7CE5A : Applications Numerical Methods in Civil Engineering (L-3, T-1) |
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| Units | Contents of the subjects |
| Errors & Approximations in Numerical Computation: Introduction to Mathematical Modeling and Engineering Problem Solving. Decimal & Binary Number system. Accuracy, Precision and Significant Digits. Errors and their types.: absolute and relative errors, approximations and round off errors, truncation errors and Taylor’s series. Propagation of errors. | |
| Roots of Equations: Iterative processes and their Convergence. Existence of roots in engineering practices & their geometrical representation. Roots of the equations by: Graphical Method, Method of Successive Substitution, Bisection Method, False Position Method, Newton-Raphson Method, Secant Method, Regula Falsi Method. Application to simple civil engineering problems. | |
Matrices and Determinants: Their types and basic operations. Rank of a matrix. Solution of Linear system of equations by Direct methods: Cramer’s Rule, Gaussian elimination method, Gauss-Jordan Method and Cholesky Method. Application to simple civil engineering problems. |
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| Iterative Methods for solving Linear system of equations: Jacobi Method, LU decomposition and Matrix inversion, Gauss Seidel method. Application to simple civil engineering problems. | |
| Interpolation and Curve Fitting: Newton’s Forward Difference, Newton’s Backward Difference, Newton’s Central Difference, Newton’s Divided Difference, Lagrangian Interpolation, Hermitian Interpolation, Method of least square. Application to simple civil engineering problems. | |
Suggested Readings:
1. Introductory Methods of Numerical Analysis, Sastry S.S., Prentice Hall India
2. Numerical Methods for Engineering and Scientific Computation, Jain and Jain, New Age
International Pvt. Ltd. New Delhi.
3. Engineering Statistics, Bowker, A.H. and Liberman G.J., Prentice Hall.
4. Probability and Statics in Engineering, Hines, John Willey and Sons.
5. Applied Statistics and Probability for Engineers, Montgomery, John Wiley and Sons.
6. Numerical Methods for Engineers by S.C. Chapra & R.P. Canale, Tata McGraw Hill
7. Numerical Methods in Science and Engineering by S. Rajasekaran, Wheeler Publishing