

2.7.      General Newton’s formula for multiple roots

2.8.      Muller’s method

Unit 3: Solution of Linear Simultaneous Equations   (6)

3.1       Gauss elimination method

3.2       Gauss – Jordan method

3.3       Jacobi – Iteration method

3.4       Gauss – Seidel iteration method

3.5.      Matrix inversion method

3.6       Factorization method

3.7       Iteration method

3.8       Partition method

 

Unit 4: Finite differences     (4)

4.1.      Forward difference operator

4.2.      Forward difference table

4.3.      The operator E

4.4.      Relation between the operator E and D

4.5.      The operator D

4.6.      Backward difference table

4.7.      Factorial polynomial

Unit 5 Central differences    (4)

5.1.      Central difference operator

5.2.      Central difference table

5.3.      Mean operator

5.4.      Relationship between operators D, Ñ, E, μ and d

 

Unit 6: Interpolation with Equal Intervals            (5)

6.1.      Newton-Gregory forward interpolation formula

6.2.      Newton-Gregory backward interpolation formula

6.3.      Error in the interpolation formula

Unit 7: Interpolation with Un-equal Intervals       (5)

7.1.      Linear interpolation

7.2.      Quadratic interpolation

7.3.      Divide differences

7.4.      Second divided difference

7.5.      Relation between divided and ordinary differences

Unit 8: Central difference Interpolation (8)

8.1.      Gauss’ forward interpolation formula

8.2.      Gauss’ backward interpolation formula

8.3.      Bessel’s formula

8.4.      Stirling’s formula

 

Unit 9: Numerical Differentiation   (4)

9.1       Numerical differentiation

9.2.      Derivative using forward difference formula

9.3.      Derivative using backward difference formula

9.4.      Derivative using central difference formula

 

Unit 10: Numerical Integration       (5)

10.1     General quadrature formula for equidistant ordinates

10.2     Trapezoidal rule

10.3     Simpson’s One –Third rule

10.4     Simpson’s Three – Eight rule

10.5     Bool’s rule

10.6     Weddle’s rule

10.7     Errors in quadrature formula

10.8     Newton Cote’s formula

10.9     Deductions from Cote’s formula

10.10   Double integration