Advanced Numerical Methods detailed syllabus for Cyber Security (Cyber Security) for 2021 regulation curriculum has been taken from the Anna Universities official website and presented for the Cyber Security students. For course code, course name, number of credits for a course and other scheme related information, do visit full semester subjects post given below.
For Cyber Security 7th Sem scheme and its subjects, do visit Cyber Security 7th Sem 2021 regulation scheme. For Open Elective-IV scheme and its subjects refer to Cyber Security Open Elective-IV syllabus scheme. The detailed syllabus of advanced numerical methods is as follows.
Course Objectives:
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Unit I
ALGEBRAIC EQUATIONS AND EIGENVALUE PROBLEM System of nonlinear equations : Fixed point iteration method – Newton’s method; System of linear equations: Thomas algorithm for tri diagonal system – SOR iteration methods ; Eigen value problems: Given’s method – Householder’s method.
Unit II
INTERPOLATION Central difference: Stirling and Bessel’s interpolation formulae ; Piecewise spline interpolation: Piecewise linear, piecewise quadratic and cubic spline ; Least square approximation for continuous data (upto 3rd degree).
Unit III
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Unit IV
FINITE DIFFERENCE METHODS FOR ELLIPTIC EQUATIONS Laplace and Poisson’s equations in a rectangular region : Five point finite difference schemes -Leibmann’s iterative methods – Dirichlet’s and Neumann conditions – Laplace equation in polar coordinates : Finite difference schemes .
Unit V
FINITE DIFFERENCE METHOD FOR TIME DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS Parabolic equations : Explicit and implicit finite difference methods – Weighted average approximation – Dirichlet’s and Neumann conditions – First order hyperbolic equations – Method of characteristics – Different explicit and implicit methods; Wave equation : Explicit scheme -Stability of above schemes.
Course Outcomes:
Upon completion of this course, the students will be able to:
- demonstrate the understandings of common numerical methods for nonlinear equations, system of linear equations and eigenvalue problems;
- understand the interpolation theory;
- understand the concepts of numerical methods for ordinary differential equations;
- demonstrate the understandings of common numerical methods for elliptic equations;
- understand the concepts of numerical methods for time dependent partial differential equations
Text Books:
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Reference Books:
- Saumyen Guha and Rajesh Srivastava, “Numerical methods for Engineering and Science”, Oxford Higher Education, New Delhi, 2010.
- Burden, R.L., and Faires, J.D., “Numerical Analysis – Theory and Applications”,th Edition, Cengage Learning, New Delhi, 2016.
- Gupta S.K., “Numerical Methods for Engineers”,4th Edition, New Age Publishers, 2019.
- Sastry, S.S., “Introductory Methods of Numerical Analysis”, 5th Edition, PHI Learning, 2015.
- Morton, K.W. and Mayers D.F., “Numerical solution of Partial Differential equations”, Cambridge University press, Cambridge, 2002.
For detailed syllabus of all the other subjects of Cyber Security 7th Sem, visit Cyber Security 7th Sem subject syllabuses for 2021 regulation.
For all Cyber Security results, visit Anna University Cyber Security all semester results direct link.