| BIOMEDICAL ENGINEERING | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT1051 | Calculus I | Fall | 3 | 2 | 4 | 7 |
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor NERMINE AHMED EL SISSI |
| Course Lecturer(s): |
Prof. Dr. SÜREYYA AKYÜZ RA DUYGU ÜÇÜNCÜ Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN RA AYSUN SOYSAL Dr. Öğr. Üyesi MESUT NEGİN Dr. Öğr. Üyesi MÜRÜVVET ASLI AYDIN Assoc. Prof. HALE GONCE KÖÇKEN Prof. Dr. NAFİZ ARICA Dr. Öğr. Üyesi DOĞAN AKCAN |
| Recommended Optional Program Components: | This is not defined for this course |
| Course Objectives: | The purpose of the course is to give to the student a mathematical understanding of relations, functions, limits, continuity and differentiation and thus provide the necessary background so that a rational approach to problem solving is attained. |
|
The students who have succeeded in this course; 1 Understand and make calculations with numbers and functions, function’s types, and interpret different type of functions; 2 Calculate limit and asymptots and prove some basic evidence about limit and continuity. 3 Define derivatives s as a rate of change; apply linearization methods on nonlinear functions and use this on calculations. 4 Learn different derivation methods 5 Solve related rate problems 6 Use derivation methods in curve sketching 7 Calculate absolute and local maximum minimum values of univariate functions 8 Solve basic optimization problems; |
| Relations, functions, limits, continuity, differentiation, rules of differentiation, The chain rule and implicit differentiation. Derivatives of trigonometric, exponential, logarithmic, inverse trigonometric functions.Related rates, linearization and differentials, extreme values, the Mean Value theorem, curve sketching, applied optimization problems. Indeterminate forms and L'Hopital's rule. Newton's method and antiderivatives. |
| Week | Subject | Related Preparation |
| 1) | Number systems and functions. | |
| 2) | Functions and their properties. | |
| 3) | Definition of limits and properties of limits. | |
| 4) | Undefined limits, horizontal and vertical asymptotes. Continuity. | |
| 5) | Definition of derivative. Tangents and derivative at a point. The derivative as a function. | |
| 6) | The derivative as a rate of change. Differentiation rules. | |
| 7) | Derivatives of functions. The chain rule and implicit differentiation. | |
| 8) | Derivatives of functions (cont'd). Approximations and differentials. | |
| 9) | Applications of the derivative. Related rate problems. | |
| 10) | Applications of differentiation (cont'd). The Mean value theorem, maximum, minimum values, increasing and decreasing functions, | |
| 11) | Curve sketching. | |
| 12) | Indeterminate forms and L'Hopital's rule. | |
| 13) | Optimization problems and Newton's method. | |
| 14) | Linearization of non linear functions |
| Course Notes / Textbooks: | Robert Adams, Christopher Essex, Calculus, Eight Edition, Pearson |
| References: | James Stewart Calculus, 5th Ed. Brooks/Cole Publishing Company C.H. Edwards,Jr. David E. Penney, Calculus with Analytic Geometry Richard Silverman, Calculus with Analytic Geometry, Prentice Hall |
| 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 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Application | 14 | 2 | 28 |
| Study Hours Out of Class | 14 | 3 | 42 |
| Midterms | 1 | 28 | 28 |
| Final | 1 | 30 | 30 |
| Total Workload | 170 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Adequate knowledge of subjects specific to mathematics (analysis, linear, algebra, differential equations, statistics), science (physics, chemistry, biology) and related engineering discipline, and the ability to use theoretical and applied knowledge in these fields in complex engineering problems. | 4 |
| 2) | Identify, formulate, and solve complex Biomedical Engineering problems; select and apply proper modeling and analysis methods for this purpose | 4 |
| 3) | Design complex Biomedical 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. | 3 |
| 4) | Devise, select, and use modern techniques and tools needed for solving complex problems in Biomedical Engineering practice; employ information technologies effectively. | 4 |
| 5) | Design and conduct numerical or physical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Biomedical Engineering. | 4 |
| 6) | Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Biomedical Engineering-related problems. | 1 |
| 7) | Ability to communicate effectively in Turkish, oral and written, to have gained the level of English language knowledge (European Language Portfolio B1 general level) to follow the innovations in the field of Biomedical Engineering; gain the ability to write and understand written reports effectively, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | 1 |
| 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. | 2 |
| 9) | Having knowledge for the importance of acting in accordance with the ethical principles of biomedical engineering and the awareness of professional responsibility and ethical responsibility and the standards used in biomedical 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 Biomedical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Biomedical Engineering; is aware of the legal consequences of Mechatronics engineering solutions. |