The aim of this course is to equip students with a solid foundation in numerical methods used to solve engineering and computational problems that cannot be addressed analytically. The course develops an understanding of error sources and propagation in numerical computations, and introduces systematic techniques for solving nonlinear equations, performing optimization, fitting and interpolating data, and approximating derivatives and integrals. Emphasis is placed on algorithmic formulation, convergence and stability analysis, and the practical implementation of numerical methods relevant to computer engineering applications. By the end of the course, students will be able to select, analyze, and apply appropriate numerical techniques to real-world engineering problems with an awareness of accuracy, efficiency, and computational limitations.
Course Content
This course contains; Introduction & Error Analysis: Role of numerical methods in computer engineering. ,Introduction & Error Analysis: Round-off vs. truncation errors. Taylor series approximations.,Roots of Equations: Bracketing methods: Bisection, False Positionç,Roots of Equations: Open methods: Newton-Raphson, Secant. Convergence analysis.,Optimization: One-Dimensional Unconstrained Optimization,Optimization: One-Dimensional Unconstrained Optimization,Optimization: Multidimensional Unconstrained Optimization ,Midterm,Optimization: Constrained Optimization ,Curve Fitting & Interpolation: Least-squares regression,Curve Fitting & Interpolation: Polynomial/Spline interpolation. ,Numerical Integration: Finite differences Trapezoidal/Simpson’s rules,Numerical Integration: Adaptive quadrature,Numerical Differentiation: High – accuracy differentiation formulas ,Numerical Differentiation: Richardson extrapolation .
Course Learning Outcomes
Teaching Methods
Assessment Methods
1- Explain the role and importance of numerical methods in computer engineering and analyze the sources and effects of round-off and truncation errors in numerical computations.
12, 16, 21, 9
A, F
2- Apply Taylor series approximations to develop and analyze numerical algorithms with respect to accuracy and stability.
12, 16, 21, 9
A, F
3- Implement and compare bracketing and open methods for solving nonlinear equations and assess their convergence characteristics.
12, 16, 21, 9
A, F
4- Solve one-dimensional and multidimensional optimization problems using appropriate numerical techniques, including constrained and unconstrained methods.
12, 16, 21, 9
A, F
5- Perform curve fitting and interpolation using least-squares regression and polynomial or spline-based approaches and evaluate their suitability for given data sets.
12, 16, 21, 9
A, F
6- Approximate definite integrals using numerical integration techniques such as finite differences, Trapezoidal and Simpson’s rules, and adaptive quadrature methods.
12, 16, 21, 9
A, F
7- Compute numerical derivatives using high-accuracy differentiation formulas and improve results through Richardson extrapolation.
12, 16, 21, 9
A, F
8- Select and apply suitable numerical methods to practical engineering problems while considering accuracy, efficiency, and computational cost.
1. Numerical Methods for Engineers (8th Ed.) – Steven C. Chapra & Raymond P. Canale
2. Numerical Methods in Engineering with Python 3, Jaan Kiusalaas
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
1. An ability to apply knowledge of mathematics, science, and engineering
2
2. An ability to identify, formulate, and solve engineering problems
3
3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
6
6. An ability to function on multidisciplinary teams
7
7. An ability to communicate effectively
8
8. A recognition of the need for, and an ability to engage in life-long learning
9
9. An understanding of professional and ethical responsibility
10
10. A knowledge of contemporary issues
11
11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
Assessment Methods
Contribution Level
Absolute Evaluation
Rate of Midterm Exam to Success
30
Rate of Final Exam to Success
70
Total
100
ECTS / Workload Table
Activities
Number of
Duration(Hour)
Total Workload(Hour)
Course Hours
14
3
42
Guided Problem Solving
14
2
28
Resolution of Homework Problems and Submission as a Report
1
30
30
Term Project
0
0
0
Presentation of Project / Seminar
0
0
0
Quiz
0
0
0
Midterm Exam
1
30
30
General Exam
1
40
40
Performance Task, Maintenance Plan
0
0
0
Total Workload(Hour)
170
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(170/30)
6
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.
