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.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
Read, understand, formulate, explain, and apply mathematical statements, and state and apply important results in key mathematical areas.
-Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
Other Sources
-K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition.
Course Schedules
Week
Contents
Learning Methods
1. Week
Review of Calculus, Round-off Errors and Computer Arithmetic
Lectures and recitation
2. Week
The Bisection Method, Fixed-Point Iteration
Lectures and recitation
3. Week
The Newton's Method, The Secant Method
Lectures and recitation
4. Week
The Method of False Position, Error Analysis for Iterative Methods
Lectures and recitation
5. Week
Interpolation and the Lagrange Polynomial
Lectures and recitation
6. Week
Data Approximation and Neville's Method
First Midterm
7. Week
Divided Differences
Lectures and recitation
8. Week
Forward, Backward and Centered Differences
Lectures and recitation
9. Week
Numerical Differentiation
Lectures and recitation
10. Week
Richardson's Extrapolation
Lectures and recitation
11. Week
Elements of Numerical Integration, the Trapezoidal and Simpson's Rule
Second Midterm
12. Week
Newton-Cotes Formulas
Lectures and recitation
13. Week
Composite Numerical Integration
Lectures and recitation
14. Week
Improper Integrals
Lectures and recitation
15. Week
Final week
Exams
16. Week
Final week
Exams
17. Week
Final week
Exams
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
2
60
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 modelling 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, analyse 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 iterative 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 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; derive the composite numerical integration using the open or closed Newton-Cotes formula.
