Numerical Methods || Unit Wise Note || Syllabus ||

This course contains the concepts of numerical method techniques for solving linear and nonlinear equations, interpolation and regression, differentiation and integration, and partial differential equations. The main objective of the course is to provide the knowledge of numerical method techniques for mathematical modeling.

Syllabus

Notes

Unit 1 - Error And Mathematical Review

Unit 2 - Interpolation and Regression Analysis

Unit 3 - Numerical Differentiation and Integration

Unit 4 - Solution of linear Algebraic Equation

Unit 5 - Solving Ordinary Differential Equation

Unit 6 - Solving Partial Differential Equation

Guest lecture

Note 1

Picards Method 1
Solution of Non Linear Equation 3
Non- Iterative Method 4
Graphical Method 5
Trial and Error Method 5
Iterative Method 6
Bisection Method 7
Rate of Convergence (Roc) 13
Newton Rapshon Method 14
N-R Algorithm 17
Secant Method 20
Fined Point Iteration Method 23
Rate of Convergene of N-R Method 28
Numerical Computation and Error 34
Numerical Computation 35
Interpolation 45
Lagrange Interpolation 45
Newton's Divided Difference Interpolation 53
Newton's Divided Difference Table 54
Newton's Forward Interpolation
Forward Difference Table 60
Backward Difference Table
Least Square Method 75
Fitting Linear Equation 75
Fitting a Polynomial Equation 78
Fitting of Transidential Equation 81
Newton's Divided Difference Algorithms 86
Newton's Forward Diff. Algorithms 89
Newton's Backward Diff. Algorithms 92
Linear Regression Algorithm 95
Numerical Differentation and Integration 97
Newton Differentation of Tabulated Function 99
Manima and Minima 103
Numerical Integration 105
Trapezoidal Rule 108
Simpson's 1/3rd Rule 111
Simpson's 3/8 Rule 114
Algorithm of Simpson's 1/3rd Rule 118
Algorithm of Simpson's 3/8 Rule 119
Gaussian Integration 120
Romberg Integration 125




Solution Of Differential Equation 129

Differential Equation 129
Initial Value Problem (IVP) 129
Taylor's Series Mathod 130

Note 2

Picards Method
Eulers Method
Heun's Method
Runge-Kutta(R.K) Method
Solution of Simultaneous Differential Equations
Boundary Value Problem (BVP)
Shooting Method
Solution of Linear Equations
Basic Gauss Elimination Method
Gauss Elimination with Pivoting
Gauss Jordan Method
Lu Decomposition/ Factorization/ Dolittel Method 62
Dterative Method
Eigen Value and Eigen Vector 82
Power Method

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