This is an advanced course on Numerical Analysis by Prof. Sachin C. Patwardhan, Department of Chemical Engineering, IIT Bombay. It has been designed with the following learning objectives in mind:
- Clearly bring out role of approximation theory in the process of developing a numerical recipe for solving an engineering problem
- Introduce geometric ideas associated with the development of numerical schemes
- Familiarize the student with ideas of convergence analysis of numerical methods and other analytical aspects associated with numerical computation
It is shown that majority of problems can be converted to computable forms (discretized) using three fundamental ideas in the approximation theory, namely Taylor series expansion, polynomial interpolation and least square approximation. In addition, the student is expected to clearly understand role of the following four fundamental tools:
- Linear Algebraic Equation
- Nonlinear Algebraic Equations
- Ordinary Differential Equations- Initial Value Problem
Prof. Patwardhan on Lecture 12: Solving ODE - BVPs Using Firute Difference Method
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