EPOKA UNIVERSITY
FACULTY OF ARCHITECTURE AND ENGINEERING
DEPARTMENT OF COMPUTER ENGINEERING
COURSE SYLLABUS
2024-2025 ACADEMIC YEAR
COURSE INFORMATIONCourse Title: NUMERICAL ANALYSIS |
| Code | Course Type | Regular Semester | Theory | Practice | Lab | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| MTH 206 | B | 4 | 4 | 0 | 0 | 4 | 6 |
| Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature) | Dr. Shkëlqim Hajrulla shhajrulla@epoka.edu.al |
| Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours: | Dr. Shkëlqim Hajrulla shhajrulla@epoka.edu.al |
| Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours: | NA |
| Language: | English |
| Compulsory/Elective: | Compulsory |
| Study program: (the study for which this course is offered) | Bachelor in Computer Engineering (3 years) |
| Classroom and Meeting Time: | A 036, 12:30 - 13:30 |
| Teaching Assistant(s) and Office Hours: | NA |
| Code of Ethics: |
Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline" |
| Attendance Requirement: | |
| Course Description: | Overview of binary Numbers. Error analysis. Solving systems of linear equations: Gaussian Elimination, modification Gaussian Elimination and L-U decomposition. Solutions of nonlinear equations and systems: Bisection, Newton’s, secant and fixed-point iteration methods. Interpolation: Lagrange Approximation, Newton’s Polynomials and Polynomial Approximation. Curve Fitting. Numerical Differentiation. Numerical Integration. Numerical Optimization. Numerical Solutions of the initial value and boundary value problems: Euler’s, Heun’s, Taylor’s, Runge-Kutta Methods |
| Course Objectives: | The students will develop an understanding of the numerical methods applied in solving equations of one variable, interpolation, differentiation, integration, differential equations and systems of linear equations. |
|
BASIC CONCEPTS OF THE COURSE
|
| 1 | Overview of the essential methods. • Overview of the essential problems during the research. Proper research questions. |
| 2 | Sufficient theoretical and practical background for a successful applying methods and with application skills of fundamental scientific knowledge num methods |
| 3 | Techniques of numerical methods on solving different equations. Bisection and Newton methods. |
| 4 | Techniques of numerical methods on solving different equations. Newton and Secant methods. |
| 5 | Techniques of numerical methods on solving different equations. Lagrange and Divided differences methods. |
| 6 | Summary in the above methods- • Sufficient theoretical and practical background for a successful application skills |
| 7 | Ability for effective oral and official communication in Num Analysis. • Conform the topic, take up suggestions and work with them. |
| 8 | Systems and their solution using numerical methods. Research question and motivate it both in practical and theoretical relevance. |
| 9 | Diff equations: Runge Kutta method and other methods. Working from a concrete empirical setting to the more practical one. |
| 10 | Diff equations: Euler method and other methods. Engage with the basic components of a theory and practice them with soft |
|
COURSE OUTLINE
|
| Week | Topics |
| 1 | Introduction of numerical methods. Solving one-variable equations. |
| 2 | Solving one-variable equations: the bisection and fixed - point methods. |
| 3 | Solving one-variable equations: Newton-Raphson, secant and false position iteration methods. |
| 4 | Interpolation. The Lagrange polynomial and the Neville's method. |
| 5 | Newton's divided differences. Cubic spline interpolation. |
| 6 | Lab. Implementation and comparison of the interpolation techniques. |
| 7 | Summary 1. Numerical differentiation techniques. |
| 8 | Midterm exam. |
| 9 | Numerical integration: trapezoidal rule, Simpson's rule. |
| 10 | Composite numerical integration. Gaussian quadrature. |
| 11 | Euler method: Numerical methods for solving diff equations and initial value problems |
| 12 | Higher order Taylor and Runge-Kutta methods. |
| 13 | Iterative techniques in matrix algebra. Jacobi and Gauss-Siedel techniques. |
| 14 | Overview. Summary 2 and 3. Approximating eigenvalues. |
| Prerequisite(s): | |
| Textbook(s): | “Numerical Analysis”, 9th edition, Richard Burden, Douglas Faires |
| Additional Literature: | |
| Laboratory Work: | |
| Computer Usage: | |
| Others: | No |
|
COURSE LEARNING OUTCOMES
|
| 1 | Students who successfully complete this course should be able to implement the numerical methods for solving equations of one variable: bisection method, Newton-Raphson, secant etc. |
| 2 | Students who successfully complete this course should be able to implement numerical methods for interpolation problems: Lagrange problem, Newton's divided differences, splines etc. |
| 3 | Students who successfully complete this course should be able to implement numerical methods for differentiation. |
| 4 | Students who successfully complete this course should be able to implement numerical methods for integration: trapezoidal rule, Simpson's rule, composite integration, Gaussian quadrature etc. |
| 5 | Students who successfully complete this course should be able to implement numerical methods for differential equations: Euler and Runge-Kutta methods. |
| 6 | Students who successfully complete this course should be able to implement numerical methods for matrix algebra. |
| 7 | Students who successfully complete this course should be able to implement numerical methods in lab's |
| 8 | Students who successfully complete this course should be able to implement comparison of numerical methods. |
| 9 | Students who successfully complete this course should be able to implement approximations |
| 10 | Students who successfully complete this course should be able to calculate relative and absolute errors |
|
COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES
(Blank : no contribution, 1: least contribution ... 5: highest contribution) |
| No | Program Competencies | Cont. |
| Bachelor in Computer Engineering (3 years) Program | ||
| 1 | Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice. | 5 |
| 2 | Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations | 5 |
| 3 | Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects. | 4 |
| 4 | Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies. | 5 |
| 5 | Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions. | 4 |
| 6 | Ability of identifying the potential resources for information or knowledge regarding a given engineering issue. | 4 |
| 7 | The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence. | 3 |
| 8 | Ability for effective oral and official communication skills in foreign language. | 3 |
| 9 | Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology. | 3 |
| 10 | Engineering graduates with well-structured responsibilities in profession and ethics. | 3 |
| 11 | Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues. | 2 |
| 12 | Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity. | 3 |
|
COURSE EVALUATION METHOD
|
| Method | Quantity | Percentage |
| Homework |
2
|
5
|
| Midterm Exam(s) |
1
|
25
|
| Quiz |
2
|
7.5
|
| Final Exam |
1
|
45
|
| Other |
1
|
5
|
| Total Percent: | 100% |
|
ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)
|
| Activities | Quantity | Duration(Hours) | Total Workload(Hours) |
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 4 | 64 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 3 | 42 |
| Mid-terms | 1 | 11 | 11 |
| Assignments | 2 | 10 | 20 |
| Final examination | 1 | 13 | 13 |
| Other | 0 | ||
|
Total Work Load:
|
150 | ||
|
Total Work Load/25(h):
|
6 | ||
|
ECTS Credit of the Course:
|
6 | ||
|
CONCLUDING REMARKS BY THE COURSE LECTURER
|
|
When computing numerical solutions to some equations, the source terms in equations usually fail to satisfy the continuity equation. Since this condition is required for the well-posedness of some equations, it is necessary to introduce generalized equations which remain well-posed when there are errors in the sources. These approaches, which involve a hyperbolic, a parabolic and an elliptic correction, have been recently analyzed mathematically. The goal of this course is to carry out the numerical analysis for several variants of some equations with an absolute-relative correction. |