CENG 216
Numerical Computation
Surveys and applications of numerical techniques related to matrix inversion, systems of linear equations and optimization, finite difference expressions, interpolation and approximation, numerical differentiation and integration. The problems of speed, accuracy and applicability of the topics are examined with related algorithms. The applications of these numerical methods and subjects on computers using efficient programming techniques and with necessary programming languages.
Learning Outcomes:
- To be able to explain effects of finite representation of real numbers for a given algorithm.
- To be able to find numerical errors in calculations and compare numerical errors of different algorithms for the same problem.
- To be able to solve numerical problems that include derivative, integral, interpolation and/or optimization.
- To be able to apply recursive solutions to numerical problems.
- To be able to implement linear/non-linear systems for the given problem.
- To be able to apply appropriate numerical algorithm for given linear/non-linear system.
| Week | Topics |
| 1 | Introduction to numerical calculation methods |
| 2 | Numerical calculation errors |
| 3 | Taylor series |
| 4 | Taylor series cont. |
| 5 | Forward and backward differences |
| 6 | Central differences, polynomials |
| 7 | Interpolation & extrapolation |
| 8 | Finding roots of equations, Newton method |
| 9 | Finding roots of equations, Secant method |
| 10 |
The solution of simultaneous linear algebraic equations
|
| 11 | Matrix inversion |
| 12 | Least-squares curve fitting |
| 13 | Functional integration |
| 14 | Numerical integration |
Reference book(s):
- Numerical Analysis, The new international edition, 2ed, Timothy Sauer
- Numerical Algorithms: Methods for Computer Vi- sion, Machine Learning, and Graphics, J. Solomon Matrix Computations (4th Ed.), G. H. Golub and C. F. Van Loan
Grading:
- Homework-I 10%
- Homework-II 10%
- Midterm Exam-I 20%
- Midterm Exam-II 20%
- Final Exam 40%
Submissions:
This course will give two comprehensive assignments that cover the theoretical topics covered throughout the semester and apply the numerical methods taught in the course to real-life problems.
Assignment1 Submission Grading: Yes
Assignment2 Submission Grading: Yes
Prerequisites: There are no prerequisite courses.
Supplementary Courses:
Sufficient knowledge of linear algebra will be very beneficial.
