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I Semester, Credits: 12 (6+6)
Instructors: Prof. Fiorella Sgallari
Introduction:
The course is designed to introduce the principles of numerical techniques to civil engineering students.
This course will consist of two parts. During the first part of the course, numerical analysis topics considered are:
accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.
Included are numerical methods for solving engineering problems that entail roots of functions, curve-fitting,
interpolation, numerical differentiation and integration, and numerical linear algebra.
In addition to discussing established solution techniques, open problems will also be presented.
Students should still come to appreciate many state-of-the-art techniques and recognize when to consider applying them.
Course Outline:
Numerical Mehtods
Key Idea: accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.
Numerical Linear Algebra: direct and iterative methods for linear systems.
Solution to single equations and multiple non-linear equations.
Interpolation and approximation: interpolating polynomials, cubic splines, least-square fitting.
Numerical differentiation and integration: Newton-Cotes quadrature formulas, Gaussian quadrature.
Classification of PDEs: elliptic, parabolic and hyperbolic equations.
Finite difference methods. Stability, consistency, and convergence theory.
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