Numerical & Statistical Methods

Errors and Floating Point Numbers: Understand different types of numerical errors, floating-point representation, arithmetic operations, and iterative methods for solving nonlinear equations.

Key Topics:

• Introduction to Errors in Numerical Computation
• Sources of Errors (Human, Truncation, Round-off, etc.)
• Types of Errors – Absolute, Relative, Percentage, and Gross Errors
• Representation of Floating-Point Numbers
• Arithmetic Operations on Floating-Point Numbers
• Normalization of Floating-Point Numbers
• Pitfalls and Limitations of Floating-Point Representation
• Solution of Nonlinear Equations – Concept of Roots and Zeros
• Methods for Solving Nonlinear Equations: Bisection, Iteration, Regula-Falsi, Newton-Raphson
• Rate of Convergence of Iterative Methods

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Solution of Linear Equations and Interpolation: Learn methods for solving systems of linear equations using direct and iterative techniques. Understand interpolation, finite differences, and polynomial formulas for equal and unequal intervals.

Key Topics:

• Introduction to Systems of Linear Equations
• Direct Methods – Gauss Elimination Method
• Gauss Jordan Method and Matrix Inversion Method
• Pivoting and Ill-Conditioned Systems of Equations
• Iterative Methods – Gauss Jacobi and Gauss Seidel Methods
• Interpolation and Approximation – Concepts and Uses
• Finite Differences and Difference Tables
• Polynomial Interpolation for Equal Intervals – Newton’s Forward and Backward Formulas
• Central Difference Formulas – Gauss Forward, Gauss Backward, Stirling’s, and Bessel’s Formulas
• Polynomial Interpolation for Unequal Intervals – Lagrange’s and Newton’s Divided Difference Formulas

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Numerical Differentiation and Integration: Study techniques for approximating derivatives and integrals numerically. Learn different rules of integration and numerical methods for solving ordinary differential equations.

Key Topics:

• Concept of Numerical Differentiation
• Numerical Differentiation using Newton’s Formulae
• Numerical Differentiation using Central Difference Formulae
• Concept of Numerical Integration
• Trapezoidal Rule for Integration
• Simpson’s 1/3 and 3/8 Rules for Integration
• Introduction to Ordinary Differential Equations (ODEs)
• Picard’s Iterative Method for ODEs
• Euler’s Method for Solving ODEs
• Runge–Kutta Method (Second and Fourth Order)

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Curve Fitting and Statistics: Explore curve fitting techniques using least squares, and understand basic statistical measures including frequency charts, central tendency, and dispersion methods.

Key Topics:

• Concept and Importance of Curve Fitting
• Least Squares Method – Theory and Applications
• Fitting of Straight Line
• Fitting of Polynomial Curves
• Fitting of Exponential and Other Nonlinear Curves
• Introduction to Statistics – Basic Terms and Concepts
• Frequency Charts – Histogram, Frequency Curve, and Pie Chart
• Measures of Central Tendency – Mean, Median, Mode
• Absolute Measures of Dispersion – Range, Interquartile Range
• Relative Measures of Dispersion – Mean Deviation and Standard Deviation

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