ISTINYE UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| Mechanical Engineering (English) | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
Course Introduction and Application Information
| Course Code: | MATH213 | ||||
| Course Name: | Numerical Methods for Engineers | ||||
| Semester: | Fall | ||||
| Course Credits: |
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| Language of instruction: | English | ||||
| Course Condition: | |||||
| Does the Course Require Work Experience?: | No | ||||
| Type of course: | Compulsory Courses | ||||
| Course Level: |
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| Mode of Delivery: | Face to face | ||||
| Course Coordinator: | Prof. Dr. SELÇUK DEMİR | ||||
| Course Lecturer(s): | Assist. Prof. Dr. GÜRSAN ÇOBAN | ||||
| Course Assistants: |
Course Objective and Content
| Course Objectives: | The course aims to teach the students the implementation of numerical methods for computer-aided solutions to problems that arise in engineering design and analysis. |
| Course Content: | Modeling, computers and error analysis, error accumulation, loss of precision, stability, condition number, roots of nonlinear equations, numerical solutions of linear equation systems (direct/iterative), interpolation (vandermonde, divided differences, spline), curve fitting (linear and nonlinear-regression), numerical derivative, numerical integration, numerical solutions of differential equations, overview of advanced topics in numerical analysis (additional topics) |
Learning Outcomes
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The students who have succeeded in this course;
1) They can perform computer coding of real numbers, function approximation (Taylor) and truncation, condition number analysis and error analysis in the basic computer environment. 2) They can solve the real roots of nonlinear functions or Linear Equation systems of equations in the form Ax=b with direct or iterative solution algorithms. 3) They can derive solver equations to calculate the unknowns of interpolation or statistical regression functions used to model a given data set. 4) They can calculate derivatives, integrals, and solution of first order differential equations numerically. 5) They can predict the convergence, stability, or order of error level of the method. |
Course Flow Plan
| Week | Subject | Related Preparation |
| 1) | Fundamentals, numbers, base concept, scientific notation, programming tools | Chapra CH1, CH2 and Supplementary Slides |
| 2) | Modeling, computers and error analysis (cutting, rounding, Taylor series) | Chapra CH3, CH4 and Supplementary Slides |
| 3) | Numerical solutions of nonlinear equations f(x)=0 | Chapra CH5, CH6 and Supplementary Slides |
| 4) | Numerical approximations for solving systems of algebraic equations A*x=b | Chapra CH9, CH10 and Supplementary Slides |
| 5) | Numerical approximations for solving systems of algebraic equations A*x=b | T.Sauer CH2, CHAPRA CH11 and Supplementary |
| 6) | Interpolation and polynomial approximations 1 | Supplementary Slides |
| 7) | Interpolation and polynomial approximations 2 | Supplementary Slides |
| 8) | Midterm Exam | |
| 9) | Curve fitting (Regression) | Chapra CH17, Supplementary Slides |
| 10) | Numerical derivative | Chapra CH23, Supplementary Slides |
| 11) | Numerical integration 1 | Chapra CH21, Supplementary Slides |
| 12) | Numerical Integration 2 | Chapra CH22, Supplementary Slides |
| 13) | Numerical solution of initial value problems | Chapra CH25 and Supplementary Slides |
| 14) | Additional topics: Finite difference and boundary value problems, Computational approaches to eigenvalue and eigenvector problems of symmetric matrices | Slides |
Sources
| Course Notes / Textbooks: | Steven C. Chapra, Raymond P. Canale, Numerical Methods for Engineers, 7th Edition, McGraw-Hill. |
| References: | Timothy Sauer, Numerical Analysis, 7th Edition, Pearson. Jaan Kiusalaas, Numerical Methods in Engineering with Python 3, Cambridge Unv. Press. (For sample codes) http://nm.mathforcollege.com/NumericalMethodsTextbookUnabridged/ (onlinesource, offline content) |
Course - Program Learning Outcome Relationship
| Course Learning Outcomes | 1 |
2 |
3 |
4 |
5 |
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|---|---|---|---|---|---|---|---|---|---|---|---|
| Program Outcomes | |||||||||||
| 1) Build up a body of knowledge in mathematics, science and Mechanical Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. | 3 | 2 | 2 | 2 | 3 | ||||||
| 2) Identify, formulate, and solve complex Mechanical Engineering problems; select and apply proper modeling and analysis methods for this purpose. | 2 | 3 | 3 | 3 | 3 | ||||||
| 3) Design complex Mechanical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. | |||||||||||
| 4) Devise, select, and use modern techniques and tools needed for solving complex problems in Mechanical Engineering practice; employ information technologies effectively. | |||||||||||
| 5) Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechanical Engineering. | |||||||||||
| 6) Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechanical-related problems. | |||||||||||
| 7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions. | |||||||||||
| 8) Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. | |||||||||||
| 9) Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechanical Engineering applications. | |||||||||||
| 10) Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. | |||||||||||
| 11) Acquire knowledge about the effects of practices of Mechanical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechanical engineering solutions. | |||||||||||
Course - Learning Outcome Relationship
| No Effect | 1 Lowest | 2 Average | 3 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Build up a body of knowledge in mathematics, science and Mechanical Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. | 2 |
| 2) | Identify, formulate, and solve complex Mechanical Engineering problems; select and apply proper modeling and analysis methods for this purpose. | 3 |
| 3) | Design complex Mechanical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. | |
| 4) | Devise, select, and use modern techniques and tools needed for solving complex problems in Mechanical Engineering practice; employ information technologies effectively. | |
| 5) | Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechanical Engineering. | |
| 6) | Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechanical-related problems. | |
| 7) | Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions. | |
| 8) | Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. | |
| 9) | Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechanical Engineering applications. | |
| 10) | Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. | |
| 11) | Acquire knowledge about the effects of practices of Mechanical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechanical engineering solutions. |
Assessment & Grading
| Semester Requirements | Number of Activities | Level of Contribution |
| Midterms | 1 | % 40 |
| Final | 1 | % 60 |
| total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 40 | |
| PERCENTAGE OF FINAL WORK | % 60 | |
| total | % 100 | |
Workload and ECTS Credit Calculation
| Activities | Number of Activities | Workload |
| Course Hours | 13 | 26 |
| Application | 13 | 26 |
| Study Hours Out of Class | 13 | 26 |
| Midterms | 2 | 15 |
| Final | 2 | 25 |
| Total Workload | 118 | |