AMAT 12543: Numerical Methods I

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Course Code             : AMAT 12543

Title                          : Numerical Methods I

Pre-requisites            : AMAT 11513

 Learning Outcomes:

At the end of the course, the student should be able;

  • to implement numerical methods for a variety of multidisciplinary applications
  • to establish the limitations, advantages and disadvantages of numerical methods
  • to develop and use algorithms and theorems to find numerical solutions and bounds on their error to various types of problems including root finding, polynomial approximation, curve fitting, solution of system of equations.

 Course Contents: 

Introduction: Floating point number system, Error in numerical computation, Strategies for minimizing round-off errors, Ill Conditioning, Condition Number, Notion of algorithm.

Solution of equations with one variable: Numerical solution of nonlinear equations using Bisection method, False Position method, Fixed-Point iteration method, Newton-Raphson method and Secant method, modified secant method, Error Analysis for Iterative methods, Accelerating Convergence and Aitken’s method, Solutions of polynomial equations and Horner’s method.

Difference Operators: Forward, Backward, Central, Averaging operators, Symbolic Relations of Difference operators, Difference Table and Error Propagation, Difference Equations, Factorial Polynomials.

Interpolation: Collocation Polynomial and its properties, Newton’s Forward and Backward Difference Formulae, Gauss’s Central Difference Formula, Interpolation with unevenly spaced points; Lagrange’s, Newton’s and,  Spline Interpolation; Linear, Quadratic and Cubic Spline Interpolation. 

Approximation of functions: Least square curve fitting for linear and non-linear functions.

Solution of System of Linear Equations (Direct  Methods):    Matrix inversion, Naïve Gauss Elimination ,Gaussian eliminations with partial pivoting, Ill conditioning Matrices, Operation counts, Matrix Decomposition Techniques; LU and QR Factorizations

of Teaching and Learning: A combination of lectures and tutorial discussions

 Assessment: Based on tutorials, tests and end of course examination

 Recommended Reading      :

  1. Burden, R.L., Faires, J.D, Burden, A.M. Numerical Analysis (10e), Cengage Learning. (2015).
  2. Sastry, S. S., Introductory Methods of Numerical Analysis (5e), Prentice Hall India. (2012).
  3. Kreyszig, E., Advanced Engineering Mathematics (10e), John Wiley. (2010).
  4. Gerald, C.F, Applied Numerical Analysis (7e), Pearson India. (2004).

 

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