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Title: Advanced Numerical Analysis
Department: Chemical Engineering
Author: Prof. Sachin C. Patwardhan
University: IIT Bombay
Type: WebLink
Abstract: This course on Numerical Analysis 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
Optimization
which are most often used for creating a numerical recipe tocompute numerical solutions.
 
   
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