NUMERICAL ANALYSIS

Course Description

Aim of this course is to give fundamental methods to solve numerical problems in mathematics, computer science, physical sciences and engineering. Topics included are as follows: Definitions: Error types, Taylor series and truncation error and rounding numbers. Numerical solution of nonlinear equations; Bracketing methods, Bisection and False position, Iterative methods: Fixed point and Newton method. Numerical methods for solution of linear systems, Iterative methods and LU decomposition methods. Interpolation and polynomial approximation, Lagrange polynomials, Least square lines, curve fitting and spline functions (linear and quadratic). Evaluate derivatives by numerical analysis, numerical differentiation, finite difference formulas. Evaluate integrals by numerical analysis, numerical integration, Simpson's rules and Trapezoidal rules.

NUMERICAL ANALYSIS

Evaluation Tools (Active Term)

Course outcomes

1. 01 Able to identify numerical analysis methods
2. 02 Able to solve nonlinear equations
3. 03 Able to solve linear/nonlinear systems
4. 04 Able to use numerical methods to find interpolation
5. 05 Able to evaluate derivatives and integrals by using numerical analysis
6. 06 Able to use numerical methods to solve engineering problems

Course Syllabus

Reference Books & Course Materials

1. 01 Numerical Analysis, Richard L. Burden, J. Dougles Faires, 9th Edition. ISBN-13: 978-0-538-73351-9
2. 02 Elementary Numerical Analysis , An Algorithm Approach, Third Edition, Samuel D. Conte,Carle de Boor, McGRAW HILL. ISBN-13: 978-0070124479 ISBN-10: 0070124477
3. 03 Numerical Methods Using Matlab, John H. Mathews, Kurtis D. Fink . ISBN 978–0–07–305194–9—ISBN 0–07–305194–2

Learning Outcomes

1. L01 Able to identify numerical analysis methods
2. L02 Able to solve nonlinear equations
3. L03 Able to solve linear/nonlinear systems
4. L04 Able to use numerical methods to find interpolation
5. L05 Able to evaluate derivatives and integrals by using numerical analysis
6. L06 Able to use numerical methods to solve engineering problems

Program Outcomes

1. P01 Knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline.
2. P02 Ability to apply knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline to the solution of complex engineering problems.
3. P03 Ability to define complex engineering problems by using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) related to the problem addressed.
4. P04 Ability to formulate complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
5. P05 Ability to analyse and solve complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
6. P06 Ability to design creative solutions to complex engineering problems.
7. P07 Ability to design complex systems, processes, devices, or products in a way that meets present and future needs while considering realistic constraints and conditions.
8. P08 Ability to select and use appropriate techniques and resources—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
9. P09 Ability to select and use modern engineering and computational tools—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
10. P10 Ability to conduct literature research and use appropriate research methods for the investigation of complex engineering problems.
11. P11 Ability to design experiments for the investigation of complex engineering problems.
12. P12 Ability to conduct experiments, collect data, analyse results, and interpret findings for the investigation of complex engineering problems.
13. P13 Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the framework of the United Nations Sustainable Development Goals (SDGs).
14. P14 Awareness of the legal implications of engineering solutions within the framework of the United Nations Sustainable Development Goals (SDGs).
15. P15 Knowledge of ethical responsibility and adherence to the principles of professional engineering conduct.
16. P16 Awareness of acting impartially without discrimination in any matter and of being inclusive of diversity.
17. P17 Ability to work effectively as an individual.
18. P18 Ability to work effectively as a team member or leader in intra-disciplinary teams (face-to-face, remote, or hybrid).
19. P19 Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote, or hybrid).
20. P20 Ability to communicate effectively in spoken form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
21. P21 Ability to communicate effectively in written form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
22. P22 Knowledge of professional practices such as project management and economic feasibility analysis.
23. P23 Awareness of entrepreneurship and innovation.
24. P24 Ability for independent and lifelong learning.
25. P25 Ability to adapt to new and emerging technologies.
26. P26 Lifelong learning ability that includes the capacity to think critically about technological changes.

Po-Lo Matrix