NUMERICAL LINEAR ALGEBRA

Course Description

This course introduces numerical methods for solving ordinary differential equations (ODEs) and partial differential equations (PDEs). It is concentrated on finite difference methods and their application to electrical and electronic engineering model problems.Numerical solution of Hyperbolic partial differential equations and its applications. Convergence and consistency. The Courant-Friedricks-Lewiy stability condition. Von Neumann Analysis. Order of Accuracy of schemes. Numerical solution of Parabolic partial differential equations and its applications. Finite difference schemes for parabolic equations. Convergence estimates for initial value problems. The matrix method for analyzing stability. Elliptic partial differential equations and its applications. Numerical solution of schemes for Poisson’s equation and its applications. The discrete maximum principle. Regularity estimates for schemes.

NUMERICAL LINEAR ALGEBRA

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Course outcomes

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Learning Outcomes

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Program Outcomes

1. 1. Analyzes, compares, and synthesizes advanced theoretical and applied knowledge in subfields of civil engineering.
2. 2. Identifies a problem in the field, formulates a research question, collects and analyzes data, and draws conclusions using scientific methods.
3. 3. Develops innovative solutions by applying modeling, analysis, and interpretation skills to complex engineering problems.
4. 4. Designs new systems, processes, or materials by considering real-world constraints such as economy, environment, sustainability, and safety.
5. 5. Plans laboratory or field studies, collects data, performs statistical analysis, and derives scientific results.
6. 6. Effectively uses modern analysis and design software, information technologies, and measurement tools in civil engineering applications.
7. 7. Recognizes, interprets, and integrates relationships between civil engineering and other engineering or scientific disciplines.
8. 8. Acts in accordance with ethical principles, demonstrates professional responsibility, and evaluates the societal impacts of engineering practices.
9. 9. Communicates research and engineering outcomes clearly and effectively through written, oral, and visual means.
10. 10. Works effectively in intra- and interdisciplinary teams and assumes leadership roles when necessary.
11. 11. Follows, critically evaluates, and continuously improves professional knowledge and skills through lifelong learning.
12. 12. Evaluates the environmental, sustainability, and societal impacts of engineering practices and develops responsible solutions.

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