15AE753 NUMERICAL METHODS syllabus for AE

Numerical Computation

Motivation and Objectives/ Number Representation/ Machine Precision/ Round-of Error/ Truncation Error/ Random Number Generation.

Linear Algebraic Systems:

Motivation and Objectives/ Gauss-Jordan Elimination/Gaussian Elimination/LU Decomposition/ III- Conditioned Systems/ Iterative Methods.

Interpolation and Approximation

Lagrangian Polynomials - Divided differences Interpolating with a cubic spline - Newton's forward and backward difference formulas.

Eigen Values and Eigenvectors

Motivation and Objectives/ The characteristics Polynominal/ Power Methods / Jacobi’s Method/ Householder Transformation/ QR Method/ Danilevsky’s Method/ Polynominal Roots.

Numerical Differentiation and Integration

Derivative from difference tables - Divided differences and finite differences - Numerical integration by trapezoidal and Simpson's 1/3 and 3/8 rules - Two and Three point Gaussian quadrature formulas - Double integrals using trapezoidal and Simpson's rules.

Curve Fitting

Motivation and objectives/ Interpolation/ Newton’s Difference Formula/ Cubic Splines/ Least Square/ Two-Dimensional Interpolation.

Root Finding

Motivation and Objectives/ Bracketing methods/ Contraction Mapping Method/ Se cant Method/ Muller’s Method/ Newton’s Method/ Polynomial Roots/ Nonlinear Systems of Equations.

Optimization

Motivation and Objectives/ Local and Global Minima/ Line Searches/ Steepest Descent Method/ Conjugate-Gradient Method/ Quasi-Newton Methods/ Penalty Functions/ Simulated Annealing.

Course outcomes:

After studying this course, students will be able to:

1. Apply the basic concepts of numerical methods.

2. Compute the Eigen values, Eigen vectors, numerical differentiation and integration.

3. Perform the curve fitting and root finding.

Graduate Attributes:

• Engineering Knowledge.
• Problem Analysis.
• Design / development of solutions
• Interpretation of data

Question paper pattern:

• The question paper will have ten questions.
• Each full question consists of 16 marks.
• There will be 2full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub questions covering all the topics under a module.
• The students will have to answer 5 full questions, selecting one full question from each module.

Text Books:

1. Robert Schilling and Sandra Harris, Applied Numerical methods for Engineers Using Mat Lab and CThomson Learning, 2002.

2. Gerald and Wheatley, Applied Numerical Analysis –Pearson Education, 2002.

Reference Books:

1. Mahinder Kumar Jain, Numerical Methods: For Scientific and Engineering Computation, New Age Publishers, 2012.

2. Rajesh Srivastava and Saumyen Guha, Numerical Methods for Engineering and Science, Oxford University Press, 2010.

3. P. Kandasamy, K. Thilagavathy and K. Gunavathi, Numerical Methods, S. Chand Publishers, 2006.