This course introduces basic methods, algorithms and programming techniques to solve engineering problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.
Prerequisite(s)
Corequisite(s)
Special Requisite(s)
Instructor(s)
Course Assistant(s)
Schedule
Office Hour(s)
Teaching Methods and Techniques
Principle Sources
Other Sources
Course Schedules
Week
Contents
Learning Methods
1. Week
Review of Calculus: Round-off Errors and Computer Arithmetic: Binary Machine Numbers, Decimal Machine Numbers, Rate of Convergence
Oral presentation and practise
2. Week
Taylor Polynomials and Series, Error Analysis
Oral presentation and practise
3. Week
The Bisection Method; Fixed-Point Iteration
Oral presentation and practise
4. Week
The Newton's Method; The Secant Method
Oral presentation and practise
5. Week
The Method of False Position; Error Analysis for Iterative Methods; Accelerating Convergence
Numerical Differentiation: Three and Five Point Formulas Numerical Integration, Undetermined Coefficient Method
Oral presentation and practise
11. Week
Numerical Differentiation: Second Derivative Midpoint Formula; Round-Off Error Instability
Oral presentation and practise
12. Week
Second Midterm, Numerical Integration: the Trapezoidal and Simpson's Rule, Richardson Extrapolation
Oral presentation and practise
13. Week
Numerical Integration: Open and Closed Newton-Cotes Formulas, Romberg Method
Oral presentation and practise
14. Week
Initial Value Problems for Ordinary Differential Equations: Huen Method, Euler Method and Runge-Kutta Method
Oral presentation and practise
15. Week
Final week
Exams
16. Week
Final week
Exams
17. Week
Final week
Exams
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
50
Final Exam
1
50
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 IEEE standard binary floating point format, machine precision and computer errors.
LO-2
Develop understanding of the Talyor series to set up approximate polynomials.
LO-3
Use the bisection method to solve the equation f(x)=0 and estimate the number of iterations in the algorithm to achieve desired accuracy with the given tolerance
LO-4
Use the fixed point iteration method to find the fixed point of the function f(x), and analyze the error of the algorithm after n steps.
LO-5
Use Newton's method, Newton-Raphson's method, or the secant method to solve the equation f(x)=0 within the given tolerance.
LO-6
Use polynomial interpolations, including the Lagrange polynomial for curve fitting, or data analysis; use Neville's iterative algorithm, Newton's divided difference algorithms to evaluate the interpolations.
LO-7
Derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations.
LO-8
Use the open or closed Newton-Cotes formula, including the Trapezoidal rule and Simpson's rule, to approximate definite integrals; use the Lagrange polynomial to estimate the degree of accuracy.
LO-9
Derive the composite numerical integration using the open or closed Newton-Cotes formula.
