| 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 |
| MAT1052 | Calculus II | Spring | 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 : | Dr. Öğr. Üyesi GÜLSEMAY YİĞİT |
| Course Lecturer(s): |
Prof. Dr. SÜREYYA AKYÜZ Prof. Dr. İRİNİ DİMİTRİYADİS RA DUYGU ÜÇÜNCÜ Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN RA AYSUN SOYSAL Dr. Öğr. Üyesi MÜRÜVVET ASLI AYDIN Assoc. Prof. HALE GONCE KÖÇKEN Prof. Dr. MURAT SARI Dr. Öğr. Üyesi DOĞAN AKCAN |
| Recommended Optional Program Components: | None |
| Course Objectives: | The objective of the course is to give to the students an understanding of the integral and its applications as well as introducing them to sequences and series so as to improve their ability to think critically, and enrich the tools they can use in analyzing and solving problems. |
|
The students who have succeeded in this course; 1) Calculate the approximate area under the curve using the sigma notation and Riemann sums over infinite number of partition 2) Calculate the definite and indefinite integrals using substitution, fractional integral, trigonometric substitution, partial fraction and anti-derivative tables 3) Solve the problems of area finding and volume and arc length using definitions of definite integral 4) Define the irregular integrals and calculate the results of irregular integrals by defining the concepts of limit, convergence and divergence. 5) Determine the convergence or divergence by applying ratio, integral, limit comparison, alternative series and root tests to geometric, alternative, telescopic and power series. 6) Use the Taylor and MacLaurin series to represent functions 7) Find the limit, continuity, partial derivatives, tangent surfaces and normal lines in multivariable functions 8) Calculate the double integrals in multivariable functions, understand the change the integral sequence, find a volume limited to a region determined under a surface |
| Definite integral, fundemantal theorem, indefinite integral and techniques of integration, application of the integral, areas, arc length, volumes and area of surfaces of revolution, numerical integration and improper integrals. Sequences and series, convergence tests of series, alternating series, power series, Taylon, MacLaurin series and their applications. Finding limit, continuity, partial derivatives, tangent surfaces and normal lines in multivariable functions. Calculating double integrals in multivariable functions, changing the integral sequence, finding a volume limited to a region determined under a surface |
| Week | Subject | Related Preparation |
| 1) | Antiderivatives, Estimating areas with finite sums.Riemann sum, upper and lower sums. | |
| 2) | Definite Integral. The Fundamental Theorem of Calculus. Properties of the definite integral. | |
| 3) | Indefinite integral, substitution rule. Area Between Curves. | |
| 4) | Basic Integration Formulas and integration by parts. Integrals of logaritmic and exponential functions. Integration of Rational Functions | |
| 5) | Trigonometric Integrals,Trigonometric substitution and additional methods of integration. Improper Integrals, | |
| 6) | Applications of Integrations, Volumes of Solids Revolution. | |
| 7) | Arc Length and Surface Area, Sequences and Convergence | |
| 8) | Review for Midterm | |
| 9) | Infinite Series, Convergence Tests for Positive Series, Integral Test , comparison ratio and root tests. | |
| 10) | Alternating Series, Absolute and Conditional Convergence, Power Series | |
| 11) | Taylor and Maclaurin Series, Convergence of Taylor Series; error estimates, applications of power series. | |
| 12) | Functions of Several Variables, Level Curves, Limits and Continuity, Partial Derivative, Higher Order Derivatives | |
| 13) | Multiple Integration, Double Integrals, Iteration of Double Integrals in Cartesian Coordinates, Improper Integrals and a Mean Value Theorem | |
| 14) | Review for Final Exam |
| Course Notes / Textbooks: | Thomas' Calculus International Edition 12th Edition George Thomas, Maurice Weir, Joel Hass, Frank Giordano |
| 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 | 47 | 1 | 47 |
| Midterms | 1 | 15 | 15 |
| Final | 1 | 25 | 25 |
| Total Workload | 157 | ||
| 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. | |
| 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. |