This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.
Numerical Differentiation, High-Accuracy Differentiation Formula and Richardson Extrapolation
Lectures and recitation
13. Week
Ordinary Differential Equations, Euler’s Method.
Lectures and recitation
14. Week
Runge-Kutta Methods
Lectures and recitation
15. Week
16. Week
17. Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
20
Quizzes
2
20
Homework / Term Projects / Presentations
2
20
Final Exam
1
40
Program Outcomes
PO-1
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.
PO-2
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3
Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
PO-4
Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language.
PO-8
Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
PO-9
Awareness of professional and ethical responsibility.
PO-10
Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
PO-11
Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.
Learning Outcomes
LO-1
Understand fundamental concepts of mathematical modeling and numerical methods.
LO-2
Analyze and estimate errors in numerical computations with Taylor series.
LO-3
Apply various methods for solving nonlinear equations.
LO-4
Solve systems of linear equations using matrix methods.
LO-5
Perform curve fitting using least-squares regression, interpolation and Fourier approximation.
LO-6
Implement numerical integration and differentiation techniques.
LO-7
Solve ordinary differential equations using numerical methods.