Detail Informations of the Course
Course Description
Course
Code
Semester
T+P (Hour)
Credit
ECTS
NUMERICAL METHODS
COE3115963
Fall Semester
3+0
3
6
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of Course
English
Course Level
First Cycle (Bachelor's Degree)
Course Type
Required
Course Coordinator
Prof.Dr. Mehmet Kemal ÖZDEMİR
Name of Lecturer(s)
Assist.Prof. Tuğba ASLAN KHALİFA
Assistant(s)
Aim
The aim of this course is to equip students with a solid foundation in numerical methods used to solve engineering and computational problems that cannot be addressed analytically. The course develops an understanding of error sources and propagation in numerical computations, and introduces systematic techniques for solving nonlinear equations, performing optimization, fitting and interpolating data, and approximating derivatives and integrals. Emphasis is placed on algorithmic formulation, convergence and stability analysis, and the practical implementation of numerical methods relevant to computer engineering applications. By the end of the course, students will be able to select, analyze, and apply appropriate numerical techniques to real-world engineering problems with an awareness of accuracy, efficiency, and computational limitations.
Course Content
This course contains; Introduction & Error Analysis: Role of numerical methods in computer engineering. ,Introduction & Error Analysis: Round-off vs. truncation errors. Taylor series approximations.,Roots of Equations: Bracketing methods: Bisection, False Positionç,Roots of Equations: Open methods: Newton-Raphson, Secant. Convergence analysis.,Optimization: One-Dimensional Unconstrained Optimization,Optimization: One-Dimensional Unconstrained Optimization,Optimization: Multidimensional Unconstrained Optimization ,Midterm,Optimization: Constrained Optimization ,Curve Fitting & Interpolation: Least-squares regression,Curve Fitting & Interpolation: Polynomial/Spline interpolation. ,Numerical Integration: Finite differences Trapezoidal/Simpson’s rules,Numerical Integration: Adaptive quadrature,Numerical Differentiation: High – accuracy differentiation formulas ,Numerical Differentiation: Richardson extrapolation .
Course Learning Outcomes
Teaching Methods
Assessment Methods
1- Explain the role and importance of numerical methods in computer engineering and analyze the sources and effects of round-off and truncation errors in numerical computations.
12, 16, 21, 9
A, F
2- Apply Taylor series approximations to develop and analyze numerical algorithms with respect to accuracy and stability.
12, 16, 21, 9
A, F
3- Implement and compare bracketing and open methods for solving nonlinear equations and assess their convergence characteristics.
12, 16, 21, 9
A, F
4- Solve one-dimensional and multidimensional optimization problems using appropriate numerical techniques, including constrained and unconstrained methods.
12, 16, 21, 9
A, F
5- Perform curve fitting and interpolation using least-squares regression and polynomial or spline-based approaches and evaluate their suitability for given data sets.
12, 16, 21, 9
A, F
6- Approximate definite integrals using numerical integration techniques such as finite differences, Trapezoidal and Simpson’s rules, and adaptive quadrature methods.
12, 16, 21, 9
A, F
7- Compute numerical derivatives using high-accuracy differentiation formulas and improve results through Richardson extrapolation.
12, 16, 21, 9
A, F
8- Select and apply suitable numerical methods to practical engineering problems while considering accuracy, efficiency, and computational cost.
1. Numerical Methods for Engineers (8th Ed.) – Steven C. Chapra & Raymond P. Canale
2. Numerical Methods in Engineering with Python 3, Jaan Kiusalaas
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
1. An ability to apply knowledge of mathematics, science, and engineering
2
2. An ability to identify, formulate, and solve engineering problems
3
3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
6
6. An ability to function on multidisciplinary teams
7
7. An ability to communicate effectively
8
8. A recognition of the need for, and an ability to engage in life-long learning
9
9. An understanding of professional and ethical responsibility
10
10. A knowledge of contemporary issues
11
11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
